Last update: Mon Aug 26 13:04:00 MDT 2024
Volume 1, Number ??, 1964Cornelius Lanczos Introduction . . . . . . . . . . . . . . 1--1 P. L. Butzer Saturation and Approximation . . . . . . 2--10 E. W. Cheney and H. L. Loeb Generalized Rational Approximation . . . 11--25 C. W. Clenshaw A Comparison of ``Best'' Polynomial Approximations with Truncated Chebyshev Series Expansions . . . . . . . . . . . 26--37 J. Favard On the Comparison of the Processes of Summation . . . . . . . . . . . . . . . 38--52 T. N. E. Greville Numerical Procedures for Interpolation by Spline Functions . . . . . . . . . . 53--68 Preston C. Hammer Topologies of Approximation . . . . . . 69--75 C. Lanczos Evaluation of Noisy Data . . . . . . . . 76--85
Cornelius Lanczos A Precision Approximation of the Gamma Function . . . . . . . . . . . . . . . . 86--96
G. G. Lorentz Entropy and Its Applications . . . . . . 97--103 A. M. Ostrowski On Approximation of Equations by Algebraic Equations . . . . . . . . . . 104--130 T. J. Rivlin A Property of the Ratio of Trigonometric Polynomials . . . . . . . . . . . . . . 131--132 L. A. Rubel Bounded Polynomial Approximation . . . . 133--136 D. D. Stancu The Remainder of Certain Linear Approximation Formulas in Two Variables 137--163 E. Stiefel Methods --- Old and New --- For Solving the Tchebycheff Approximation Problem 164--176 P. Wynn On Some Recent Developments in the Theory and Application of Continued Fractions . . . . . . . . . . . . . . . 177--197
J. H. Bramble and B. E. Hubbard A Finite Difference Analog of the Neumann Problem for Poisson's Equation 1--14 D. G. Moursund and A. H. Stroud The Best Çeby\vsev Approximation to a Function and its Derivative on $ n + 2 $ Points . . . . . . . . . . . . . . . . . 15--23 James E. Gunn The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques . . . . . . . . . . . . . . . 24--45 Gilbert Strang Unbalanced Polynomials and Difference Methods for Mixed Problems . . . . . . . 46--51 Don Secrest Numerical Integration of Arbitrarily Spaced Data and Estimation of Errors . . 52--68 C. W. Gear Hybrid Methods for Initial Value Problems in Ordinary Differential Equations . . . . . . . . . . . . . . . 69--86 J. R. Cannon and Keith Miller Some Problems in Numerical Analytic Continuation . . . . . . . . . . . . . . 87--98 Randall E. Cline Representations for the Generalized Inverse of Sums of Matrices . . . . . . 99--114 W. Oettli On the Solution Set of a Linear System with Inaccurate Coefficients . . . . . . 115--118 K. W. Morton and S. Schechter On the Stability of Finite Difference Matrices . . . . . . . . . . . . . . . . 119--128 A. H. Stroud and D. D. Stancu Quadrature Formulas with Multiple Gaussian Nodes . . . . . . . . . . . . . 129--143 I. J. Schoenberg On Monosplines of Least Deviation and Best Quadrature Formulae . . . . . . . . 144--170 Wayne T. Ford Mathematical Programming and Integro-Differential Equations . . . . . 171--202 P. L. Butzer Errata: ``Saturation and Approximation'' [J. Soc. Ind. Appl. Math., Ser. B Numer. anal. \bf 1] (1964), 2-10 . . . . . . . 203--203 A. M. Ostrowski Errata: ``On Approximation of Equations by Algebraic Equations'' [J. Soc. Ind. Appl. Math., Ser. B Numer. anal. \bf 1] (1964), 104--130 . . . . . . . . . . . . 203--203
G. H. Golub and W. Kahan Calculating the Singular Values and Pseudo-Inverse of a Matrix . . . . . . . 205--224 F. W. J. Olver On the Asymptotic Solutions of Second-Order Differential Equations having an Irregular Singularity of Rank One, with an Application to Whittaker Functions . . . . . . . . . . . . . . . 225--243 F. W. J. Olver and F. Stenger Error Bounds for Asymptotic Solutions of Second-Order Differential Equations having an Irregular Singularity of Arbitrary Rank . . . . . . . . . . . . . 244--249 A. Meir and A. Sharma On the Method of Romberg Quadrature . . 250--258 I. Navot The Euler--Maclaurin Functional for Functions with a Complex Singularity Near the Range of Integration . . . . . 259--264 Hans J. Stetter A Study of Strong and Weak Stability in Discretization Algorithms . . . . . . . 265--280 Herbert B. Keller On the Solution of Singular and Semidefinite Linear Systems by Iteration 281--290 W. Oettli and W. Prager and J. H. Wilkinson Admissible Solutions of Linear Systems with Not Sharply Defined Coefficients 291--299 E. E. Osborne Smallest Least Squares Solutions of Linear Equations . . . . . . . . . . . . 300--307 Eldon Hansen Interval Arithmetic in Matrix Computations, Part I . . . . . . . . . . 308--320 Robert E. Barnhill The Convergence of Quadratures on Complex Contours . . . . . . . . . . . . 321--336 Milos Zlamal Asymptotic Error Estimates in Solving Elliptic Equations of the Fourth Order by the Method of Finite Differences . . 337--344 Donald V. Steward Partitioning and Tearing Systems of Equations . . . . . . . . . . . . . . . 345--365
Philip J. Davis and Philip Rabinowitz Ignoring the Singularity in Approximate Integration . . . . . . . . . . . . . . 367--383 William B. Gragg On Extrapolation Algorithms for Ordinary Initial Value Problems . . . . . . . . . 384--403 W. V. Petryshyn Constructional Proof of Lax-Milgram Lemma and Its Application to Non-$ {K}$-P.D. Abstract and Differential Operator Equations . . . . . . . . . . . 404--420 Ivan Erdélyi An Iterative Least-Square Algorithm Suitable for Computing Partial Eigensystems . . . . . . . . . . . . . . 421--436 J. F. Traub The Principle of Differentiated Quotients . . . . . . . . . . . . . . . 437--439 Don Secrest Error Bounds for Interpolation and Differentiation by the Use of Spline Functions . . . . . . . . . . . . . . . 440--447 Bert E. Hubbard Alternating Direction Schemes for the Heat Equation in a General Domain . . . 448--463 D. G. Moursund Some Computational Aspects of the Uniform Approximation of a Function and Its Derivative . . . . . . . . . . . . . 464--472 M. A. Hanson Error Bounds in Constrained Best Approximation . . . . . . . . . . . . . 473--479 A. H. Stroud Error Estimates for Romberg Quadrature 480--488 R. A. Spinelli Poisson Equation on a Sphere . . . . . . 489--499 Seymour V. Parter Numerical Methods for Generalized Axially Symmetric Potentials . . . . . . 500--516
J. H. Bramble Error Estimates for Difference Methods in Forced Vibration Problems . . . . . . 1--12 G. T. McAllister Quasilinear Uniformly Elliptic Partial Differential Equations and Difference Equations . . . . . . . . . . . . . . . 13--33 H. L. Loeb Approximation by Generalized Rationals 34--55 J. E. Midgley Calculation of Subdominant Solutions of Linear Differential Equations . . . . . 56--66 Peter Henrici An Algorithm for Analytic Continuation 67--78 R. B. Kellogg An Error Estimate for Elliptic Difference Equations on a Convex Polygon 79--90 P. Wynn On the Convergence and Stability of the Epsilon Algorithm . . . . . . . . . . . 91--122 Gerald Berman Minimization by Successive Approximation 123--133 Leon Wegge On a Discrete Version of the Newton--Raphson Method . . . . . . . . . 134--142 James M. Ortega and Werner C. Rheinboldt On Discretization and Differentiation of Operators with Application to Newton's Method . . . . . . . . . . . . . . . . . 143--156 T. N. E. Greville On Stability of Linear Smoothing Formulas . . . . . . . . . . . . . . . . 157--170
D. V. Widder Joseph Leonard Walsh . . . . . . . . . . 171--172 J. H. Ahlberg and E. N. Nilson The Approximation of Linear Functionals 173--182 Lars V. Ahlfors Remarks on Carleman's Formula for Functions in a Halfplane . . . . . . . . 183--187 G. Birkhoff and C. De Boor and B. Swartz and B. Wendroff Rayleigh--Ritz Approximation by Piecewise Cubic Polynomials . . . . . . 188--203 J. H. Curtiss Solutions of the Dirichlet Problem in the Plane by Approximation with Faber Polynomials . . . . . . . . . . . . . . 204--228 J. L. Doob Remarks on the Boundary Limits of Harmonic Functions . . . . . . . . . . . 229--235 O. J. Farrell On Approximation Measured by a Surface Integral . . . . . . . . . . . . . . . . 236--247 Dieter Gaier On the Coefficients and the Growth of Gap Power Series . . . . . . . . . . . . 248--265 Maurice Heins On the Pseudoperiods of the Weierstrass Zeta Functions . . . . . . . . . . . . . 266--268 Morris Marden A Generalization of a Theorem of Bocher 269--275 Theodore S. Motzkin Approximation in the Sense of a Deviator Integral . . . . . . . . . . . . . . . . 276--286 John R. Rice A Theory of Condition . . . . . . . . . 287--310 T. J. Rivlin and E. W. Cheney A Comparison of Uniform Approximations on an Interval and a Finite Subset Thereof . . . . . . . . . . . . . . . . 311--320 I. J. Schoenberg On Monosplines of Least Square Deviation and Best Quadrature Formulae II . . . . 321--328 W. E. Sewell Integrated Lipschitz Conditions and Approximation in the Mean by Interpolating Polynomials . . . . . . . 329--343 W. E. Sewell Remarks on the Mathematical Researches of J. L. Walsh . . . . . . . . . . . . . 344--348 O. Shisha On Infrapolynomials with Prescribed Center of Gravity of Their Zeros . . . . 349--354 Richard S. Varga On a Discrete Maximum Principle . . . . 355--359 Mishael Zedek On Approximation by Solutions of Ordinary Linear Differential Equations 360--365
Wayne T. Ford Mathematical Programming and Linear Operators in Frechet Spaces . . . . . . 367--371 Neil M. Wigley On the Convergence of Discrete Approximations to Solutions of Mixed Boundary Value Problems . . . . . . . . 372--382 Wayne T. Ford Mathematical Programming and Integro-Differential Equations: II. Variable Coefficients . . . . . . . . . 383--389 G. F. Miller On the Convergence of the Chebyshev Series for Functions Possessing a Singularity in the Range of Representation . . . . . . . . . . . . . 390--409 Adi Ben-Israel and Dan Cohen On Iterative Computation of Generalized Inverses and Associated Projections . . 410--419 A. H. Stroud Estimating Quadrature Errors for Functions with Low Continuity . . . . . 420--424 F. Max Stein and R. G. Huffstutler The Approximate Solution of Riccati's Equation . . . . . . . . . . . . . . . . 425--434 David G. Moursund Chebyshev Approximation Using a Generalized Weight Function . . . . . . 435--450 J. R. Cannon and Maria M. Cecchi The Numerical Solution of Some Biharmonic Problems by Mathematical Programming Techniques . . . . . . . . . 451--466 John Gary A Generalization of the Lax--Richtmyer Theorem on Finite Difference Schemes . . 467--473 A. R. Gourlay and A. R. Mitchell Two-Level Difference Schemes for Hyperbolic Systems . . . . . . . . . . . 474--485 E. P. Merkes On Truncation Errors for Continued Fraction Computations . . . . . . . . . 486--496 James M. Ortega and Maxine L. Rockoff Nonlinear Difference Equations and Gauss--Seidel Type Iterative Methods . . 497--513 Samuel Karlin and Zvi Ziegler Chebyshevian Spline Functions . . . . . 514--543
Dennis Eisen Stability and Convergence of Finite Difference Schemes with Singular Coefficients . . . . . . . . . . . . . . 545--552 A. Meir and A. Sharma Simultaneous Approximation of a Function and its Derivatives . . . . . . . . . . 553--563 Alfred Brauer A Method for the Computation of the Greatest Root of a Nonnegative Matrix 564--569 Jim Douglas, Jr. and A. O. Garder and Carl Pearcy Multistage Alternating Direction Methods 570--581 Ben Noble A Method for Computing the Generalized Inverse of a Matrix . . . . . . . . . . 582--584 Adi Ben-Israel On Error Bounds for Generalized Inverses 585--592 J. Douglas Lawson An Order Five Runge--Kutta Process with Extended Region of Stability . . . . . . 593--597 C. R. Cassity Solutions of the Fifth-Order Runge--Kutta Equations . . . . . . . . . 598--606 L. F. Shampine Monotone Iterations and Two-Sided Convergence . . . . . . . . . . . . . . 607--615 Mary Louise Buchanan Norms of Powers of Matrices in a Special Class . . . . . . . . . . . . . . . . . 616--623 Max K. Miller and W. T. Guy, Jr. Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials 624--635 R. A. Spinelli Numerical Inversion of a Laplace Transform . . . . . . . . . . . . . . . 636--649 Stephen M. Robinson Interpolative Solution of Systems of Nonlinear Equations . . . . . . . . . . 650--658
Eldon Hansen and Roberta Smith Interval Arithmetic in Matrix Computations, Part II . . . . . . . . . 1--9 James W. Daniel The Conjugate Gradient Method for Linear and Nonlinear Operator Equations . . . . 10--26 Victor Pereyra Iterative Methods for Solving Nonlinear Least Squares Problems . . . . . . . . . 27--36 A. H. Stroud Some Seventh Degree Integration Formulas for Symmetric Regions . . . . . . . . . 37--44 John E. Osborn Approximation of the Eigenvalues of a Class of Unbounded, Nonself-Adjoint Operators . . . . . . . . . . . . . . . 45--54 Vidar Thomee Generally Unconditionally Stable Difference Operators . . . . . . . . . . 55--69 Karl H. Usow On $ {L}_1 $ Approximation I: Computation for Continuous Functions and Continuous Dependence . . . . . . . . . 70--88 L. Fox and P. Henrici and C. Moler Approximations and Bounds for Eigenvalues of Elliptic Operators . . . 89--102 J. E. Dennis, Jr. On Newton's Method and Nonlinear Simultaneous Displacements . . . . . . . 103--108 T. M. Whitney and R. K. Meany Two Algorithms Related to the Method of Steepest Descent . . . . . . . . . . . . 109--118 B. Dejon Numerical Stability of Difference Equations with Matrix Coefficients . . . 119--128 Richard S. Varga Abstract: Some Applications of Numerical Analysis to Physical Problems . . . . . 129--129
Pierre Jamet and Seymour V. Parter Numerical Methods for Elliptic Differential Equations whose Coefficients are Singular on a Portion of the Boundary . . . . . . . . . . . . 131--146 J. R. Cannon and Maria M. Cecchi Numerical Experiments on the Solution of Some Biharmonic Problems by Mathematical Programming Techniques . . . . . . . . . 147--154 C. W. Cryer The Difference Analogue of Gauss' Theorem . . . . . . . . . . . . . . . . 155--162 G. Fairweather and A. R. Mitchell A New Computational Procedure for A.D.I. Methods . . . . . . . . . . . . . . . . 163--170 James M. Ortega and Werner C. Rheinboldt Monotone Iterations for Nonlinear Equations with Application to Gauss--Seidel Methods . . . . . . . . . 171--190 Philip Rabinowitz Gaussian Integration in the Presence of a Singularity . . . . . . . . . . . . . 191--201 J. N. Lyness and C. B. Moler Numerical Differentiation of Analytic Functions . . . . . . . . . . . . . . . 202--210 J. L. Walsh On the Convergence of Sequences of Rational Functions . . . . . . . . . . . 211--221 J. E. Dennis, Jr. A Stationary Newton Method for Nonlinear Functional Equations . . . . . . . . . . 222--232 Karl H. Usow On $ {L}_1 $ Approximation II: Computation for Discrete Functions and Discretization Effects . . . . . . . . . 233--244 P. M. Anselone Uniform Approximation Theory for Integral Equations with Discontinuous Kernels . . . . . . . . . . . . . . . . 245--253 W. B. Sweezy and W. J. Thron Estimates of the Speed of Convergence of Certain Continued Fractions . . . . . . 254--270 A. H. Zemanian and R. P. Tewarson The Numerical Evaluation of Distributional Transforms . . . . . . . 271--282 D. Gries and J. Stoer Some Results on Fields of Values of a Matrix . . . . . . . . . . . . . . . . . 283--300 J. N. Lyness The Calculation of Fourier Coefficients 301--315
J. R. Cannon and Jim Douglas, Jr. The Cauchy Problem for the Heat Equation 317--336 Kendall E. Atkinson The Numerical Solution of Fredholm Integral Equations of the Second Kind 337--348 Dennis Eisen On the Construction of Consistent Finite Difference Schemes with Certain Invariant Subspaces . . . . . . . . . . 349--356 Walter Gautschi Numerical Quadrature in the Presence of a Singularity . . . . . . . . . . . . . 357--362 H. L. Gray and T. A. Atchison Nonlinear Transformations Related to the Evaluation of Improper Integrals. I . . 363--371 J. Douglas Lawson Generalized Runge--Kutta Processes for Stable Systems with Large Lipschitz Constants . . . . . . . . . . . . . . . 372--380 A. H. Stroud Integration Formulas and Orthogonal Polynomials . . . . . . . . . . . . . . 381--389 Robert E. Barnhill Optimal Quadratures in $ {L}^2 ({E}_\rho) $. I . . . . . . . . . . . . 390--397 John H. Rowland On the Structure of the Error Curve in Chebyshev Approximation by Polynomials 398--405 James S. Vandergraft Newton's Method for Convex Operators in Partially Ordered Spaces . . . . . . . . 406--432 Frank R. Loscalzo and Thomas D. Talbot Spline Function Approximations for Solutions of Ordinary Differential Equations . . . . . . . . . . . . . . . 433--445 John D. Brooks and David A. Pope Asymptotic Error Estimates and the Numerical Solution of the Equations of Orbital Motion . . . . . . . . . . . . . 446--456 Dennis Eisen On the Numerical Analysis of a Fourth Order Wave Equation . . . . . . . . . . 457--464 R. A. Spinelli Poisson Equation on a Sphere. II . . . . 465--473 W. Kahan Laguerre's Method and a Circle Which Contains at Least One Zero of a Polynomial . . . . . . . . . . . . . . . 474--482
Karl L. E. Nickel Extension of a Recent Paper by Fox, Henrici and Moler on Eigenvalues of Elliptic Operators . . . . . . . . . . . 483--488 G. J. Kurowski The Semidiscrete Riemann Function . . . 489--498 R. P. Tewarson A Direct Method for Generalized Matrix Inversion . . . . . . . . . . . . . . . 499--507 Victor Pereyra Accelerating the Convergence of Discretization Algorithms . . . . . . . 508--533 Robert E. Barnhill Optimal Quadratures in $ {L}^2 ({E}_\rho) $. II . . . . . . . . . . . . 534--541 A. Pelios Rational Function Approximation as a Well-Conditioned Matrix Eigenvalue Problem . . . . . . . . . . . . . . . . 542--547 Gary P. Herring A Note on Generalized Interpolation and the Pseudoinverse . . . . . . . . . . . 548--556 John R. Rice Characterization of Chebyshev Approximations by Splines . . . . . . . 557--565 Lloyd Rosenberg Bernstein Polynomials and Monte Carlo Integration . . . . . . . . . . . . . . 566--574 Richard Saylor Numerical Elliptic Continuation . . . . 575--581 James Hurt Some Stability Theorems for Ordinary Difference Equations . . . . . . . . . . 582--596 Robert J. Lambert An Analysis of the Numerical Stability of Predictor-Corrector Solutions of Nonlinear Ordinary Differential Equations . . . . . . . . . . . . . . . 597--606 H. P. Konen and H. A. Luther Some Singular Explicit Fifth Order Runge--Kutta Solutions . . . . . . . . . 607--619 J. Douglas Lawson An Order Six Runge--Kutta Process with Extended Region of Stability . . . . . . 620--625 Milos Zlamal Discretization and Error Estimates for Elliptic Boundary Value Problems of the Fourth Order . . . . . . . . . . . . . . 626--639
J. H. Bramble and B. E. Hubbard and M. Zlamal Discrete Analogues of the Dirichlet Problem with Isolated Singularities . . 1--25 R. Bruce Simpson Approximation of the Minimizing Element for a Class of Functionals . . . . . . . 26--41 Werner C. Rheinboldt A Unified Convergence Theory for a Class of Iterative Processes . . . . . . . . . 42--63 C. B. Moler and L. E. Payne Bounds for Eigenvalues and Eigenvectors of Symmetric Operators . . . . . . . . . 64--70 Burton Wendroff Well-Posed Problems and Stable Difference Operators . . . . . . . . . . 71--82 David D. Morrison Optimization by Least Squares . . . . . 83--88 Kendall E. Atkinson On the Order of Convergence of Natural Cubic Spline Interpolation . . . . . . . 89--101 J. Abate and H. Dubner A New Method for Generating Power Series Expansions of Functions . . . . . . . . 102--112 C. A. Hall and J. Spanier Nested Bounds for the Spectral Radius 113--125 D. G. Moursund Computational Aspects of Chebyshev Approximation Using a Generalized Weight Function . . . . . . . . . . . . . . . . 126--137 D. G. Moursund and G. D. Taylor Optimal Starting Values for the Newton--Raphson Calculation of Inverses of Certain Functions . . . . . . . . . . 138--150 Charles A. Bryan Approximate Solutions to Nonlinear Integral Equations . . . . . . . . . . . 151--155 H. H. Rachford, Jr. Rounding Errors in Parabolic Problems. I: The One-Space Variable Case . . . . . 156--171 M. M. Chawla On the Estimation of Errors of Gaussian Cubature Formulas . . . . . . . . . . . 172--181 Randall E. Cline Inverses of Rank Invariant Powers of a Matrix . . . . . . . . . . . . . . . . . 182--197
Richard Askey and James Fitch Positivity of the Cotes Numbers for Some Ultraspherical Abscissas . . . . . . . . 199--201 Minoru Urabe Roundoff Error Distribution in Fixed-Point Multiplication and a Remark about the Rounding Rule . . . . . . . . 202--210 J. R. Cannon and C. Denson Hill A Finite-Difference Method for Degenerate Elliptic-Parabolic Equations 211--218 L. F. Shampine Boundary Value Problems for Ordinary Differential Equations . . . . . . . . . 219--242 A. H. Stroud and Edward H. Goit, Jr. Some Extensions of Integration Formulas 243--251 John E. Buchanan and Donald H. Thomas On Least-Squares Fitting of Two-Dimensional Data with a Special Structure . . . . . . . . . . . . . . . 252--257 G. D. Taylor On Approximation by Polynomials Having Restricted Ranges . . . . . . . . . . . 258--268 C. A. Hall and T. A. Porsching Computing the Maximal Eigenvalue and Eigenvector of a Positive Matrix . . . . 269--274 J. R. Cannon Determination of an Unknown Heat Source from Overspecified Boundary Data . . . . 275--286 Otto Neall Strand and Ed R. Westwater Minimum-RMS Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind . . . . . . . . . . . 287--295 L. W. Johnson and D. R. Scholz On Steffensen's Method . . . . . . . . . 296--302 M. Stuart Lynn and William P. Timlake The Use of Multiple Deflations in the Numerical Solution of Singular Systems of Equations, with Applications to Potential Theory . . . . . . . . . . . . 303--322 Julius Smith The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. I . . . 323--339 F. de la Vallée Poussin An Accelerated Relaxation Algorithm for Iterative Solution of Elliptic Equations 340--351 Ralph L. James The Numerical Solution of Singular Volterra Integral Equations . . . . . . 352--362 G. W. Hedstrom The Rate of Convergence of Some Difference Schemes . . . . . . . . . . . 363--406 H. H. Rachford, Jr. Rounding Errors in Alternating Direction Methods for Parabolic Problems . . . . . 407--421 Frank Stenger Kronecker Product Extensions of Linear Operators . . . . . . . . . . . . . . . 422--435 R. Hersh On the Theory of Difference Schemes for Mixed Initial Boundary Value Problems 436--450 T. A. Atchison and H. L. Gray Nonlinear Transformations Related to the Evaluation of Improper Integrals. II . . 451--459
Manfred Reimer Bounds for the Horner Sums . . . . . . . 461--469 C. A. Hall and T. A. Porsching Computing the Maximal Eigenvalue and Eigenvector of a Nonnegative Irreducible Matrix . . . . . . . . . . . . . . . . . 470--474 R. J. Thompson On Some Functional Differential Equations: Existence of Solutions and Difference Approximations . . . . . . . 475--487 A. Meir and A. Sharma An Extension of Obreshkov's Formula . . 488--490 C. S. Duris and V. P. Sreedharan Chebyshev and $ l^1$-Solutions of Linear Equations Using Least Squares Solutions 491--505 Gilbert Strang On the Construction and Comparison of Difference Schemes . . . . . . . . . . . 506--517 Jean-Pierre Aubin Best Approximation of Linear Operators in Hilbert Spaces . . . . . . . . . . . 518--521 Robert E. Barnhill and James A. Wixom An Error Analysis for Interpolation of Analytic Functions . . . . . . . . . . . 522--529 Herbert L. Stone Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations . . . . . 530--558 Todd Dupont and Richard P. Kendall and H. H. Rachford, Jr. An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference Equations . . . . . . . . . . 559--573 R. C. Jones and L. A. Karlovitz Iterative Construction of Constrained Chebyshev Approximation of Continuous Functions . . . . . . . . . . . . . . . 574--585 David Slepian A Numerical Method for Determining the Eigenvalues and Eigenfunctions of Analytic Kernels . . . . . . . . . . . . 586--600 Samuel Schechter Relaxation Methods for Convex Problems 601--612 Robert E. Huddleston Maximum Principle Methods for the Discretization Error in the Approximation of the Bergman Harmonic Kernel by Finite Difference Methods . . 613--625 Vidar Thomee Discrete Interior Schauder Estimates for Elliptic Difference Operators . . . . . 626--645
Larry Schumaker Uniform Approximation by Chebyshev Spline Functions. II: Free Knots . . . . 647--656 J. W. Jerome and L. L. Schumaker A Note on Obtaining Natural Spline Functions by the Abstract Approach of Atteia and Laurent . . . . . . . . . . . 657--663 Harold J. Kushner On the Numerical Solution of Degenerate Linear and Nonlinear Elliptic Boundary Value Problems . . . . . . . . . . . . . 664--679 Joel N. Franklin and Eugene R. Rodemich Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation . . . . . . . . . . . . . . . . 680--716 C. Denson Hill On the Numerical Solution of Degenerate Elliptic-Parabolic Equations . . . . . . 717--724 Manfred Reimer Finite Difference Forms Containing Derivatives of Higher Order . . . . . . 725--738 Gunter H. Meyer On Solving Nonlinear Equations with a One-Parameter Operator Imbedding . . . . 739--752 Todd Dupont A Factorization Procedure for the Solution of Elliptic Difference Equations . . . . . . . . . . . . . . . 753--782 Christopher T. H. Baker On the Nature of Certain Quadrature Formulas and Their Errors . . . . . . . 783--804 Peter Wynn Upon the Padé Table Derived from a Stieltjes Series . . . . . . . . . . . . 805--834 J. H. Bramble and B. E. Hubbard Effects of Boundary Regularity on the Discretization Error in the Fixed Membrane Eigenvalue Problem . . . . . . 835--863 A. Sharma and J. Prasad On Abel--Hermite--Birkhoff Interpolation 864--881 D. G. Moursund and G. D. Taylor Uniform Rational Approximation Using a Generalized Weight Function . . . . . . 882--889
G. Wilson Factorization of the Covariance Generating Function of a Pure Moving Average Process . . . . . . . . . . . . 1--7 Herbert B. Keller Accurate Difference Methods for Linear Ordinary Differential Systems Subject to Linear Constraints . . . . . . . . . . . 8--30 L. L. Schumaker and G. D. Taylor On Approximation by Polynomials Having Restricted Ranges. II . . . . . . . . . 31--36 A. R. Gourlay and A. R. Mitchell The Equivalence of Certain Alternating Direction and Locally One-Dimensional Difference Methods . . . . . . . . . . . 37--46 J. D. P. Donnelly Eigenvalues of Membranes with Reentrant Corners . . . . . . . . . . . . . . . . 47--61 A. R. Gourlay and A. R. Mitchell A Classification of Split Difference Methods for Hyperbolic Equations in Several Space Dimensions . . . . . . . . 62--71 T. S. Tucker Stability of Nonlinear Computing Schemes 72--81 Robert E. Barnhill The Convergence of Complex Cubatures . . 82--89 A. H. Stroud A Fifth Degree Integration Formula for the $n$-Simplex . . . . . . . . . . . . 90--98 Geneva G. Belford An Initial Value Problem Approach to the Solution of Eigenvalue Problems . . . . 99--103 R. K. Meany A Matrix Inequality . . . . . . . . . . 104--107 M. M. Chawla On Davis's Method for the Estimation of Errors of Gauss--Chebyshev Quadratures 108--117 John H. Rowland On the Location of the Deviation Points in Chebyshev Approximation by Polynomials . . . . . . . . . . . . . . 118--126 Charlotte Froese Fischer and Riaz A. Usmani Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems . . . . . . . . . . . . . . . . 127--142 Myron S. Henry A Best Approximate Solution of Certain Nonlinear Differential Equations . . . . 143--148 J. R. Cannon and George H. Knightly The Approximation of the Solution to the Heat Equation in a Half-Strip from Data Specified on the Bounding Characteristics . . . . . . . . . . . . 149--159
Martin H. Schultz $ {L}^\infty $-Multivariate Approximation Theory . . . . . . . . . . 161--183 Martin H. Schultz $ {L}^2$-Multivariate Approximation Theory . . . . . . . . . . . . . . . . . 184--209 William B. Jones and R. I. Snell Truncation Error Bounds for Continued Fractions . . . . . . . . . . . . . . . 210--221 A. H. Stroud Integration Formulas and Orthogonal Polynomials for Two Variables . . . . . 222--229 K. Atkinson and A. Sharma A Partial Characterization of Poised Hermite--Birkhoff Interpolation Problems 230--235 Theodore Katsanis Numerical Solution of Tricomi Equation Using Theory of Symmetric Positive Differential Equations . . . . . . . . . 236--253 David W. Kammler An Error Bound for Capacitance Calculations . . . . . . . . . . . . . . 254--257 R. B. Simpson The Rayleigh--Ritz Process for the Simplest Problem in the Calculus of Variations . . . . . . . . . . . . . . . 258--271 Stanley E. Weinstein Solution of Nonlinear Equations by Iterative Procedures which Use Approximation Techniques . . . . . . . . 272--283 H. L. Loeb and D. G. Moursund and L. L. Schumaker and G. D. Taylor Uniform Generalized Weight Function Polynomial Approximation with Interpolation . . . . . . . . . . . . . 284--293 Ian Gladwell Some Extensions of a Paper by Birkhoff and Priver . . . . . . . . . . . . . . . 294--298 Tomasz Pietrzykowski An Exact Potential Method for Constrained Maxima . . . . . . . . . . . 299--304 F. J. Schuurmann Uniqueness in the Uniform Approximation of a Function and Its Derivatives . . . 305--315
Olin G. Johnson Error Bounds for Sturm--Liouville Eigenvalue Approximations by Several Piecewise Cubic Rayleigh--Ritz Methods 317--333 Yasuhiko Ikebe and M. Stuart Lynn and William P. Timlake The Numerical Solution of the Integral Equation Formulation of the Single Interface Neumann Problem . . . . . . . 334--346 S. M. Roberts and J. S. Shipman and W. J. Ellis A Perturbation Technique for Nonlinear Two-Point Boundary Value Problems . . . 347--358 Thomas H. Jefferson Truncation Error Estimates for $ {T}$-Fractions . . . . . . . . . . . . . 359--364 Peter Linz Numerical Methods for Volterra Integral Equations with Singular Kernels . . . . 365--374 Kendall Atkinson The Numerical Solution of Integral Equations on the Half-Line . . . . . . . 375--397 M. J. D. Powell The Local Dependence of Least Squares Cubic Splines . . . . . . . . . . . . . 398--413 L. F. Shampine Boundary Value Problems for Ordinary Differential Equations. II: Patch Bases and Monotone Methods . . . . . . . . . . 414--431 C. R. Cassity The Complete Solution of the Fifth Order Runge--Kutta Equations . . . . . . . . . 432--436 T. A. Porsching Jacobi and Gauss--Seidel Methods for Nonlinear Network Problems . . . . . . . 437--449 Robert E. Barnhill and James A. Wixom An Error Analysis for the Bivariate Interpolation of Analytic Functions . . 450--457 Pierre Jamet Numerical Solution of the Dirichlet Problem for Elliptic Parabolic Equations 458--466 Martin H. Schultz $ {L}^2$-Approximation Theory of Even Order Multivariate Splines . . . . . . . 467--475 John J. H. Miller The Construction of Unbalanced Difference Operators for Parabolic Initial Boundary Value Problems . . . . 476--479 Eduardo L. Ortiz The Tau Method . . . . . . . . . . . . . 480--492 J. E. Dennis, Jr. On the Kantorovich Hypothesis for Newton's Method . . . . . . . . . . . . 493--507 Bertil Gustafsson On Difference Approximations to Hyperbolic Differential Equations Over Long Time Intervals . . . . . . . . . . 508--522
Martin H. Schultz Rayleigh--Ritz--Galerkin Methods for Multidimensional Problems . . . . . . . 523--538 Richard A. Tapia The Weak Newton Method and Boundary Value Problems . . . . . . . . . . . . . 539--550 David K. Kahaner On Equal and Almost Equal Weight Quadrature Formulas . . . . . . . . . . 551--556 R. D. Riess and L. W. Johnson Estimating Gauss--Chebyshev Quadrature Errors . . . . . . . . . . . . . . . . . 557--559 Kenneth M. Brown A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination 560--569 Martin H. Schultz Approximation Theory of Multivariate Spline Functions in Sobolev Spaces . . . 570--582 J. H. Bramble and V. Thomee Pointwise Bounds for Discrete Green's Functions . . . . . . . . . . . . . . . 583--590 David Glasser Numerical Solution of Two-Point Boundary Value Problems on Total Differential Equations . . . . . . . . . . . . . . . 591--597 Gerald N. Minerbo and Maurice E. Levy Inversion of Abel's Integral Equation by Means of Orthogonal Polynomials . . . . 598--616
Chandler Davis and W. M. Kahan The Rotation of Eigenvectors by a Perturbation. III . . . . . . . . . . . 1--46 Werner Liniger and Ralph A. Willoughby Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations . . . . . . . . . . . . . . . 47--66 Nira Richter Properties of Minimal Integration Rules 67--78 J. B. Rosen Approximate Solution and Error Bounds for Quasi-Linear Elliptic Boundary Value Problems . . . . . . . . . . . . . . . . 80--103 Julius Smith The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. II . . . 104--111 J. H. Bramble and S. R. Hilbert Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation . . . . . . . . . . . . . 112--124 Raphael Loewy Gerschgorin-Type Theorems for Partitioned Matrices . . . . . . . . . . 125--128 Myron S. Henry A Sequence of Best Approximate Solutions of $ y'' = {F}(x, y, y') $ . . . . . . . 129--133 M. Wayne Wilson Necessary and Sufficient Conditions for Equidistant Quadrature Formula . . . . . 134--141 A. J. Keeping Band Matrices Arising from Finite Difference Approximations to a Third Order Partial Differential Equation . . 142--156 Yonathan Bard Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems . . . . . . . . . . 157--186 Walter Gautschi Efficient Computation of the Complex Error Function . . . . . . . . . . . . . 187--198
Stanley Osher Mesh Refinements for the Heat Equation 199--205 James R. Kuttler Finite Difference Approximations for Eigenvalues of Uniformly Elliptic Operators . . . . . . . . . . . . . . . 206--232 L. Wuytack Some Remarks on a Paper of D. G. Moursund . . . . . . . . . . . . . . . . 233--237 Gray Jennings Digital Filtering of Random Digits . . . 238--247 G. D. Taylor and M. J. Winter Calculation of Best Restricted Approximations . . . . . . . . . . . . . 248--255 N. F. Stewart Certain Equivalent Requirements of Approximate Solutions of $ x' = f(t, x) $ . . . . . . . . . . . . . . . . . . . 256--270 A. H. Stroud Integration Formulas and Orthogonal Polynomials. II . . . . . . . . . . . . 271--276 James W. Daniel A Correction Concerning the Convergence Rate for the Conjugate Gradient Method 277--280 Fred W. Dorr The Numerical Solution of Singular Perturbations of Boundary Value Problems 281--313 Bernard H. Rosman Extension of Results by Rice and Schumaker on Spline Approximation . . . 314--316 Christopher T. H. Baker and Pauline A. Radcliffe Error Bounds for Some Chebyshev Methods of Approximation and Integration . . . . 317--327
Jet Wimp Derivative-Free Iteration Processes . . 329--334 S.-A. Gustafson and K. O. Kortanek and W. Rom Non-Chebyshevian Moment Problems . . . . 335--342 S.-A. Gustafson On the Computational Solution of a Class of Generalized Moment Problems . . . . . 343--357 M. Z. Nashed Steepest Descent for Singular Linear Operator Equations . . . . . . . . . . . 358--362 Frank Lether An Error Representation for Product Cubature Rules . . . . . . . . . . . . . 363--365 D. F. Shanno Parameter Selection for Modified Newton Methods for Function Minimization . . . 366--372 J. H. Verner Quadratures for Implicit Differential Equations . . . . . . . . . . . . . . . 373--385 Zdislav Kovarik Some Iterative Methods for Improving Orthonormality . . . . . . . . . . . . . 386--389 David G. Luenberger The Conjugate Residual Method for Constrained Minimization Problems . . . 390--398 David L. Russell Numerical Solution of Singular Initial Value Problems . . . . . . . . . . . . . 399--417 Karl Scherer On the Best Approximation of Continuous Functions by Splines . . . . . . . . . . 418--423 Henryk Minc On the Maximal Eigenvector of a Positive Matrix . . . . . . . . . . . . . . . . . 424--427 J. Prasad On the Weighted (0,2) Interpolation . . 428--446 S. N. Afriat The Progressive Support Method for Convex Programming . . . . . . . . . . . 447--457 J. D. P. Donnelly Bounds for the Eigenvalues of Self-Adjoint Operators . . . . . . . . . 458--478
G. Peters and J. H. Wilkinson $ A x = \lambda B x $ and the Generalized Eigenproblem . . . . . . . . 479--492 Richard S. Varga Minimal Gerschgorin Sets for Partitioned Matrices . . . . . . . . . . . . . . . . 493--507 Hans Schneider and Mathukumalli Vidyasagar Cross-Positive Matrices . . . . . . . . 508--519 D. K. Faddeev and V. N. Faddeeva Natural Norms in Algebraic Processes . . 520--531 V. N. Kublanovskaya On an Approach to the Solution of the Generalized Latent Value Problem for $ \lambda $-Matrices . . . . . . . . . . . 532--537 Peter Henrici Upper Bounds for the Abscissa of Stability of a Stable Polynomial . . . . 538--544 M. A. Jenkins and J. F. Traub A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration 545--566 A. M. Ostrowski A Theorem on Clusters of Roots of Polynomial Equations . . . . . . . . . . 567--570 Alan J. Hoffman and Richard S. Varga Patterns of Dependence in Generalizations of Gerschgorin's Theorem 571--574 Jim Douglas, Jr. and Todd Dupont Galerkin Methods for Parabolic Equations 575--626 B. L. Buzbee and G. H. Golub and C. W. Nielson On Direct Methods for Solving Poisson's Equations . . . . . . . . . . . . . . . 627--656
Christopher T. H. Baker The Deferred Approach to the Limit for Eigenvalues of Integral Equations . . . 1--10 Robert S. Stepleman Finite-Dimensional Analogues of Variational Problems in the Plane . . . 11--23 Irene Gargantini The Numerical Stability of the Schur--Cohn Criterion . . . . . . . . . 24--29 John Roulier Linear Operators Invariant on Nonnegative Monotone Functions . . . . . 30--35 Frank G. Lether Cubature Error Bounds for Gauss--Legendre Product Rules . . . . . 36--42 G. G. Lorentz and K. L. Zeller Birkhoff Interpolation . . . . . . . . . 43--48 Frank G. Lether Error Bounds for Fully Symmetric Cubature Rules . . . . . . . . . . . . . 49--60 E. David Callender Single Step Methods and Low Order Splines for Solutions of Ordinary Differential Equations . . . . . . . . . 61--66 D. Kershaw A Note on the Convergence of Interpolatory Cubic Splines . . . . . . 67--74 David K. Kahaner and J. L. Ullman Equal Weight Quadrature on Infinite Intervals . . . . . . . . . . . . . . . 75--79 Gary G. Sackett An Implicit Free Boundary Problem for the Heat Equation . . . . . . . . . . . 80--96 A. Bacopoulos and B. Gaff On the Reduction of a Problem of Minimization of $ n + 1 $ Variables to a Problem of One Variable . . . . . . . . 97--103 James M. Garnett, III and Adi Ben-Israel and Stephen S. Yau A Hyperpower Iterative Method for Computing Matrix Products Involving the Generalized Inverse . . . . . . . . . . 104--109 Ruben J. Espinosa-Maldonado and George D. Byrne On the Convergence of Quadrature Formulas . . . . . . . . . . . . . . . . 110--114 Lois E. Mansfield On the Optimal Approximation of Linear Functionals in Spaces of Bivariate Functions . . . . . . . . . . . . . . . 115--126 Robert G. Voigt Rates of Convergence for a Class of Iterative Procedures . . . . . . . . . . 127--134 George A. Costello The Approximate Solution of the Dirichlet Problem by Means of Integral Equations . . . . . . . . . . . . . . . 135--136 John Donelson, III and Eldon Hansen Cyclic Composite Multistep Predictor-Corrector Methods . . . . . . 137--157 William J. Gordon Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation . . . . . . . . . . . . . 158--177
Stanley E. Weinstein Product Approximations of Functions of Several Variables . . . . . . . . . . . 178--189 R. B. Simpson Finite Difference Methods for Mildly Nonlinear Eigenvalue Problems . . . . . 190--211 F. N. Fritsch On Self-Contained Numerical Integration Formulas for Symmetric Regions . . . . . 213--221 Robert G. Voigt Orders of Convergence for Iterative Procedures . . . . . . . . . . . . . . . 222--243 Kenneth Schoen Fifth and Sixth Order PECE Algorithms with Improved Stability Properties . . . 244--248 Frank G. Lether A Generalized Product Rule for the Circle . . . . . . . . . . . . . . . . . 249--253 Jane Cullum Numerical Differentiation and Regularization . . . . . . . . . . . . . 254--265 N. K. Madsen Pointwise Convergence of the Three-Dimensional Discrete Ordinate Method . . . . . . . . . . . . . . . . . 266--269 M. D. Hebden A Bound on the Difference Between the Chebyshev Norm and the Holder Norms of a Function . . . . . . . . . . . . . . . . 270--277 Louis W. Ehrlich Solving the Biharmonic Equation as Coupled Finite Difference Equations . . 278--287 A. J. Keeping On Certain Almost-Triangular Band Matrices . . . . . . . . . . . . . . . . 288--303 Ivo Babu\vska The Rate of Convergence for the Finite Element Method . . . . . . . . . . . . . 304--315 Bruce A. Finlayson Convergence of the Galerkin Method for Nonlinear Problems Involving Chemical Reaction . . . . . . . . . . . . . . . . 316--324 Jorge J. More Global Convergence of Newton--Gauss--Seidel Methods . . . . . 325--336 J. D. Lambert Predictor-Corrector Algorithms with Identical Regions of Stability . . . . . 337--344 M. N. Spijker Reduction of Roundoff Error by Splitting of Difference Formulas . . . . . . . . . 345--357 Å. Björck and C. Bowie An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix 358--364 H. L. Gray and T. A. Atchison and G. V. McWilliams Higher Order $ {G}$-Transformations . . 365--381 Josef Stoer On the Numerical Solution of Constrained Least-Squares Problems . . . . . . . . . 382--411 M. E. A. El-Tom On Ignoring the Singularity in Approximate Integration . . . . . . . . 412--424 A. A. Grau The Simultaneous Newton Improvement of a Complete Set of Approximate Factors of a Polynomial . . . . . . . . . . . . . . . 425--438 Winifred L. Wood Periodicity Effects on the Iterative Solution of Elliptic Difference Equations . . . . . . . . . . . . . . . 439--464 G. J. Auslaender A Novel, Hermite Type, Interpolation Procedure . . . . . . . . . . . . . . . 465--472 Christopher T. H. Baker and Graham S. Hodgson Asymptotic Expansions for Integration Formulas in One or More Dimensions . . . 473--480 T. Pietrzykowski Erratum: ``An Exact Potential Method for Constrained Maxima'' [SIAM J. Numer. Anal. \bf 6 (1969), no. 2, 299--304] . . 481--481
Werner Haussmann On Interpolation with Derivatives . . . 483--485 W. L. Miranker Galerkin Approximations and the Optimization of Difference Schemes for Boundary Value Problems . . . . . . . . 486--496 Nira Richter-Dyn Properties of Minimal Integration Rules. II . . . . . . . . . . . . . . . . . . . 497--508 R. D. Riess A Note on Error Bounds for Gauss--Chebyshev Quadrature . . . . . . 509--511 Hans J. Stetter Local Estimation of the Global Discretization Error . . . . . . . . . . 512--523 Pierre Jamet A Finite Difference Scheme and an Existence Theorem for a Nonlinear Hyperbolic System of Differential Equations . . . . . . . . . . . . . . . 524--535 George J. Fix and Kate Larsen On the Convergence of SOR Iterations for Finite Element Approximations to Elliptic Boundary Value Problems . . . . 536--547 Jerome Spanier A New Multistage Procedure for Systematic Variance Reduction in Monte Carlo . . . . . . . . . . . . . . . . . 548--554 Gunter H. Meyer A Numerical Method for Two-Phase Stefan Problems . . . . . . . . . . . . . . . . 555--568 J. M. Varah Stability of High Order Accurate Difference Methods for Parabolic Equations with Boundary Conditions . . . 569--574 T. A. Porsching On Rates of Convergence of Jacobi and Gauss--Seidel Methods for $ {M}$-Functions . . . . . . . . . . . . . 575--582 Nira Richter-Dyn Minimal Interpolation and Approximation in Hilbert Spaces . . . . . . . . . . . 583--597 J. M. Varah Stability of Difference Approximations to the Mixed Initial Boundary Value Problems for Parabolic Systems . . . . . 598--615 Richard J. Hanson A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular Values . . . . . . . . . 616--622
A. M. Ostrowski Some Properties of Reduced Polynomial Equations . . . . . . . . . . . . . . . 623--638 J. R. Bunch and B. N. Parlett Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations 639--655 J. R. Bunch Analysis of the Diagonal Pivoting Method 656--680 A. H. Stroud and Kwan-Wei Chen and Ping-Lei Wang and Zunkwang Mao Some Second and Third Degree Harmonic Interpolation Formulas . . . . . . . . . 681--692 William B. Jones and W. J. Thron \em A Posteriori Bounds for the Truncation Error of Continued Fractions 693--705 Herbert L. Dershem Approximation of the Bessel Eigenvalue Problem by Finite Differences . . . . . 706--716 V. N. Murty Best Approximation with Chebyshev Polynomials . . . . . . . . . . . . . . 717--721 B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub The Direct Solution of the Discrete Poisson Equation on Irregular Regions 722--736 Martin H. Schultz $ {L}^2 $ error bounds for the Rayleigh--Ritz--Galerkin method . . . . 737--748 Charles B. Dunham Chebyshev Approximation with the Local Haar Condition . . . . . . . . . . . . . 749--753 Edgar A. Cohen, Jr. Note on a Truncated Chebyshev Series Modified to Match Function Values at Interval Endpoints . . . . . . . . . . . 754--756 Richard Franke Orthogonal Polynomials and Approximate Multiple Integration . . . . . . . . . . 757--766 Paul T. Boggs The Solution of Nonlinear Systems of Equations by $ {A}$-Stable Integration Techniques . . . . . . . . . . . . . . . 767--785 Lucio Tavernini One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations . . . . . . . . . 786--795 G. W. Stewart Error Bounds for Approximate Invariant Subspaces, of Closed Linear Operator . . 796--808
James R. Kuttler Remarks on a Stekloff Eigenvalue Problem 1--5 W. Robert Boland The Convergence of Product-Type Quadrature Formulas . . . . . . . . . . 6--13 James L. Phillips The Use of Collocation as a Projection Method for Solving Linear Operator Equations . . . . . . . . . . . . . . . 14--28 Charlie H. Cooke On Stiffly Stable Implicit Linear Multistep Methods . . . . . . . . . . . 29--34 S. K. Aalto The Representation of Functionals on Subspaces by Functionals Having Certain Support Sets . . . . . . . . . . . . . . 35--39 James M. Ortega and Werner C. Rheinboldt A General Convergence Result for Unconstrained Minimization Methods . . . 40--43 Binh Lam and David Elliott On a Conjecture of C. W. Clenshaw . . . 44--52 Ivo Babu\vska Numerical Stability in Problems of Linear Algebra . . . . . . . . . . . . . 53--77 G. Fix and R. Heiberger An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem . . . . . 78--88 David M. Young On the consistency of linear stationary iterative methods . . . . . . . . . . . 89--96 James S. Vandergraft Applications of Partial Orderings to the Study of Positive Definiteness, Monotonicity, and Convergence of Iterative Methods for Linear Systems . . 97--104 Colin W. Cryer and Lucio Tavernini The Numerical Solution of Volterra Functional Differential Equations by Euler's Method . . . . . . . . . . . . . 105--129 Marvin Marcus and William R. Gordon An Analysis of Equality in Certain Matrix Inequalities. II . . . . . . . . 130--136 J. G. Pierce and R. S. Varga Higher Order Convergence Results for the Rayleigh--Ritz Method Applied to Eigenvalue Problems. I: Estimates Relating Rayleigh--Ritz and Galerkin Approximations to Eigenfunctions . . . . 137--151 C. M. Ablow A Characteristic Finite Difference Method for the Wave Equation in Two Dimensions . . . . . . . . . . . . . . . 152--164 W. J. Kammerer and M. Z. Nashed On the Convergence of the Conjugate Gradient Method for Singular Linear Operator Equations . . . . . . . . . . . 165--181 H. F. Weinberger On Optimal Numerical Solution of Partial Differential Equations . . . . . . . . . 182--198
Jitka Segethova Numerical Construction of the Hill Functions . . . . . . . . . . . . . . . 199--204 A. C. Hindmarsh Optimality in a Class of Rootfinding Algorithms . . . . . . . . . . . . . . . 205--214 J. Thomas King The Approximate Solution of Parabolic Initial Boundary Value Problems by Weighted Least-Squares Methods . . . . . 215--229 J. E. Dennis, Jr. and Roland A. Sweet Some Minimum Properties of the Trapezoidal Rule . . . . . . . . . . . . 230--236 Charles K. Chui Concerning Gaussian--Chebyshev Quadrature Errors . . . . . . . . . . . 237--240 R. H. Estes and E. R. Lancaster Some Generalized Power Series Inversions 241--247 Arthur I. Cohen Rate of Convergence of Several Conjugate Gradient Algorithms . . . . . . . . . . 248--259 Jean Descloux On Finite Element Matrices . . . . . . . 260--265 S. Eisenberg and B. Wood On the Order of Approximation of Unbounded Functions by Positive Linear Operators . . . . . . . . . . . . . . . 266--276 K. Nickel and K. Ritter Termination Criterion and Numerical Convergence . . . . . . . . . . . . . . 277--283 Kendall Atkinson The Numerical Evaluation of the Cauchy Transform on Simple Closed Curves . . . 284--299 Paul N. Swarztrauber On the Numerical Solution of the Dirichlet Problem for a Region of General Shape . . . . . . . . . . . . . 300--306 William F. Trench Stability of a Class of Discrete Minimum Variance Smoothing Formulas . . . . . . 307--315 George D. Byrne and Donald N. H. Chi Linear Multistep Formulas Based on $g$-Splines . . . . . . . . . . . . . . 316--324 J. K. Reid The Use of Conjugate Gradients for Systems of Linear Equations Possessing ``Property A'' . . . . . . . . . . . . . 325--332 A. H. Stroud and Kwan-Wei Chen Peano Error Estimates for Gauss--Laguerre Quadrature Formulas . . 333--340 Thomas R. Lucas and George W. Reddien, Jr. Some Collocation Methods for Nonlinear Boundary Value Problems . . . . . . . . 341--356 Jorge J. More Nonlinear Generalizations of Matrix Diagonal Dominance with Application to Gauss--Seidel Iterations . . . . . . . . 357--378
Bruno O. Shubert A Sequential Method Seeking the Global Maximum of a Function . . . . . . . . . 379--388 G. J. Cooper and J. H. Verner Some Explicit Runge--Kutta Methods of High Order . . . . . . . . . . . . . . . 389--405 Alfred Carasso The Backward Beam Equation: Two $ {A}$-Stable Schemes for Parabolic Problems . . . . . . . . . . . . . . . . 406--434 R. A. Nicolaides On a Class of Finite Elements Generated by Lagrange Interpolation . . . . . . . 435--445 James Alan Cochran and Erold W. Hinds Improved Error Bounds for the Eigenvalues of Certain Normal Operators 446--453 David M. Young Generalizations of property $ {A} $ and consistent ordering . . . . . . . . . . 454--463 M. P. Epstein and R. W. Hamming Noninterpolatory Quadrature Formulas . . 464--475 Bruce Chartres and Robert Stepleman A General Theory of Convergence for Numerical Methods . . . . . . . . . . . 476--492 I. Barrodale and M. J. D. Powell and F. D. K. Roberts The Differential Correction Algorithm for Rational $ \mathcal {l}_\infty $-Approximation . . . . . . . . . . . . 493--504 Arthur D. Snider An Improved Estimate of the Accuracy of Trigonometric Interpolation . . . . . . 505--508 S. E. Weinstein Uniform Approximation of Functions Through Optimal Partitioning . . . . . . 509--517 A. H. Stroud Two Fifth Degree Harmonic Interpolation Formulas for the $n$-Box . . . . . . . . 518--521
Albert C. Reynolds, Jr. Convergent Finite Difference Schemes for Nonlinear Parabolic Equations . . . . . 523--533 Paul S. Jensen The Solution of Large Symmetric Eigenproblems by Sectioning . . . . . . 534--545 N. L. Schryer Constructive Approximation of Solutions to Linear Elliptic Boundary Value Problems . . . . . . . . . . . . . . . . 546--572 J. D. Donaldson and David Elliott A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders . . . . . . . . . . . . . . . 573--602 T. E. Hull and W. H. Enright and B. M. Fellen and A. E. Sedgwick Comparing Numerical Methods for Ordinary Differential Equations . . . . . . . . . 603--637 Jack Williams Numerical Chebyshev Approximation in the Complex Plane . . . . . . . . . . . . . 638--649 David Gottlieb Strang-type Difference Schemes for Multidimensional Problems . . . . . . . 650--661 Bengt Lindberg A Simple Interpolation Algorithm for Improvement of the Numerical Solution of a Differential Equation . . . . . . . . 662--668 G. W. Stewart On the Sensitivity of the Eigenvalue Problem $ A x = \lambda B x $ . . . . . 669--686 W. J. Kammerer and G. W. Reddien, Jr. Local Convergence of Smooth Cubic Spline Interpolates . . . . . . . . . . . . . . 687--694 Melvyn Ciment Stable Matching of Difference Schemes 695--701 Graeme Fairweather Galerkin Methods for Vibration Problems in Two Space Variables . . . . . . . . . 702--714 J. D. Lambert and S. T. Sigurdsson Multistep Methods with Variable Matrix Coefficients . . . . . . . . . . . . . . 715--733 J. W. Matthews An Algorithm for Obtaining Best Approximations on Sets of Positive Polynomials . . . . . . . . . . . . . . 734--742
A. S. Householder George E. Forsythe (January 8, 1917--April 9, 1972) . . . . . . . . . . viii--xi
W. C. Pye and T. A. Atchison An Algorithm for the Computation of the Higher Order G-Transformation . . . . . 1--7 Ian Barrodale Best Rational Approximation and Strict Quasi-Convexity . . . . . . . . . . . . 8--12 J. D. Donaldson Estimates of Upper Bounds for Quadrature Errors . . . . . . . . . . . . . . . . . 13--22 J. Prasad and H. Hayashi On the Uniform Convergence of Fourier--Jacobi Series . . . . . . . . . 23--27 Marie-Jeanne Munteanu Generalized Smoothing Spline Functions for Operators . . . . . . . . . . . . . 28--34 W. E. Bosarge, Jr. and O. G. Johnson and C. L. Smith A Direct Method Approximation to the Linear Parabolic Regulator Problem Over Multivariate Spline Bases . . . . . . . 35--49 S. J. Poreda Approximation by $ \delta $-Polynomials 50--54 Steven Pruess Estimating the Eigenvalues of Sturm--Liouville Problems by Approximating the Differential Equation 55--68 David C. Shreve Interior Estimates in $ l^p $ for Elliptic Difference Operators . . . . . 69--80 James H. Bramble and Joachim A. Nitsche A Generalized Ritz-Least-Squares Method for Dirichlet Problems . . . . . . . . . 81--93 W. E. Bosarge, Jr. and O. G. Johnson and R. S. McKnight and W. P. Timlake The Ritz--Galerkin Procedure for Nonlinear Control Problems . . . . . . . 94--111 John De Pillis Gauss--Seidel Convergence for Operators on Hilbert Space . . . . . . . . . . . . 112--122 S. N. Dua and H. L. Loeb Further Remarks on the Differential Correction Algorithm . . . . . . . . . . 123--126 Peter R. Lipow Spline Functions and Intermediate Best Quadrature Formulas . . . . . . . . . . 127--136 Annette Sinclair Determination of Extremal Functions in $ {H}^p $ by a Fortran Program . . . . . . 137--146 R. C. Ackerberg and J. H. Phillips A Numerical Method for Highly Accelerated Laminar Boundary-Layer Flows 147--160 O. Pironneau and E. Polak Rate of Convergence of a Class of Methods of Feasible Directions . . . . . 161--174 Paul Nelson, Jr. Convergence of the Discrete-Ordinates Method for Anisotropically Scattering Multiplying Particles in a Subcritical Slab . . . . . . . . . . . . . . . . . . 175--181 R. A. Nicolaides On a Class of Finite Elements Generated by Lagrange Interpolation. II . . . . . 182--189 Amnon Bracha-Barak and Paul E. Saylor A Symmetric Factorization Procedure for the Solution of Elliptic Boundary Value Problems . . . . . . . . . . . . . . . . 190--206 Steven W. Rauch A Convergence Theory for a Class of Nonlinear Programming Problems . . . . . 207--228 Milos Zlamal Curved Elements in the Finite Element Method. I . . . . . . . . . . . . . . . 229--240
C. B. Moler and G. W. Stewart An Algorithm for Generalized Matrix Eigenvalue Problems . . . . . . . . . . 241--256 J. M. Varah On the Numerical Solution of Ill-Conditioned Linear Systems with Applications to Ill-Posed Problems . . . 257--267 James M. Ortega Stability of Difference Equations and Convergence of Iterative Processes . . . 268--282 A. K. Cline An Elimination Method for the Solution of Linear Least Squares Problems . . . . 283--289 A. M. Ostrowski \em A Posteriori Error Estimates in Iterative Procedures . . . . . . . . . . 290--298 James W. Daniel On Perturbations in Systems of Linear Inequalities . . . . . . . . . . . . . . 299--307 David R. Stoutemyer Numerical Implementation of the Schwarz Alternating Procedure for Elliptic Partial Differential Equations . . . . . 308--326 Richard P. Brent Some Efficient Algorithms for Solving Systems of Nonlinear Equations . . . . . 327--344 Alan George Nested Dissection of a Regular Finite Element Mesh . . . . . . . . . . . . . . 345--363 Alan J. Hoffman and Michael S. Martin and Donald J. Rose Complexity Bounds for Regular Finite Difference and Finite Element Grids . . 364--369 Charles McCarthy and Gilbert Strang Optimal Conditioning of Matrices . . . . 370--388 B. N. Parlett and W. G. Poole, Jr. A Geometric Theory for the $ {QR} $, $ {LU} $ and Power Iterations . . . . . . 389--412 G. H. Golub and V. Pereyra The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate . . . . . . . . 413--432 Anonymous Collection of articles dedicated to the memory of George E. Forsythe . . . . . . i--xi + 241--432
A. Meir and A. Sharma Lacunary Interpolation by Splines . . . 433--442 Blair K. Swartz and Richard S. Varga A Note on Lacunary Interpolation by Splines . . . . . . . . . . . . . . . . 443--447 O. L. Mangasarian and L. L. Schumaker Best Summation Formulae and Discrete Splines . . . . . . . . . . . . . . . . 448--459 Nancy K. Nichols On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations . . . . . . . . . . . . . . . 460--469 J. C. Mason Some Methods of Near-Minimax Approximation Using Laguerre Polynomials 470--477 K. R. James Convergence of Matrix Iterations Subject to Diagonal Dominance . . . . . . . . . 478--484 N. K. Basu Errors in the Representation of a Function by Chebyshev Polynomials of the Second Kind . . . . . . . . . . . . . . 485--488 F. J. Burkowski and D. D. Cowan The Numerical Derivation of a Periodic Solution of a Second Order Differential Difference Equation . . . . . . . . . . 489--495 N. K. Basu On Double Chebyshev Series Approximation 496--505 A. Settari and K. Aziz A Generalization of the Additive Correction Methods for the Iterative Solution of Matrix Equations . . . . . . 506--521 Gunter H. Meyer Multidimensional Stefan Problems . . . . 522--538 Charles B. Huelsman, III Quadrature Formulas Over Fully Symmetric Planar Regions . . . . . . . . . . . . . 539--552
Franz Locher Norm Bounds of Quadrature Processes . . 553--558 A. H. Stroud Some Cubature Formulas for the Surface of the $n$-Sphere . . . . . . . . . . . 559--569 P. M. Prenter A Collection Method for the Numerical Solution of Integral Equations . . . . . 570--581 Carl de Boor and Blair Swartz Collocation at Gaussian Points . . . . . 582--606 James A. Cadzow A Finite Algorithm for the Minimum $ l_\infty $ Solution to a System of Consistent Linear Equations . . . . . . 607--617 A. N. Willson, Jr. A Note on Pairs of Matrices and Matrices of Monotone Kind . . . . . . . . . . . . 618--622 Robert J. Fornaro Numerical Evaluation of Integrals Around Simple Closed Curves . . . . . . . . . . 623--634 M. B. Rosenzweig Finite Difference Approximation of the Weak Solution of a Mildly Nonlinear Dirichlet Problem . . . . . . . . . . . 635--646 Frank de Hoog and Richard Weiss High Order Methods for Volterra Integral Equations of the First Kind . . . . . . 647--664 Philip B. Zwart Multivariate Splines with Nondegenerate Partitions . . . . . . . . . . . . . . . 665--673 Axel Ruhe Algorithms for the Nonlinear Eigenvalue Problem . . . . . . . . . . . . . . . . 674--689 C. S. Duris and M. G. Temple A Finite Step Algorithm for Determining the ``Strict'' Chebyshev Solution to $ A x = b $ . . . . . . . . . . . . . . . . 690--699 H. D. Meyer The Numerical Solution of Nonlinear Parabolic Problems by Variational Methods . . . . . . . . . . . . . . . . 700--722 Mary Fanett Wheeler \em A Priori $ {L}_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations . . . . . 723--759 Andrew R. Conn Constrained Optimization Using a Nondifferentiale Penalty Function . . . 760--784 Robert T. Walsh Optimization and Comparison of Partial Difference Methods . . . . . . . . . . . 785--797
Kendall E. Atkinson The Numerical Evaluation of Fixed Points for Completely Continuous Operators . . 799--807 Joseph W. Jerome Minimization Problems and Linear and Nonlinear Spline Functions. I: Existence 808--819 Joseph W. Jerome Minimization Problems and Linear and Nonlinear Spline Functions. II: Convergence . . . . . . . . . . . . . . 820--830 P. Keast Optimal Parameters for Multidimensional Integration . . . . . . . . . . . . . . 831--838 I. Barrodale and F. D. K. Roberts An Improved Algorithm for Discrete $ l_1 $ Linear Approximation . . . . . . . . . 839--848 Richard Franke Minimal Point Cubatures of Precision Seven for Symmetric Planar Regions . . . 849--862 Ivo Babu\vska and Milos Zlamal Nonconforming Elements in the Finite Element Method with Penalty . . . . . . 863--875 Richard F. King A Family of Fourth Order Methods for Nonlinear Equations . . . . . . . . . . 876--879 Todd Dupont $ {L}^2$-Estimates for Galerkin Methods for Second Order Hyperbolic Equations 880--889 Todd Dupont Galerkin Methods for First Order Hyperbolics: An Example . . . . . . . . 890--899 Paul N. Swarztrauber and Roland A. Sweet The Direct Solution of the Discrete Poisson Equation on a Disk . . . . . . . 900--907 Mary Fanett Wheeler $ {L}_\infty $ Estimates of Optimal Orders for Galerkin Methods for One-Dimensional Second Order Parabolic and Hyperbolic Equations . . . . . . . . 908--913 Mary Fanett Wheeler An Optimal $ {L}_\infty $ Error Estimate for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems . . 914--917 D. O. Banks and G. J. Kurowski Computation of Eigenvalues for Vibrating Beams by Use of a Prufer Transformation 918--932 Charles W. Schelin Monotone Convergence of the Sor-Newton Iterative Technique . . . . . . . . . . 933--938 Françoise Chatelin Convergence of Approximation Methods to Compute Eigenelements of Linear Operations . . . . . . . . . . . . . . . 939--948 Fred T. Krogh Algorithms for Changing the Step Size 949--965
Julius Smith On the Approximate Solution of the First Boundary Value Problem for $ \nabla^4 u = f $ . . . . . . . . . . . . . . . . . 967--982 C. A. Micchelli and W. L. Miranker Optimal Difference Schemes for Linear Initial Value Problems . . . . . . . . . 983--1009 H. H. Rachford, Jr. Two-Level Discrete-time Galerkin Approximations for Second Order Nonlinear Parabolic Partial Differential Equations . . . . . . . . . . . . . . . 1010--1026 Tom Lyche and Larry L. Schumaker Computation of smoothing and interpolating natural splines via local bases . . . . . . . . . . . . . . . . . 1027--1038 D. E. Koster Stability of a Finite Difference Scheme with ``Wrong'' Boundary Conditions . . . 1039--1046 David Ferguson Sufficient Conditions for Peano's Kernel to be of One Sign . . . . . . . . . . . 1047--1054 C. A. Hall Natural Cubic and Bicubic Spline Interpolation . . . . . . . . . . . . . 1055--1060 To-Yat Cheung Quasilinear Parabolic Boundary Value Problems. Approximate Solutions and Error Bounds by Linear Programming . . . 1061--1079 Sven-Åke Gustafson A Method of Computing Limit Values . . . 1080--1090 David Elliott and Binh Lam An Estimate of $ {E}_n(f) $ for Large $n$ . . . . . . . . . . . . . . . . . . 1091--1102 Paul Concus and Gene H. Golub Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations . . . . 1103--1120
F. G. Lether Error Bounds for Fully Symmetric Quadrature Rules . . . . . . . . . . . . 1--9 W. B. Gragg and R. A. Tapia Optimal Error Bounds for the Newton--Kantorovich Theorem . . . . . . 10--13 Johnnie William McLaurin A General Coupled Equation Approach for Solving the Biharmonic Boundary Value Problem . . . . . . . . . . . . . . . . 14--33 L. B. Rall A Note on the Convergence of Newton's Method . . . . . . . . . . . . . . . . . 34--36 Robert E. Barnhill and Gregory M. Nielson Reproducing Kernel Functions for Sard Spaces of Type $ {B} $ . . . . . . . . . 37--44 Christian Reinsch Two Extensions of the Sard-Schoenberg Theory of Best Approximation . . . . . . 45--51 Luc Wuytack On Some Aspects of the Rational Interpolation Problem . . . . . . . . . 52--60 Torsten Söderström and G. W. Stewart On the Numerical Properties of an Iterative Method for Computing the Moore--Penrose Generalized Inverse . . . 61--74 D. Krabill and M. Reichaw Expansions of Real Numbers Relative to a Sequence of Functions . . . . . . . . . 75--86 F. L. Bauer Computational Graphs and Rounding Error 87--96 Kendall E. Atkinson The Numerical Solution of an Abel Integral Equation by a Product Trapezoidal Method . . . . . . . . . . . 97--101 J. H. Avila, Jr. The Feasibility of Continuation Methods for Nonlinear Equations . . . . . . . . 102--122 R. Fletcher and J. A. Grant and M. D. Hebden Linear Minimax Approximation as the Limit of Best $ {L}_p$-Approximation . . 123--136 Peter Linz A Method for the Approximate Solution of Linear Integro-Differential Equations 137--144 Abraham Berman and Robert J. Plemmons Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems . . . . . . . . . . . . . . . . 145--154 William H. Ford and T. W. Ting Uniform Error Estimates for Difference Approximations to Nonlinear Pseudo-Parabolic Partial Differential Equations . . . . . . . . . . . . . . . 155--169 Martha Ann Griesel A Linear Remes-Type Algorithm for Relative Error Approximation . . . . . . 170--173 R. A. Tapia Newton's Method for Problems with Equality Constraints . . . . . . . . . . 174--196 C. C. Paige Bidiagonalization of Matrices and Solution of Linear Equations . . . . . . 197--209
David R. Kincaid On Complex Second-Degree Iterative Methods . . . . . . . . . . . . . . . . 211--218 D. R. Gimlin and R. K. Cavin, III and M. C. Budge, Jr. A Multiple Exchange Algorithm for Calculation of Best Restricted Approximations . . . . . . . . . . . . . 219--231 F. G. Lether Cubature Error Constants for Analytic Functions . . . . . . . . . . . . . . . 232--236 G. Alefeld and J. Herzberger On the Convergence Speed of Some Algorithms for the Simultaneous Approximation of Polynomial Roots . . . 237--243 R. D. Riess and L. W. Johnson Errors in Interpolating Functions at the Zeros of $ {T}_{n + 1}({X}) $ . . . . . 244--253 B. L. Chalmers and D. J. Johnson and F. T. Metcalf and G. D. Taylor Remarks on the Rank of Hermite--Birkhoff Interpolation . . . . . . . . . . . . . 254--259 V. Girault Theory of a Finite Difference Method on Irregular Networks . . . . . . . . . . . 260--282 Karl Scherer Characterization of Generalized Lipschitz Classes by Best Approximation with Splines . . . . . . . . . . . . . . 283--304 Herbert B. Keller Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 305--320 W. H. Enright Second Derivative Multistep Methods for Stiff Ordinary Differential Equations 321--331 Don R. Wilhelmsen Nonnegative Cubature on Convex Sets . . 332--346 Milos Zlamal Curved Elements in the Finite Element Method. II . . . . . . . . . . . . . . . 347--362 Gary K. Leaf and Hans G. Kaper $ {L}^\infty $-Error Bounds for Multivariate Lagrange Approximation . . 363--381 F. Aleixo Oliveira Interval Analysis and Two-Point Boundary Value Problems . . . . . . . . . . . . . 382--391 Todd Dupont and Graeme Fairweather and J. Peter Johnson Three-Level Galerkin Methods for Parabolic Equations . . . . . . . . . . 392--410 Robert Gaines Difference Equations Associated with Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations . . . . . . . . . . . . . . . 411--434 Gregory M. Nielson Multivariate Smoothing and Interpolating Splines . . . . . . . . . . . . . . . . 435--446 R. E. Shafer On Quadratic Approximation . . . . . . . 447--460
Stanley E. Weinstein On Numerical Solution of Nonlinear Equations Through Nonlinear Interpolation or Approximation . . . . . 461--471 G. H. Golub and J. M. Varah On a Characterization of the Best $ l_2$-Scaling of a Matrix . . . . . . . . 472--479 C. Gunther Third Degree Integration Formulas with Four Real Points and Positive Weights in Two Dimensions . . . . . . . . . . . . . 480--493 George Hall Stability Analysis of Predictor-Corrector Algorithms of Adams Type . . . . . . . . . . . . . . . . . . 494--505 Roland A. Sweet A Generalized Cyclic Reduction Algorithm 506--520 James R. Bunch Partial Pivoting Strategies for Symmetric Matrices . . . . . . . . . . . 521--528 E. Polak A Globally Converging Secant Method with Applications to Boundary Value Problems 529--537 Arun N. Netravali and Rui J. P. de Figueiredo Spline Approximation to the Solution of the Linear Fredholm Integral Equation of the Second Kind . . . . . . . . . . . . 538--549 Richard Weiss On the Approximation of Fixed Points of Nonlinear Compact Operators . . . . . . 550--553 Charles K. Chui and Philip W. Smith On $ {H}^{m, \infty }$-Splines . . . . . 554--558 Don Heller A Determinant Theorem with Applications to Parallel Algorithms . . . . . . . . . 559--568 Thomas R. Lucas Error Bounds for Interpolating Cubic Splines Under Various End Conditions . . 569--584 Alan George On Block Elimination for Sparse Linear Systems . . . . . . . . . . . . . . . . 585--603 J. E. Dendy, Jr. Penalty Galerkin Methods for Partial Differential Equations . . . . . . . . . 604--636 J. E. Dendy Two Methods of Galerkin Type Achieving Optimum $ {L}^2 $ Rates of Convergence for First Order Hyperbolics . . . . . . 637--653 Stanley C. Eisenstat On the Rate of Convergence of the Bergman-Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems . . . . . . . . . . . . . . . . 654--680 T. E. Hull and W. H. Enright and B. M. Fellen and A. E. Sedgwick Errata: ``Comparing Numerical Methods for Ordinary Differential Equations'' [SIAM J. Numer. Anal. \bf 9 (1972), no. 4, 603--637] . . . . . . . . . . . . . . 681--681
I. Norman Katz and Leon Cooper An Always-Convergent Numerical Scheme for a Random Locational Equilibrium Problem . . . . . . . . . . . . . . . . 683--692 G. A. Watson The Calculation of Best Restricted Approximations . . . . . . . . . . . . . 693--699 Garrett Birkhoff and Surender Gulati Optimal Few-Point Discretizations of Linear Source Problems . . . . . . . . . 700--728 Charles B. Dunham Convergence of Stiefel's Exchange Method On an Infinite Set . . . . . . . . . . . 729--731 J. R. Kuttler Direct Methods for Computing Eigenvalues of the Finite-Difference Laplacian . . . 732--740 Lars Wahlbin Maximum Norm Estimates for Friedrichs' Scheme in Two Dimensions . . . . . . . . 741--752 B. L. Buzbee and Fred W. Dorr The Direct Solution of the Biharmonic Equation on Rectangular Regions and the Poisson Equation on Irregular Regions 753--763 Mary Fanett Wheeler A Galerkin Procedure for Estimating the Flux for Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 764--768 David R. Ferguson Sign Changes and Minimal Support Properties of Hermite--Birkhoff Splines with Compact Support . . . . . . . . . . 769--779 H. Wozniakowski Rounding Error Analysis for the Evaluation of a Polynomial and Some of its Derivatives . . . . . . . . . . . . 780--787 Colin W. Cryer Highly Stable Multistep Methods for Retarded Differential Equations . . . . 788--797 Otto Neall Strand Theory and Methods Related to the Singular-Function Expansion and Landweber's Iteration for Integral Equations of the First Kind . . . . . . 798--825 Alan Feldstein and John R. Sopka Numerical Methods for Nonlinear Volterra Integro-Differential Equations . . . . . 826--846
James R. Bunch Analysis of Sparse Elimination . . . . . 847--873 R. A. Tapia Newton's Method for Optimization Problems with Equality Constraints . . . 874--886 Amnon Bracha-Barak A Factorization Procedure for the Solution of Multidimensional Ellipti Partial Differential Equations . . . . . 887--893 Paul E. Saylo Second Order Strongly Implicit Symmetric Factorization Methods for the Solution of Elliptic Difference Equations . . . . 894--908 William J. Gordon and James A. Wixom Pseudo-Harmonic Interpolation on Convex Domains . . . . . . . . . . . . . . . . 909--933 H. Wozniakowski Maximal Stationary Iterative Methods for the Solution of Operator Equations . . . 934--949 Bruce L. Chalmers and Frederic T. Metcalf Taylor-Like Remainder Formulas for Interpolation by Arbitrary Linear Functionals . . . . . . . . . . . . . . 950--964 L. W. Jackson and Surender Kumar Kenue A Fourth Order Exponentially Fitted Method . . . . . . . . . . . . . . . . . 965--978 Blair Swartz and Burton Wendroff The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines . . . 979--993 Blair Swartz and Burton Wendroff The Relation between the Galerkin and Collocation Methods Using Smooth Splines 994--996 Linda Kaufman The $ {LZ}$-Algorithm to Solve the Generalized Eigenvalue Problem . . . . . 997--1024 C. W. Gear and K. W. Tu The Effect of Variable Mesh Size on the Stability of Multistep Methods . . . . . 1025--1043 C. W. Gear and D. S. Watanabe Stability and Convergence of Variable Order Multistep Methods . . . . . . . . 1044--1058 Vidar Thomee and Burton Wendroff Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems . . . . . . . . . . . . . 1059--1068 Werner C. Rheinboldt and James S. Vandergraft On the Local Convergence of Update Methods . . . . . . . . . . . . . . . . 1069--1085
Donna K. Dunaway Calculation of Zeros of a Real Polynomial Through Factorization Using Euclid's Algorithm . . . . . . . . . . . 1087--1104 G. W. Stewart The Convergence of Multipoint Iterations to Multiple Zeros . . . . . . . . . . . 1105--1120 C. S. Caldwell Rates of Convergence of Approximate Solutions of Parabolic Initial-Boundary Value Problems . . . . . . . . . . . . . 1121--1135 Paul N. Swarztrauber A Direct Method for the Discrete Solution of Separable Elliptic Equations 1136--1150 James A. Cadzow An Efficient Algorithmic Procedure for Obtaining a Minimum $ l_\infty $-Norm Solution to a System of Consistent Linear Equations . . . . . . . . . . . . 1151--1165 Frank De Hoog and Richard Weiss High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels . . . . . . . . . . . . 1166--1180 Alfred Carasso On Least Squares Methods for Parabolic Equations and the Computation of Time-Periodic Solutions . . . . . . . . 1181--1192 Bruce A. Chartres and Robert S. Stepleman Actual Order of Convergence of Runge--Kutta Methods on Differential Equations with Discontinuities . . . . . 1193--1206
E. Gekeler A-Convergence of Finite Difference Approximations of Parabolic Initial-Boundary Value Problems . . . . 1--12 R. D. Russell and L. F. Shampine Numerical Methods for Singular Boundary Value Problems . . . . . . . . . . . . . 13--36 To-Yat Cheung Approximate Solutions and Error Bounds for Quasi-Linear Hyperbolic Initial Boundary Value Problems . . . . . . . . 37--45 G. A. Watson A Multiple Exchange Algorithm for Multivariate Chebyshev Approximation . . 46--52 Nai-Kuan Tsao A Note on Implementing the Householder Transformation . . . . . . . . . . . . . 53--58 J. Thomas King Semidiscrete Perturbed Variational Methods for the Numerical Solution of Parabolic Boundary Value Problems . . . 59--72 Gene A. Kemper Spline Function Approximation for Solutions of Functional Differential Equations . . . . . . . . . . . . . . . 73--88 H. T. Kung The Computational Complexity of Algebraic Numbers . . . . . . . . . . . 89--96 P. J. Eberlein and C. P. Huang Global Convergence of the $ {QR} $ Algorithm for Unitary Matrices with some Results for Normal Matrices . . . . . . 97--104 C. B. Dunham Nonlinear Mean-Square Approximation on Finite Sets . . . . . . . . . . . . . . 105--110 K. O. Geddes and J. C. Mason Polynomial Approximation by Projections on the Unit Circle . . . . . . . . . . . 111--120 H. Wozniakowski Generalized Information and Maximal Order of Iteration for Operator Equations . . . . . . . . . . . . . . . 121--135
K. R. James and W. Riha Convergence Criteria for Successive Overrelaxation . . . . . . . . . . . . . 137--143 J. E. Dendy, Jr. and G. Fairweather Alternating-Direction Galerkin Methods for Parabolic and Hyperbolic Problems on Rectangular Polygons . . . . . . . . . . 144--163 Niel K. Madsen Convergent Centered Difference Schemes for the Discrete Ordinate Neutron Transport Equations . . . . . . . . . . 164--176 Lars Wahlbin On Maximum Norm Error Estimates for Galerkin Approximations to One-Dimensional Second Order Parabolic Boundary Value Problems . . . . . . . . 177--182 Darell J. Johnson On the Nontriviality of Restricted Range Polynomial Approximation . . . . . . . . 183--187 Michael R. Gorelick Stability of Families of Matrices of Unbounded Order . . . . . . . . . . . . 188--202 Jorg Hertling Numerical Treatment of Algebraic Integral Equations by Variational Methods . . . . . . . . . . . . . . . . 203--212 Kendall Atkinson Convergence Rates for Approximate Eigenvalues of Compact Integral Operators . . . . . . . . . . . . . . . 213--222 L. W. Jackson Interval Arithmetic Error-Bounding Algorithms . . . . . . . . . . . . . . . 223--238 Frank Stenger An Analytic Function which is an Approximate Characteristic Function . . 239--254 Helmut Werner Interpolation and Integration of Initial Value Problems of Ordinary Differential Equations by Regular Splines . . . . . . 255--271
Klaus Ritter A Method of Conjugate Directions for Linearly Constrained Nonlinear Programming Problems . . . . . . . . . . 273--303 J. C. Butcher An Order Bound for Runge--Kutta Methods 304--315 L. A. Hageman and T. A. Porsching Aspects of Nonlinear Block Successive Overrelaxation . . . . . . . . . . . . . 316--335 J. A. Brown and M. S. Henry Best Chebyshev Composite Approximation 336--344 Richard E. Ewing Numerical Solution of Sobolev Partial Differential Equations . . . . . . . . . 345--363 Murli M. Gupta Discretization Error Estimates for Certain Splitting Procedures for Solving First Biharmonic Boundary Value Problems 364--377 Vidar Thomee and Lars Wahlbin On Galerkin Methods in Semilinear Parabolic Problems . . . . . . . . . . . 378--389 Frank Deutsch and John H. McCabe and George M. Phillips Some Algorithms for Computing Best Approximations from Convex Cones . . . . 390--403 Ridgway Scott Interpolated Boundary Conditions in the Finite Element Method . . . . . . . . . 404--427 Tetsuro Yamamoto The Rayleigh--Ritz and Weinstein--Bazley Methods Applied to a Class of Ordinary Differential Equations of the Second Order. II . . . . . . . . . . . . . . . 428--438 R. B. Simpson A Method for the Numerical Determination of Bifurcation States of Nonlinear Systems of Equations . . . . . . . . . . 439--451 Alan George and Wai-Hung Liu A Note on Fill for Sparse Matrices . . . 452--455 R. E. Showalter \em A Priori Error Estimates for Approximation of Parabolic Boundary Value Problems . . . . . . . . . . . . . 456--463 J. F. Ciavaldini Analyse Numérique d'un Probl\`eme de Stefan \`a Deux Phases Par Une M\`ethode d'Éléments Finis [French: Numerical Analysis of a Problem of Stefan in Two Phases by a Finite-Element Method] . . . 464--487 R. Jonathan Lermit Numerical Methods for the Identification of Differential Equations . . . . . . . 488--500 L. Garey Solving Nonlinear Second Kind Volterra Equations by Modified Increment Methods 501--508
Bengt Fornberg On a Fourier Method for the Integration of Hyperbolic Equations . . . . . . . . 509--528 Randolph E. Bank and Donald J. Rose An $ {O}(n^2) $ Method for Solving Constant Coefficient Boundary Value Problems in Two Dimensions . . . . . . . 529--540 J. E. Dendy, Jr. An Analysis of Some Galerkin Schemes for the Solution of Nonlinear Time-Dependent Problems . . . . . . . . . . . . . . . . 541--565 C. P. Huang A Jacobi-Type Method for Triangularizing an Arbitrary Matrix . . . . . . . . . . 566--570 M. R. Osborne Some Special Nonlinear Least Squares Problems . . . . . . . . . . . . . . . . 571--592 A. H. Stroud Some Interpolation Formulas for the Neumann Problem for the $n$-Sphere . . . 593--604 M. M. Chawla and N. Jayarajan Bivariate Cardinal Interpolation and Cubature Formulas . . . . . . . . . . . 605--616 C. C. Paige and M. A. Saunders Solution of Sparse Indefinite Systems of Linear Equations . . . . . . . . . . . . 617--629 Eckard Schmidt and Peter Lancaster and David Watkins Bases of Splines Associated with Constant Coefficient Differential Operators . . . . . . . . . . . . . . . 630--645 Alan E. Berger and Melvyn Ciment and Joel C. W. Rogers Numerical Solution of a Diffusion Consumption Problem with a Free Boundary 646--672
T. O'Neil and J. W. Thomas The Calculation of the Topological Degree by Quadrature . . . . . . . . . . 673--680 C. S. Duris and J. N. Lyness Compound Quadrature Rules for the Product of Two Functions . . . . . . . . 681--697 P. A. W. Holyhead and S. McKee and P. J. Taylor Multistep Methods for Solving Linear Volterra Integral Equations of the First Kind . . . . . . . . . . . . . . . . . . 698--711 T. J. Rivlin Optimally Stable Lagrangian Numerical Differentiation . . . . . . . . . . . . 712--725 Philip Brenner Maximum-Norm Estimates of the Rate of Convergence of Dissipative Difference Schemes for Strictly Hyperbolic Systems 726--740 Torsten Strom On Logarithmic Norms . . . . . . . . . . 741--753 Stephen M. Robinson Stability Theory for Systems of Inequalities. Part I: Linear Systems . . 754--769 James W. Daniel Remarks on Perturbations in Linear Inequalities . . . . . . . . . . . . . . 770--772 Louis W. Ehrlich and Murli M. Gupta Some Difference Schemes for the Biharmonic Equation . . . . . . . . . . 773--790 H. B. Keller and A. B. White, Jr. Difference Methods for Boundary Value Problems in Ordinary Differential Equations . . . . . . . . . . . . . . . 791--802 Mary F. Wheeler An $ {H}^{-1} $ Galerkin Method for Parabolic Problems in a Single Space Variable . . . . . . . . . . . . . . . . 803--817
Charles F. Van Loan A General Matrix Eigenvalue Algorithm 819--834 Robert C. Ward The Combination Shift $ {QZ} $ Algorithm 835--853 William W. Hager The Ritz--Trefftz Method for State and Control Constrained Optimal Control Problems . . . . . . . . . . . . . . . . 854--867 I. Babu\vska and R. B. Kellogg Nonuniform Error Estimates for the Finite Element Method . . . . . . . . . 868--875 Bruce A. Chartres and Robert S. Stepleman Order of Convergence of Linear Multistep Methods for Functional Differential Equations . . . . . . . . . . . . . . . 876--886 Robert S. Stepleman A Characterization of Local Convergence for Fixed Point Iterations in $ {R}^1 $ 887--894 P. Beaudet and T. Feagin The Use of Back Corrections in Multistep Methods of Numerical Integration . . . . 895--918 Mary Anne McCarthy and R. A. Tapia Computable a Posteriori $ {L}_\infty $-Error Bounds for the Approximate Solution of Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 919--937 Charles Hunt and Nabil R. Nassif On a Variational Inequality and its Approximation, in the Theory of Semiconductors . . . . . . . . . . . . . 938--950
E. Rakotch Numerical Solution with Large Matrices of Fredholm's Integral Equation . . . . 1--7 Rolf Jeltsch Stiff Stability and its Relation to $ {A}_0$-and $ {A}(0)$-Stability . . . . . 8--17 David L. Barrow and A. H. Stroud Existence of Gauss Harmonic Interpolation Formulas . . . . . . . . . 18--26 Russell C. Thompson Convergence and Error Estimates for the Method of Lines for Certain Nonlinear Elliptic and Elliptic-Parabolic Equations . . . . . . . . . . . . . . . 27--43 E. Kimchi Chebyshev Spaces of Polynomials . . . . 44--50 E. Kimchi and D. Leviatan On Restricted Best Approximation to Functions with Restricted Derivatives 51--53 Martin A. Diamond and Dulcinea L. V. Ferreira On a Cyclic Reduction Method for the Solution of Poisson's Equations . . . . 54--70 J. M. Varah Alternate Row and Column Elimination for Solving Certain Linear Systems . . . . . 71--75 Charles F. Van Loan Generalizing the Singular Value Decomposition . . . . . . . . . . . . . 76--83 H. T. Kung and J. F. Traub Optimal Order and Efficiency for Iterations with Two Evaluations . . . . 84--99 Peter Percell On Cubic and Quartic Clough--Tocher Finite Elements . . . . . . . . . . . . 100--103 M. P. Carroll and W. R. Woodward An Algorithm for Approximate Integration Using Near Best Approximates . . . . . . 104--108 Robert Beauwens Semistrict Diagonal Dominance . . . . . 109--112 M. M. Chawla and T. R. Ramakrishnan Minimum Variance Approximate Formulas 113--128 David Gottlieb and Bertil Gustafsson Generalized Du Fort-Frankel Methods for Parabolic Initial-Boundary Value Problems . . . . . . . . . . . . . . . . 129--144 A. R. Conn Linear Programming Via a Nondifferentiable Penalty Function . . . 145--154
T. Mahadeva Rao and K. Subramanian and E. V. Krishnamurthy Residue Arithmetic Algorithms for Exact Computation of $g$-Inverses of Matrices 155--171 John W. Hilgers On the Equivalence of Regularization and Certain Reproducing Kernel Hilbert Space Approaches for Solving First Kind Problems . . . . . . . . . . . . . . . . 172--184 John E. Osborn Approximation of the Eigenvalues of a Nonselfadjoint Operator Arising in the Study of the Stability of Stationary Solutions of the Navier--Stokes Equations . . . . . . . . . . . . . . . 185--197 Wai-Hung Liu and Andrew H. Sherman Comparative Analysis of the Cuthill--McKee and the Reverse Cuthill--McKee Ordering Algorithms for Sparse Matrices . . . . . . . . . . . . 198--213 I. Babu\vska and A. K. Aziz On the Angle Condition in the Finite Element Method . . . . . . . . . . . . . 214--226 Thomas E. Price, Jr. Cubature Error Bounds for a Class of Analytic Functions . . . . . . . . . . . 227--235 Norman E. Gibbs and William G. Poole, Jr. and Paul K. Stockmeyer An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix . . . . . 236--250 Vincent G. Sigillito \em A Priori Inequalities and Approximate Solutions of the First Boundary Value Problem for $ {\Delta }^2 u = f $ . . . . . . . . . . . . . . . . 251--260 M. P. Epstein On the Influence of Parametrization in Parametric Interpolation . . . . . . . . 261--268 P. A. W. Holyhead and S. McKee Stability and Convergence of Multistep Methods for Linear Volterra Integral Equations of the First Kind . . . . . . 269--292
A. K. Cline A Descent Method for the Uniform Solution to Over-Determined Systems of Linear Equations . . . . . . . . . . . . 293--309 S. Ellacott and Jack Williams Rational Chebyshev Approximation in the Complex Plane . . . . . . . . . . . . . 310--323 Michael S. Borowsky Characterizations of Best Complex Chebyshev Approximate Solutions of $ A v = b $ . . . . . . . . . . . . . . . . . 324--336 G. F. McCormick and V. A. Sposito Using the $ {L}_2$-Estimator in $ {L}_1$-Estimation . . . . . . . . . . . 337--343 Paul D. Patent The Effect of Quadrature Errors in the Computation of $ {L}^2 $ Piecewise Polynomial Approximations . . . . . . . 344--361 Todd Dupont A Unified Theory of Superconvergence for Galerkin Methods for Two-Point Boundary Problems . . . . . . . . . . . . . . . . 362--368 Stephen Demko Lacunary Polynomial Spline Interpolation 369--381 Webb Miller Roundoff Analysis by Direct Comparison of Two Algorithms . . . . . . . . . . . 382--392 J. T. Oden and J. N. Reddy On Mixed Finite Element Approximations 393--404 G. W. Reddien Approximation Methods for Two-Point Boundary Value Problems with Nonlinear Boundary Conditions . . . . . . . . . . 405--411 Glenn Allinger and Myron Henry Approximate Solutions of Differential Equations with Deviating Arguments . . . 412--426 David G. Herr On Strand and Westwater's Minimum-RMS Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind . . . . . . . . . . . . . . . 427--431 Gerd-Peter Ehile and Hubert Schwetlick Discretized Euler--Chebyshev Multistep Methods . . . . . . . . . . . . . . . . 432--447
William W. Hager Rates of Convergence for Discrete Approximations to Unconstrained Control Problems . . . . . . . . . . . . . . . . 449--472 R. B. Kellogg and T. Y. Li and J. Yorke A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results . . . . . . . . . . . . . . . . 473--483 Don Heller Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems . . . . . . . . . . . . . . . . 484--496 Stephen M. Robinson Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems . . . . . . . . . . . 497--513 C. S. Caldwell Convergence Estimates for a Locally One-Dimensional Finite Difference Scheme for Parabolic Initial-Boundary Value Problems . . . . . . . . . . . . . . . . 514--519 A. G. Buckley Constrained Minimization Using Powell's Conjugacy Approach . . . . . . . . . . . 520--535 E. Gekeler Linear Multistep Methods and Galerkin Procedures for Initial Boundary Value Problems . . . . . . . . . . . . . . . . 536--548 Paul S. Jensen Stiffly Stable Methods for Undamped Second Order Equations of Motion . . . . 549--563 Garth A. Baker Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations . . . . . . . . . . . . . . . 564--576 Garth A. Baker and Vassilios A. Dougalis The Effect of Quadrature Errors on Finite Element Approximations for Second Order Hyperbolic Equations . . . . . . . 577--598 Claes Johnson A Convergence Estimate for an Approximation of a Parabolic Variational Inequality . . . . . . . . . . . . . . . 599--606 A. B. Stephens The Convergence of the Residual for Projective Approximations . . . . . . . 607--614 Robert Beauwens and Lena Quenon Existence Criteria for Partial Matrix Factorizations in Iterative Methods . . 615--643 J. E. Dendy, Jr. and G. Fairweather Errata: ``Alternating-Direction Galerkin Methods for Parabolic and Hyperbolic Problems on Rectangular Polygons'' [SIAM J. Numer. Anal. \bf 12 (1975), no. 2, 144--163] . . . . . . . . . . . . . . . 644--644
E. Hofer A Partially Implicit Method for Large Stiff Systems of ODE's with Only Few Equations Introducing Small Time-Constants . . . . . . . . . . . . . 645--663 Robert Skeel Analysis of Fixed-Stepsize Methods . . . 664--685 Iain S. Duff and A. M. Erisman and J. K. Reid On George's Nested Dissection Method . . 686--695 R. R. Meyer On the Convergence of Algorithms with Restart . . . . . . . . . . . . . . . . 696--704 John M. Bownds and Bruce Wood On Numerically Solving Nonlinear Volterra Integral Equations with Fewer Computations . . . . . . . . . . . . . . 705--719 Roderick J. Dunn, Jr. and Mary Fanett Wheeler Some Collocation-Galerkin Methods for Two-Point Boundary Value Problems . . . 720--733 S. Cabay and L. W. Jackson A Polynomial Extrapolation Method for Finding Limits and Antilimits of Vector Sequences . . . . . . . . . . . . . . . 734--752 Ian H. Sloan Iterated Galerkin Method for Eigenvalue Problems . . . . . . . . . . . . . . . . 753--760 David W. Kammler Chebyshev Approximation of Completely Monotonic Functions by Sums of Exponentials . . . . . . . . . . . . . . 761--774 Frank R. De Hoog and Richard Weiss Difference Methods for Boundary Value Problems with a Singularity of the First Kind . . . . . . . . . . . . . . . . . . 775--813 Richard S. Falk and J. Thomas King A Penalty and Extrapolation Method for the Stationary Stokes Equations . . . . 814--829
J. E. Dennis, Jr. and J. F. Traub and R. P. Weber The Algebraic Theory of Matrix Polynomials . . . . . . . . . . . . . . 831--845 Alan George A Negative Result on Sparse Matrix Splitting and Gaussian Elimination . . . 846--853 C. R. Crawford A Stable Generalized Eigenvalue Problem 854--860 Richard P. Kendall and Mary F. Wheeler A Crank--Nicolson-$ H^{-1}$--Galerkin Procedure for Parabolic Problems in a Single-Space Variable . . . . . . . . . 861--876 Abraham Berman and Michael Neumann Consistency and Splittings . . . . . . . 877--888 W. B. Gragg and G. W. Stewart A Stable Variant of the Secant Method for Solving Nonlinear Equations . . . . 889--903 R. Cranley and T. N. L. Patterson Randomization of Number Theoretic Methods for Multiple Integration . . . . 904--914 A. Sharma and J. Tzimbalario Cardinal $t$-Perfect $ {L}$-Splines . . 915--922 P. M. Prenter and R. D. Russell Orthogonal Collocation for Elliptic Partial Differential Equations . . . . . 923--939 J. D. Hamilton and H. D. Meyer Finite Element Solutions for Steady State Visco-Plastic Flow . . . . . . . . 940--943 W. H. Enright and T. E. Hull Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations . . . . . . . . . . . . . . . 944--961 Binh Lam A Note on Best Uniform Rational Approximation . . . . . . . . . . . . . 962--965
Andrew M. Olson A Two-Point Series Method for Two-Point Boundary Value Problems: Theoretical Foundation . . . . . . . . . . . . . . . 2--18 Robert D. Russell A Comparison of Collocation and Finite Differences for Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 19--39 Melvin R. Scott and Herman A. Watts Computational Solution of Linear Two-Point Boundary Value Problems Via Orthonormalization . . . . . . . . . . . 40--70 Mary Fanett Wheeler A $ {C}^0$-Collocation-Finite Element Method for Two-Point Boundary Value Problems and One Space Dimensional Parabolic Problems . . . . . . . . . . . 71--90 M. Lentini and V. Pereyra An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers . . . . . . . 91--111 R. F. Sincovec On the Relative Efficiency of Higher Order Collocation Methods for Solving Two-Point Boundary Value Problems . . . 112--123 Paul Nelson and Ira T. Elder Calculation of Eigenfunctions in the Context of Integration-to-Blowup . . . . 124--136 J. H. George and H. G. Harris Mathematical Modeling of in Situ Oil Shale Retorting . . . . . . . . . . . . 137--151 Michael A. Goldberg Invariant Imbedding and Critical Length Problems . . . . . . . . . . . . . . . . 152--160
Alan George Numerical Experiments Using Dissection Methods to Solve $n$ by $n$ Grid Problems . . . . . . . . . . . . . . . . 161--179 C. C. Paige and M. A. Saunders Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations . . . . . . . . . . . . 180--193 Jet Wimp New Methods for Accelerating the Convergence of Sequences Arising in Laplace Transform Theory . . . . . . . . 194--204 B. L. Buzbee Application of Fast Poisson Solvers to $ {A}$-Stable Marching Procedures for Parabolic Problems . . . . . . . . . . . 205--217 J. H. Bramble and A. H. Schatz and V. Thomee and L. B. Wahlbin Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations 218--241 Erich Bohl On a Stability Inequality for Nonlinear Operators . . . . . . . . . . . . . . . 242--253 Michael A. Malcolm On the Computation of Nonlinear Spline Functions . . . . . . . . . . . . . . . 254--282 J. N. Lyness and G. Monegato Quadrature Rules for Regions having Regular Hexagonal Symmetry . . . . . . . 283--295 Thomas J. Aird and John R. Rice Systematic Search in High Dimensional Sets . . . . . . . . . . . . . . . . . . 296--312 J. E. Dendy, Jr. Alternating Direction Methods for Nonlinear Time-Dependent Problems . . . 313--326 J. E. Dendy, Jr. Galerkin's Method for Some Highly Nonlinear Problems . . . . . . . . . . . 327--347 Andrew R. Conn and Tomasz Pietrzykowski A Penalty Function Method Converging Directly to a Constrained Optimum . . . 348--375
Rutger J. Hangelbroek and Hans G. Kaper and Gary K. Leaf Collocation Methods for Integro-Differential Equations . . . . . 377--390 Francis Mantel and Philip Rabinowitz The Application of Integer Programming to the Computation of Fully Symmetric Integration Formulas in Two and Three Dimensions . . . . . . . . . . . . . . . 391--425 Adir Pridor Estimation of Moments for the Numerical Solution of Transport Problems . . . . . 426--440 Carl de Boor Package for Calculating with B-Splines 441--472 J. R. Cannon and P. DuChateau Approximating the Solution to the Cauchy Problem for Laplace's Equation . . . . . 473--483 To-Yat Cheung Three Nonlinear Initial Value Problems of the Hyperbolic Type . . . . . . . . . 484--491 Ann Haegemans and Robert Piessens Construction of Cubature Formulas of Degree Seven and Nine Symmetric Planar Regions, Using Orthogonal Polynomials 492--508 G. W. Stewart Perturbation Bounds for the $ {QR} $ Factorization of a Matrix . . . . . . . 509--518 Uri Ascher Linear Programming Algorithms for the Chebyshev Solution to a System of Consistent Linear Equations . . . . . . 519--526 W. F. Langford A Shooting Algorithm for the Best Least Squares Solution of Two-Point Boundary Value Problems . . . . . . . . . . . . . 527--542 Peter Linz A General Theory for the Approximate Solution of Operator Equations of the Second Kind . . . . . . . . . . . . . . 543--554 Ronald D. Armstrong and John W. Hultz An Algorithm for a Restricted Discrete Approximation Problem in the $ {L}_1 $ Norm . . . . . . . . . . . . . . . . . . 555--565 A. Buckley On the Solution of Certain Skew Symmetric Linear Systems . . . . . . . . 566--570 David W. Boyd Nonconvergence in Bairstow's Method . . 571--574
C. Johnson A Mixed Finite Element Method for Plasticity Problems With Hardening . . . 575--583 Kendall E. Atkinson The Numerical Solution of a Bifurcation Problem . . . . . . . . . . . . . . . . 584--599 Robert C. Ward Numerical Computation of the Matrix Exponential With Accuracy Estimate . . . 600--610 R. E. Moore A Test for Existence of Solutions to Nonlinear Systems . . . . . . . . . . . 611--615 Stephen Demko Inverses of Band Matrices and Local Convergence of Spline Projections . . . 616--619 David Archer An $ {O}(h^4) $ Cubic Spline Collocation Method for Quasilinear Parabolic Equations . . . . . . . . . . . . . . . 620--637 Rudolf Mathon and R. L. Johnston The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions . . . . . . . . . . . . . . . 638--650 Grace Wahba Practical Approximate Solutions to Linear Operator Equations when the Data are Noisy . . . . . . . . . . . . . . . 651--667 Seymour Haber The Tanh Rule for Numerical Integration 668--685 C. S. Duris Discrete Interpolating and Smoothing Spline Functions . . . . . . . . . . . . 686--698 Carl D. Meyer, Jr. and R. J. Plemmons Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems . . . . . . . . 699--705 Roland A. Sweet A Cyclic Reduction Algorithm for Solving Block Tridiagonal Systems of Arbitrary Dimension . . . . . . . . . . . . . . . 706--720 David S. Watkins Error Bounds for Polynomial Blending Function Methods . . . . . . . . . . . . 721--734 K. C. Chung and T. H. Yao On Lattices Admitting Unique Lagrange Interpolations . . . . . . . . . . . . . 735--743 Eli Turkel Composite Methods for Hyperbolic Equations . . . . . . . . . . . . . . . 744--759 R. Jeltsch Stiff Stability of Multistep Multiderivative Methods . . . . . . . . 760--772 H. D. Mittelmann On Pointwise Estimates for a Finite Element Solution of Nonlinear Boundary Value Problems . . . . . . . . . . . . . 773--778
D. C. Brabston and H. B. Keller A Numerical Method for Singular Two Point Boundary Value Problems . . . . . 779--791 Randolph E. Bank and Donald J. Rose Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case . . . . . . . . . . . . 792--829 Paul T. Boggs An Algorithm, Based on Singular Perturbation Theory, for Ill-Conditioned Minimization Problems . . . . . . . . . 830--843 Julio Cesar Diaz A Collocation-Galerkin Method for the Two Point Boundary Value Problem Using Continuous Piecewise Polynomial Spaces 844--858 Bengt Lindberg Characterization of Optimal Stepsize Sequences for Methods for Stiff Differential Equations . . . . . . . . . 859--887 A. H. Stroud and David L. Barrow Integration Formulas for the Poisson Equations . . . . . . . . . . . . . . . 888--903 Eli Passow and John A. Roulier Monotone and Convex Spline Interpolation 904--909 R. D. Skeel and L. W. Jackson Consistency of Nordsieck Methods . . . . 910--924 Pierre Jamet Estimation of the Interpolation Error for Quadrilateral Finite Elements which Can Degenerate into Triangles . . . . . 925--930 Lucio Tavernini Finite Difference Approximations for a Class of Semilinear Volterra Evolution Problems . . . . . . . . . . . . . . . . 931--949 Randolph E. Bank Marching Algorithms for Elliptic Boundary Value Problems. II: The Variable Coefficient Case . . . . . . . 950--970
Charles Van Loan The Sensitivity of the Matrix Exponential . . . . . . . . . . . . . . 971--981 R. Leonard Brown Some Characteristics of Implicit Multistep Multi-Derivative Integration Formulas . . . . . . . . . . . . . . . . 982--993 John C. Bruch, Jr. and James M. Sloss Harmonic Approximation with Dirichlet Data on Doubly Connected Regions . . . . 994--1005 Roger Alexander Diagonally Implicit Runge--Kutta Methods for Stiff O.D.E.'s . . . . . . . . . . . 1006--1021 Theodore A. Bickart An Efficient Solution Process for Implicit Runge--Kutta Methods . . . . . 1022--1027 J. E. Dendy, Jr. An Alternating Direction Method for Schrödinger's Equation . . . . . . . . . 1028--1032 James W. Daniel and Andrew J. Martin Numerov's Method with Deferred Corrections for Two-Point Boundary-Value Problems . . . . . . . . . . . . . . . . 1033--1050 R. E. Moore and S. T. Jones Safe Starting Regions for Iterative Methods . . . . . . . . . . . . . . . . 1051--1065 John A. Trangenstein A Finite Element Method for the Tricomi Problem in the Elliptic Region . . . . . 1066--1077 David Elliott and J. D. Donaldson On Quadrature Rules for Ordinary and Cauchy Principal Value Integrals over Contours . . . . . . . . . . . . . . . . 1078--1087 R. Sacks-Davis Solution of Stiff Ordinary Differential Equations by a Second Derivative Method 1088--1100 Ahmed H. Sameh and Richard P. Brent Solving Triangular Systems on a Parallel Computer . . . . . . . . . . . . . . . . 1101--1113 J. M. Varah On the Stability of Boundary Conditions for Separable Difference Approximations to Parabolic Equations . . . . . . . . . 1114--1125 Philip Brenner $ {L}_p$-Estimates of Difference Schemes for Strictly Hyperbolic Systems with Nonsmooth Data . . . . . . . . . . . . . 1126--1144 J. H. Rowland and G. J. Miel Exit Criteria for Newton--Cotes Quadrature Rules . . . . . . . . . . . . 1145--1150 Bernard J. Omodei On the Numerical Stability of the Rayleigh--Ritz Method . . . . . . . . . 1151--1171
Werner C. Rheinboldt Numerical Methods for a Class of Finite Dimensional Bifurcation Problems . . . . 1--11 Linda Kaufman and Victor Pereyra A Method for Separable Nonlinear Least Squares Problems with Separable Nonlinear Equality Constraints . . . . . 12--20 Heinz-Otto Kreiss Difference methods for stiff ordinary differential equations . . . . . . . . . 21--58 R. D. Russell and J. Christiansen Adaptive Mesh Selection Strategies for Solving Boundary Value Problems . . . . 59--80 M. Dryja Alternating Direction Galerkin Methods for the Systems of Hyperbolic Equations of First Order . . . . . . . . . . . . . 81--89 Alan George and David R. McIntyre On the Application of the Minimum Degree Algorithm to Finite Element Systems . . 90--112 Richard L. Hanson and James L. Phillips Numerical Solution of Two-Dimensional Integral Equations Using Linear Elements 113--121 J. N. Lyness Quadrature Over a Simplex: Part 1. A Representation for the Integrand Function . . . . . . . . . . . . . . . . 122--133 D. M. Cruickshank and K. Wright Computable Error Bounds for Polynomial Collocation Methods . . . . . . . . . . 134--151 Mary Fanett Wheeler An Elliptic Collocation-Finite Element Method with Interior Penalties . . . . . 152--161 C. Charalambous and A. R. Conn An Efficient Method to Solve the Minimax Problem Directly . . . . . . . . . . . . 162--187 C. William Gear The Stability of Numerical Methods for Second Order Ordinary Differential Equations . . . . . . . . . . . . . . . 188--197 Frank R. De Hoog and Richard Weiss Collocation Methods for Singular Boundary Value Problems . . . . . . . . 198--217
Wayne T. Ford Polynomial Deflation Using Regression Analysis . . . . . . . . . . . . . . . . 219--223 Richard H. Bartels and Andrew R. Conn and James W. Sinclair Minimization Techniques for Piecewise Differentiable Functions: The $ l_1 $ Solution to an Overdetermined Linear System . . . . . . . . . . . . . . . . . 224--241 David Archer and Julio Cesar Diaz A Family of Modified Collocation Methods for Second Order Two Point Boundary Value Problems . . . . . . . . . . . . . 242--254 Richard H. Bartels and Andrew R. Conn and Christakis Charalambous On Cline's Direct Method for Solving Overdetermined Linear Systems in the $ l_\infty $ Sense . . . . . . . . . . . . 255--270 David Archer Collocation in $ {C}^0 $ Spaces for First Order Hyperbolic Equations. I: Optimal Order Global Estimates for Quasilinear Problems . . . . . . . . . . 271--281 Axel Grundmann and H. M. Möller Invariant integration formulas for the $n$-simplex by combinatorial methods . . 282--290 D. R. Wilhelmsen Optimal Quadrature for Periodic Analytic Functions . . . . . . . . . . . . . . . 291--296 Alan George and Joseph W. H. Liu Algorithms for matrix partitioning and the numerical solution of finite element systems . . . . . . . . . . . . . . . . 297--327 David L. B. Jupp Approximation to Data by Splines with Free Knots . . . . . . . . . . . . . . . 328--343 Alfred S. Carasso and James G. Sanderson and James M. Hyman Digital Removal of Random Media Image Degradations by Solving the Diffusion Equation Backwards in Time . . . . . . . 344--367 F. W. J. Olver A New Approach to Error Arithmetic . . . 368--393 Christopher T. H. Baker and Malcolm S. Keech Stability Regions in the Numerical Treatment of Volterra Integral Equations 394--417 Jens Frehse and Rolf Rannacher Asymptotic $ {L}^\infty $-Error Estimates for Linear Finite Element Approximations of Quasilinear Boundary Value Problems . . . . . . . . . . . . . 418--431
Rainer Kress On Error Norms of the Trapezoidal Rule 433--443 David A. Field Error Bounds for Elliptic Convergence Regions for Continued Fractions . . . . 444--449 Eusebius J. Doedel The Construction of Finite Difference Approximations to Ordinary Differential Equations . . . . . . . . . . . . . . . 450--465 R. W. Thatcher On the Finite Element Method for Unbounded Regions . . . . . . . . . . . 466--477 Uri Ascher Discrete least squares approximations for ordinary differential equations . . 478--496 Irene Gargantini Further Applications of Circular Arithmetic: Schroeder-Like Algorithms with Error Bounds for Finding Zeros of Polynomials . . . . . . . . . . . . . . 497--510 G. R. Richter Numerical Solution of Integral Equations of the First Kind with Nonsmooth Kernels 511--522 J. E. Dennis, Jr. and J. F. Traub and R. P. Weber Algorithms for Solvents of Matrix Polynomials . . . . . . . . . . . . . . 523--533 V. Girault A Mixed Finite Element Method for the Stationary Stokes Equations . . . . . . 534--555 Richard S. Falk Approximation of the Biharmonic Equation by a Mixed Finite Element Method . . . . 556--567 Lois Mansfield Approximation of the Boundary in the Finite Element Solution of Fourth Order Problems . . . . . . . . . . . . . . . . 568--579 J. C. Nedelec Computation of Eddy Currents on a Surface in $ {R}^3 $ by Finite Element Methods . . . . . . . . . . . . . . . . 580--594 Charles R. Johnson Numerical Determination of the Field of Values of a General Complex Matrix . . . 595--602 I. Barrodale and F. D. K. Roberts An Efficient Algorithm for Discrete $ l_1 $ Linear Approximation with Linear Constraints . . . . . . . . . . . . . . 603--611 Bruce A. Chalmers On the Rate of Convergence of Discretization in Chebyshev Approximation . . . . . . . . . . . . . 612--617 K. R. Jackson and W. H. Enright and T. E. Hull A Theoretical Criterion for Comparing Runge--Kutta Formulas . . . . . . . . . 618--641
G. J. Cooper The Order of Convergence of General Linear Methods for Ordinary Differential Equations . . . . . . . . . . . . . . . 643--661 Alan George and William G. Poole, Jr. and Robert G. Voigt Incomplete Nested Dissection for Solving $n$ by $n$ Grid Problems . . . . . . . . 662--673 H. Mukai and E. Polak On the use of approximations in algorithms for optimization problems with equality and inequality constraints 674--693 L. Brutman On the Lebesgue Function for Polynomial Interpolation . . . . . . . . . . . . . 694--704 Peter Percell and Mary Fanett Wheeler A Local Residual Finite Element Procedure for Elliptic Equations . . . . 705--714 Richard Holley Exact Error Bounds for the Phase Velocity in an Acoustic Wave Guide . . . 715--735 I. Babu\vska and W. C. Rheinboldt Error estimates for adaptive finite element computations . . . . . . . . . . 736--754 Andrew H. Sherman On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations . . . . . . . . . . . . . . . 755--771 J. H. Verner Explicit Runge--Kutta Methods with Estimates of the Local Truncation Error 772--790 Richard Franke On the Computation of Optimal Approximations in Sard Corner Spaces . . 791--800 Olof Widlund A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations 801--812 Dennis Jespersen Ritz--Galerkin Methods for Singular Boundary Value Problems . . . . . . . . 813--834 T. H. Chong A Variable Mesh Finite Difference Method for Solving a Class of Parabolic Differential Equations in one Space Variable . . . . . . . . . . . . . . . . 835--857
Juhani Pitkäranta On the Spatial Differencing of the Discrete Ordinate Neutron Transport Equation . . . . . . . . . . . . . . . . 859--869 J. N. Lyness Quadrature over a Simplex: Part 2. A Representation for the Error Functional 870--887 John de Pillis Faster Convergence for Iterative Solutions to Systems via Three-Part Splittings . . . . . . . . . . . . . . . 888--911 Pierre Jamet Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain . . . . . 912--928 W. Hoffmann and B. N. Parlett A new proof of global convergence for the tridiagonal QL algorithm . . . . . . 929--937 Tateaki Sasaki Multidimensional Monte Carlo integration based on factorized approximation functions . . . . . . . . . . . . . . . 938--952 C. R. Morrow and T. N. L. Patterson Construction of algebraic cubature rules using polynomial ideal theory . . . . . 953--976 Philip E. Gill and Walter Murray Algorithms for the solution of the nonlinear least-squares problem . . . . 977--992 G. W. Reddien On Newton's Method for Singular Problems 993--996 R. Saigal and M. J. Todd Efficient acceleration techniques for fixed point algorithms . . . . . . . . . 997--1007 Syvert P. Norsett Restricted Padé Approximations to the Exponential Function . . . . . . . . . . 1008--1029 E. Kimchi and N. Richter-Dyn Restricted range approximation of $k$-convex functions in monotone norms 1030--1038 Lucio Tavernini The approximate solution of Volterra differential systems with state-dependent time lags . . . . . . . 1039--1052 Alan George and Joseph W. H. Liu An automatic nested dissection algorithm for irregular finite element problems 1053--1069 C. R. Crawford Errata: ``A Stable Generalized Eigenvalue Problem'' [SIAM J. Numer. Anal. \bf 13 (1976), no. 6, 854--860] 1070--1070
J. T. Marti An algorithm for computing minimum norm solutions of Fredholm integral equations of the first kind . . . . . . . . . . . 1071--1076 David W. Kammler Numerical Evaluation of $ \exp (t A) $ when $ {A} $ is a Companion Matrix . . . 1077--1102 A. K. Aziz and S. Leventhal Finite Element Approximation for First Order Systems . . . . . . . . . . . . . 1103--1111 Françoise E. Chatelin Numerical computation of the eigenelements of linear integral operators by iterations . . . . . . . . 1112--1124 Richard E. Ewing Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations . . . . . . . . . . . . . . . 1125--1150 John Locker and P. M. Prenter Optimal $ {L}^2 $ and $ {L}^{\infty } $ error estimates for continuous and discrete least squares methods for boundary value problems . . . . . . . . 1151--1160 David Hoff Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations 1161--1177 James A. Wixom Interpolation to networks of curves in $ {E}^3 $ . . . . . . . . . . . . . . . . 1178--1193 R. E. Moore A computational test for convergence of iterative methods for nonlinear systems 1194--1196 J. N. Henry and M. S. Henry and D. Schmidt Numerical comparisons of algorithms for polynomial and rational multivariate approximations . . . . . . . . . . . . . 1197--1207 Carl de Boor A Comment on ``Numerical Comparisons of Algorithms for Polynomial and Rational Multivariate Approximations'' [SIAM J. Numer. Anal. \bf 15 (1978), no. 6, 1197--1207, by J. N. Henry, M. S. Henry and D. Schmidt] . . . . . . . . . . . . 1208--1211 J. D. Lawson and J. Ll. Morris The extrapolation of first order methods for parabolic partial differential equations. I . . . . . . . . . . . . . . 1212--1224 K. O. Geddes Near-minimax polynomial approximation in an elliptical region . . . . . . . . . . 1225--1233 J. M. Varah Stiffly stable linear multistep methods of extended order . . . . . . . . . . . 1234--1246 D. F. Shanno On the convergence of a new conjugate gradient algorithm . . . . . . . . . . . 1247--1257 Kenneth P. Bube $ {C}^m $ Convergence of Trigonometric Interpolants . . . . . . . . . . . . . . 1258--1268 John M. Karon Computing improved Chebyshev approximations by the continuation method. I. Description of an algorithm 1269--1288 S. Yakowitz and J. E. Krimmel and F. Szidarovszky Weighted Monte Carlo Integration . . . . 1289--1300 J. W. Hilgers Erratum: ``On the Equivalence of Regularization and Certain Reproducing Kernel Hilbert Space Approaches for Solving First Kind Problems'' [SIAM J. Numer. Anal. \bf 13 (1976), no. 2, 172--184] . . . . . . . . . . . . . . . 1301--1301
P. Deuflhard and G. Heindl Affine invariant convergence theorems for Newton's method and extensions to related methods . . . . . . . . . . . . 1--10 P. Keast and J. N. Lyness On the structure of fully symmetric multidimensional quadrature rules . . . 11--29 David W. Kammler $ {L}_1$-approximation of completely monotonic functions by sums of exponentials . . . . . . . . . . . . . . 30--45 Kevin Burrage and J. C. Butcher Stability criteria for implicit Runge--Kutta methods . . . . . . . . . . 46--57 O. Axelsson Preconditioning of indefinite problems by regularization . . . . . . . . . . . 58--69 R. A. El-Attar and M. Vidyasagar and S. R. K. Dutta An algorithm for $ {L}_1$-norm minimization with application to nonlinear $ {L}_1$-approximation . . . . 70--86 Avraham A. Melkman and Charles A. Micchelli Optimal estimation of linear operators in Hilbert spaces from inaccurate data 87--105 S. McKee Cyclic multistep methods for solving Volterra integro-differential equations 106--114 M. L. Dow and David Elliott The numerical solution of singular integral equations over $ ( - 1, \, 1) $ 115--134 Peter D. Robinson and Michael F. Barnsley Pointwise bivariational bounds on solutions of Fredholm integral equations 135--144 Mitchell Luskin An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with integral boundary conditions . . . . . . . . . . . . . . . 145--164 C. C. Paige Fast numerically stable computations for generalized linear least squares problems . . . . . . . . . . . . . . . . 165--171
Eusebius J. Doedel Finite difference collocation methods for nonlinear two-point boundary value problems . . . . . . . . . . . . . . . . 173--185 Wilhelm Niethammer On different splittings and the associated iteration methods . . . . . . 186--200 W. Hackbusch On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method . . . . . . . . . . . 201--215 J. M. Varah On the Separation of Two Matrices . . . 216--222 David A. Smith and William F. Ford Acceleration of Linear and Logarithmic Convergence . . . . . . . . . . . . . . 223--240 H. B. Keller and V. Pereyra Difference methods and deferred corrections for ordinary boundary value problems . . . . . . . . . . . . . . . . 241--259 J. H. Avila and P. Concus Updata Methods for Highly Structured Systems of Nonlinear Equations . . . . . 260--269 Paul Nelson, Jr. and H. Dean Victory, Jr. Theoretical properties of one-dimensional discrete ordinates . . . 270--283 Mitchell Luskin A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions . . . . . . . . . . 284--299 M. Y. Cosnard On the Behavior of Successive Approximations . . . . . . . . . . . . . 300--310 Hans J. Stetter Interpolation and error estimation in Adams PC-codes . . . . . . . . . . . . . 311--323 Shmuel Kaniel and Achiya Dax A modified Newton's method for unconstrained minimization . . . . . . . 324--331 J. R. Kuttler Dirichlet Eigenvalues . . . . . . . . . 332--338 Rolf Jeltsch Corrigendum: ``Stiff Stability of Multistep Multiderivative Methods'' [SIAM J. Numer. Anal. \bf 14 (1977), no. 4, 760--772, MR \bf 57 #11058] . . . . . 339--345 Richard J. Lipton and Donald J. Rose and Robert Endre Tarjan Generalized Nested Dissection . . . . . 346--358 Connice A. Bavely and G. W. Stewart An Algorithm for Computing Reducing Subspaces by Block Diagonalization . . . 359--367 A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson An Estimate for the Condition Number of a Matrix . . . . . . . . . . . . . . . . 368--375
Stephen M. Robinson Quadratic Interpolation is Risky . . . . 377--379 Zenon Fortuna Some convergence properties of the conjugate gradient method in Hilbert space . . . . . . . . . . . . . . . . . 380--384 G. W. Hedstrom The Galerkin Method Based on Hermite Cubics . . . . . . . . . . . . . . . . . 385--393 Layne T. Watson An Algorithm that is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 394--401 Michael Steuerwalt The existence, computation, and number of solutions of periodic parabolic problems . . . . . . . . . . . . . . . . 402--420 Heinz-Otto Kreiss and Joseph Oliger Stability of the Fourier Method . . . . 421--433 José Mario Martínez Generalization of the Methods of Brent and Brown for Solving Nonlinear Simultaneous Equations . . . . . . . . . 434--448 Friedrich Stummel The Generalized Patch Test . . . . . . . 449--471 Andrew B. White, Jr. On selection of equidistributing meshes for two-point boundary-value problems 472--502 Jim Douglas, Jr. and Todd Dupont and Richard E. Ewing Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem . . . . . . . . . . . 503--522 P. J. van der Houwen Stabilized Runge--Kutta Methods for Second Order Differential Equations without First Derivatives . . . . . . . 523--537 David Westreich and Yaakov L. Varol Numerical Bifurcation at Simple Eigenvalues . . . . . . . . . . . . . . 538--546
Janina Jankowska Theory of Multivariate Secant Methods 547--562 Joel C. W. Rogers and Alan E. Berger and Melvyn Ciment The alternating phase truncation method for numerical solution of a Stefan problem . . . . . . . . . . . . . . . . 563--587 Earl Marwil Convergence results for Schubert's method for solving sparse nonlinear equations . . . . . . . . . . . . . . . 588--604 J. F. Andrus Numerical solution of systems of ordinary differential equations separated into subsystems . . . . . . . 605--611 Nira Richter-Dyn On Best Nonlinear Approximation in Sign-Monotone Norms and in Norms Induced by Inner Products . . . . . . . . . . . 612--622 David M. Gay Some Convergence Properties of Broyden's Method . . . . . . . . . . . . . . . . . 623--630 Arieh Iserles On the generalized Padé approximations to the exponential function . . . . . . . . 631--636 Frank R. de Hoog and Richard Weiss The Numerical Solution of Boundary Value Problems with an Essential Singularity 637--669 Reuben Hersh and Tosio Kato High-accuracy stable difference schemes for well-posed initial value problems 670--682 Philip Brenner and Vidar Thomée On Rational Approximations of Semigroups 683--694 Wendell H. Mills, Jr. The resolvent stability condition for spectra convergence with application to the finite element approximation of noncompact operators . . . . . . . . . . 695--703 Wendell H. Mills, Jr. Optimal error estimates for the finite element spectral approximation of noncompact operators . . . . . . . . . . 704--718
Richard F. King An extrapolation method of order four for linear sequences . . . . . . . . . . 719--725 Ole H. Hald Convergence of vortex methods for Euler's equations. II . . . . . . . . . 726--755 Arthur G. Deacon and Stanley Osher A finite element method for a boundary value problem of mixed type . . . . . . 756--778 Sandro Incerti and Valerio Parisi and Francesco Zirilli A new method for solving nonlinear simultaneous equations . . . . . . . . . 779--789 I. M. Sobol' On the Systematic Search in a Hypercube 790--793 Larry Nazareth A relationship between the BFGS and conjugate gradient algorithms and its implications for new algorithms . . . . 794--800 David W. Kammler Least squares approximation of completely monotonic functions by sums of exponentials . . . . . . . . . . . . 801--818 Jack Williams Characterization and computation of rational Chebyshev approximations in the complex plane . . . . . . . . . . . . . 819--827 A. Granas and R. B. Guenther and J. W. Lee The shooting method for the numerical solution of a class of nonlinear boundary value problems . . . . . . . . 828--836 Said Doss and Keith Miller Dynamic ADI Methods for Elliptic Equations . . . . . . . . . . . . . . . 837--856 J. H. Verner Families of Imbedded Runge--Kutta Methods . . . . . . . . . . . . . . . . 857--875
Stephen W. Brady and Alan R. Elcrat Some results on a posteriori error estimation for approximate solutions of second order elliptic problems . . . . . 877--889 Christopher T. H. Baker and Athena Makroglou and Edward Short Regions of stability in the numerical treatment of Volterra integro-differential equations . . . . . 890--910 Julio César Díaz Collocation-$ {H}^{-1}$-Galerkin Method for Parabolic Problems with Time Dependent Coefficients . . . . . . . . . 911--922 M. R. Osborne The Stabilized March is Stable . . . . . 923--933 Paul N. Swarztrauber On the spectral approximation of discrete scalar and vector functions on the sphere . . . . . . . . . . . . . . . 934--949 J. E. Cope and B. W. Rust Bounds on solutions of linear systems with inaccurate data . . . . . . . . . . 950--963 P. L. Lions and B. Mercier Splitting algorithms for the sum of two nonlinear operators . . . . . . . . . . 964--979 Heinz-Otto Kreiss Problems with different time scales for ordinary differential equations . . . . 980--998 Thomas E. Price, Jr. Orthogonal polynomials for nonclassical weight functions . . . . . . . . . . . . 999--1006 Robert Schaback Suboptimal Exponential Approximations 1007--1018 Tze Chien Sun A finite element method for random differential equations with random coefficients . . . . . . . . . . . . . . 1019--1035 Ph. Toint On the superlinear convergence of an algorithm for solving a sparse minimization problem . . . . . . . . . . 1036--1045 Joseph Pasciak The penalty correction method for elliptic boundary value problems . . . . 1046--1059 M. J. D. Powell and Ph. L. Toint On the Estimation of Sparse Hessian Matrices . . . . . . . . . . . . . . . . 1060--1074 J. Prasad and A. K. Varma Lacunary Interpolation by Quintic Splines . . . . . . . . . . . . . . . . 1075--1079 I. M. Sobol' Erratum: ``On the Systematic Search in a Hypercube'' [SIAM J. Numer. Anal. \bf 16 (1979), no. 5, 790--793, MR 80f:65072] 1080--1080
William E. Smith and Ian H. Sloan Product-integration rules based on the zeros of Jacobi polynomials . . . . . . 1--13 Ragnar Winther Some superlinear convergence results for the conjugate gradient method . . . . . 14--17 Zahari Zlatev On some pivotal strategies in Gaussian elimination by sparse technique . . . . 18--30 Eric Braaten An improved measure of the nonuniformity of the distribution of a sequence . . . 31--32 Lars B. Wahlbin A remark on parabolic smoothing and the finite element method . . . . . . . . . 33--38 D. Meek The inverses of some matrices deviating slightly from a symmetric, tridiagonal, Toeplitz form . . . . . . . . . . . . . 39--43 G. Nielson Minimum Norm Interpolation in Triangles 44--62 Charles B. Dunham and Charles R. Crawford Minimax Approximation by a Semi-Circle 63--65 D. W. Decker and C. T. Kelley Newton's Method at Singular Points. I 66--70 H. D. Victory, Jr. Convergence properties of discrete-ordinates solutions for neutron transport in three-dimensional media . . 71--83 D. C. Sorensen The $ {Q}$-superlinear convergence of a collinear scaling algorithm for unconstrained optimization . . . . . . . 84--114 N. I. Ioakimidis and P. S. Theocaris A comparison between the direct and the classical numerical methods for the solution of Cauchy type singular integral equations . . . . . . . . . . . 115--118 Philip Brenner and Vidar Thomée On Rational Approximations of Groups of Operators . . . . . . . . . . . . . . . 119--125 J. N. Lyness and A. C. Genz On Simplex Trapezoidal Rule Families . . 126--147 L. B. Rall A comparison of the existence theorems of Kantorovich and Moore . . . . . . . . 148--161 Miente Bakker On the numerical solution of parabolic equations in a single space variable by the continuous time Galerkin method . . 162--177
Wolfgang Dahmen On Multivariate B-Splines . . . . . . . 179--191 Joseph W. Jerome Convergence of successive iterative semidiscretizations for FitzHugh--Nagumo reaction diffusion systems . . . . . . . 192--206 J. Barkley Rosser Majorization formulas for a biharmonic function of two variables . . . . . . . 207--220 Werner C. Rheinboldt Solution fields of nonlinear equations and continuation methods . . . . . . . . 221--237 F. N. Fritsch and R. E. Carlson Monotone Piecewise Cubic Interpolation 238--246 John Locker and P. M. Prenter Regularization with differential operators. II. Weak least squares finite element solutions to first kind integral equations . . . . . . . . . . . . . . . 247--267 William C. Davidon Conic approximations and collinear scalings for optimizers . . . . . . . . 268--281 Alan George and Joseph W. H. Liu A minimal storage implementation of the minimum degree algorithm . . . . . . . . 282--299 J. M. Varah Stability Restrictions on Second Order, Three Level Finite Difference Schemes for Parabolic Equations . . . . . . . . 300--309 C. W. Clenshaw and F. W. J. Olver An unrestricted algorithm for the exponential function . . . . . . . . . . 310--331
H. Ratschek and J. Rokne About the Centered Form . . . . . . . . 333--337 Lars Eldén Perturbation Theory for the Least Squares Problem with Linear Equality Constraints . . . . . . . . . . . . . . 338--350 Richard E. Ewing and Mary Fanett Wheeler Galerkin methods for miscible displacement problems in porous media 351--365 L. Brutman On the polynomial and rational projections in the complex plane . . . . 366--372 L. Brutman and A. Pinkus On the Erd\Hos Conjecture Concerning Minimal Norm Interpolation on the Unit Circle . . . . . . . . . . . . . . . . . 373--375 M. A. Wolfe A Modification of Krawczyk's Algorithm 376--379 W. Dahmen and R. De Vore and K. Scherer Multi-Dimensional Spline Approximation 380--402 G. W. Stewart The efficient generation of random orthogonal matrices with an application to condition estimators . . . . . . . . 403--409 (loose microfiche supplement) P. J. van der Houwen Multistep Splitting Methods of High Order for Initial Value Problems . . . . 410--427 Charles B. Dunham Behavior of the one-sided alternating Chebyshev operator . . . . . . . . . . . 428--430 Vassilios A. Dougalis and Steven M. Serbin On the superconvergence of Galerkin approximations to second-order hyperbolic equations . . . . . . . . . . 431--446 Kathie L. Hiebert Solving Systems of Linear Equations and Inequalities . . . . . . . . . . . . . . 447--464 D. W. Decker and C. T. Kelley Newton's Method at Singular Points. II 465--471 John W. Hilgers A note on estimating the optimal regularization parameter . . . . . . . . 472--473 W. S. Ericksen Inverse Pairs of Matrices with Integer Elements . . . . . . . . . . . . . . . . 474--477
George E. Backus The Topping Algorithm for Calculating Extrema of Polynomials on Subsets of $ {R}^n $ . . . . . . . . . . . . . . . . 479--511 R. Günttner Evaluation of Lebesgue Constants . . . . 512--520 R. E. Moore and J. B. Kioustelidis A simple test for accuracy of approximate solutions to nonlinear (or linear) systems . . . . . . . . . . . . 521--529 Pierre Jamet Stability and convergence of a generalized Crank--Nicolson scheme on a variable mesh for the heat equation . . 530--539 C. B. García and T. Y. Li On the number of solutions to polynomial systems of equations . . . . . . . . . . 540--546 Robert Schreiber Finite element methods of high-order accuracy for singular two-point boundary value problems with nonsmooth solutions 547--566 G. Moore and A. Spence The calculation of turning points of nonlinear equations . . . . . . . . . . 567--576 Marianela Lentini and Herbert B. Keller Boundary value problems on semi-infinite intervals and their numerical solution 577--604
Peter Percell and Mary Fanett Wheeler A $ {C}^1 $ finite element collocation method for elliptic equations . . . . . 605--622 Bertil Gustafsson Asymptotic expansions for hyperbolic problems with different time-scales . . 623--634 Charles B. Dunham The rate of convergence of discretization in Chebyshev approximation on rectangular sets . . . 635--638 Charles B. Dunham Stability of differential correction for rational Chebyshev approximation . . . . 639--640 A. R. Gourlay and J. Ll. Morris The extrapolation of first order methods for parabolic partial differential equations. II . . . . . . . . . . . . . 641--655 H. Ratschek Centered Forms . . . . . . . . . . . . . 656--662 Manfred Dobrowolski $ {L}^{\infty }$-convergence of linear finite element approximation to nonlinear parabolic problems . . . . . . 663--674 D. J. Evans On the solution of certain Toeplitz tridiagonal linear systems . . . . . . . 675--680 A. K. Aziz and A. Werschulz On the Numerical Solution of Helmholtz's Equation by the Finite Element Method 681--686 Y. Saad On the rates of convergence of the Lanczos and the block Lanczos methods 687--706 W. W. Symes Numerical Stability in an Inverse Scattering Problem . . . . . . . . . . . 707--732
R. B. Kellogg and G. R. Shubin and A. B. Stephens Uniqueness and the Cell Reynolds Number 733--739 Alan George An automatic one-way dissection algorithm for irregular finite element problems . . . . . . . . . . . . . . . . 740--751 Lois Mansfield On the Solution of Nonlinear Finite Element Systems . . . . . . . . . . . . 752--765 Werner C. Rheinboldt On a Theory of Mesh-Refinement Processes 766--778 G. J. Fix and R. A. Nicolaides An analysis of mixed finite element approximations for periodic acoustic wave propagation . . . . . . . . . . . . 779--786 R. S. Varga and E. B. Saff and V. Mehrmann Incomplete factorizations of matrices and connections with $ {H}$-matrices . . 787--793 I. K. Abu-Shumays Resolution of Singularities of the Diamond Difference Approximation . . . . 794--805 R. E. Bank and D. J. Rose Parameter selection for Newton-like methods applicable to nonlinear partial differential equations . . . . . . . . . 806--822 Seymour V. Parter and Michael Steuerwalt On $ {K}$-Line and $ {K} \times {K}$ Block Iterative Schemes for a Problem Arising in Three-Dimensional Elliptic Difference Equations . . . . . . . . . . 823--839 C. A. Hall and T. A. Porsching Padé approximants, fractional step methods and Navier--Stokes discretizations . . . . . . . . . . . . 840--851 Louis A. Hageman and Franklin T. Luk and David M. Young On the Equivalence of Certain Iterative Acceleration Methods . . . . . . . . . . 852--873 R. B. Barrar and H. L. Loeb Fundamental theorem of algebra for monosplines and related results . . . . 874--882 Gene H. Golub and Charles F. Van Loan An Analysis of the Total Least Squares Problem . . . . . . . . . . . . . . . . 883--893 Carl de Boor Dichotomies for Band Matrices . . . . . 894--907 A. Weiser and S. C. Eisenstat and M. H. Schultz On Solving Elliptic Equations to Moderate Accuracy . . . . . . . . . . . 908--929
Arieh Iserles Rational Interpolation to $ \exp ( - x) $ with Application to Certain Stiff Systems . . . . . . . . . . . . . . . . 1--12 David S. Watkins Determining Initial Values for Stiff Systems of Ordinary Differential Equations . . . . . . . . . . . . . . . 13--20 J. R. Cash Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems 21--36 J. C. Butcher Stability Properties for a General Class of Methods for Ordinary Differential Equations . . . . . . . . . . . . . . . 37--44 M. van Veldhuizen $ {D}$-Stability . . . . . . . . . . . . 45--64 G. J. Cooper Error Estimates for General Linear Methods for Ordinary Differential Equations . . . . . . . . . . . . . . . 65--82 J. D. Lambert Safe Point Methods for Separably Stiff Systems of Ordinary Differential Equations . . . . . . . . . . . . . . . 83--101 David S. Scott Solving sparse symmetric generalized eigenvalue problems without factorization . . . . . . . . . . . . . 102--110 Nabil R. Nassif and Fabrice Pini Semi-Discrete and Fully Discrete Finite-Element Methods with Penalty for the Numerical Solution of the Waterhammer Problem . . . . . . . . . . 111--128 Stanley Osher Nonlinear singular perturbation problems and one-sided difference schemes . . . . 129--144 Andreas Griewank and M. R. Osborne Newton's method for singular problems when the dimension of the null space is $ > 1 $ . . . . . . . . . . . . . . . . . 145--149 Gunter H. Meyer The method of lines and invariant imbedding for elliptic and parabolic free boundary problems . . . . . . . . . 150--164 Gunter H. Meyer An analysis of the method of lines for the Reynolds equation in hydrodynamic lubrication . . . . . . . . . . . . . . 165--177
Bertil Gustafsson The convergence rate for difference approximations to general mixed initial-boundary value problems . . . . 179--190 Paul N. Swarztrauber The approximation of vector functions and their derivatives on the sphere . . 191--210 John Gary The multigrid iteration applied to the collocation method . . . . . . . . . . . 211--224 H. Turner Laquer and Burton Wendroff Bounds for the Model Quench Front . . . 225--241 G. I. Marchuk and V. I. Agoshkov Kinetic Equations and Variational Principles . . . . . . . . . . . . . . . 242--261 Barbro Kreiss and Heinz-Otto Kreiss Numerical Methods for Singular Perturbation Problems . . . . . . . . . 262--276 Eugene Isaacson and Gideon Zwas Mountain Winds Revisited . . . . . . . . 277--288 Amiram Harten and Peter D. Lax A random choice finite difference scheme for hyperbolic conservation laws . . . . 289--315 Roger B. Lazarus Self-similar solutions for converging shocks and collapsing cavities . . . . . 316--371 Milton E. Rose A ``unified'' numerical treatment of the wave equation and the Cauchy--Riemann equations . . . . . . . . . . . . . . . 372--376
Donald R. Smith On boundary layer approximations in the numerical solution of certain stiff boundary value problems . . . . . . . . 377--380 J. P. Butler and J. A. Reeds and S. V. Dawson Estimating solutions of first kind integral equations with nonnegative constraints and optimal smoothing . . . 381--397 C. C. Paige and M. A. Saunders Towards a Generalized Singular Value Decomposition . . . . . . . . . . . . . 398--405 Hans-Jürgen Reinhardt \em A Posteriori Error Estimates for the Finite Element Solution of a Singularly Perturbed Linear Ordinary Differential Equation . . . . . . . . . . . . . . . . 406--430 Gershon Kedem A posteriori error bounds for two-point boundary value problems . . . . . . . . 431--448 Robert D. Skeel Effect of equilibration on residual size for partial pivoting . . . . . . . . . . 449--454 Linda R. Petzold An efficient numerical method for highly oscillatory ordinary differential equations . . . . . . . . . . . . . . . 455--479 Arieh Iserles On Multivalued Exponential Approximations . . . . . . . . . . . . . 480--499 Asen L. Dontchev Error estimates for a discrete approximation to constrained control problems . . . . . . . . . . . . . . . . 500--514 I. Babu\vska and B. A. Szabò and I. N. Katz The $p$-Version of the Finite Element Method . . . . . . . . . . . . . . . . . 515--545 Robert Schreiber and Stanley C. Eisenstat Finite element methods for spherically symmetric elliptic equations . . . . . . 546--558 J. P. Milaszewicz On Criticality and the Stein--Rosenberg Theorem . . . . . . . . . . . . . . . . 559--564 Ivo Babu\vska and Werner C. Rheinboldt \em A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems . . . . . . . . 565--589
Nikolaos M. Missirlis and David J. Evans On the convergence of some generalized preconditioned iterative methods . . . . 591--596 A. Dax and S. Kaniel The ELR method for computing the eigenvalues of a general matrix . . . . 597--605 O. L. Mangasarian Iterative Solution of Linear Programs 606--614 Zdzis\law Jackiewicz The Numerical Solution of Volterra Functional Differential Equations of Neutral Type . . . . . . . . . . . . . . 615--626 Linda J. Hayes Galerkin alternating-direction methods for nonrectangular regions using patch approximations . . . . . . . . . . . . . 627--643 Mark J. Friedman Mathematical study of the nonlinear singular integral magnetic field equation. II . . . . . . . . . . . . . . 644--653 David M. Gay Perturbation Bounds for Nonlinear Equations . . . . . . . . . . . . . . . 654--663 D. L. Clements A boundary integral procedure for the numerical solution of a class of mixed boundary value problems . . . . . . . . 664--680 W. Hackbusch Optimal $ {H}^{p, \, p / 2} $ error estimates for a parabolic Galerkin method . . . . . . . . . . . . . . . . . 681--692 Wolfgang Bunse A class of diagonal transformation methods for the computation of the spectral radius of a nonnegative irreducible matrix . . . . . . . . . . . 693--704 Pavol Sermer and Rudolf Mathon Least-Squares Methods for Mixed-Type Equations . . . . . . . . . . . . . . . 705--723 Randolph E. Bank A comparison of two multilevel iterative methods for nonsymmetric and indefinite elliptic finite element equations . . . 724--743 George J. Miel Evaluation of complex logarithms and related functions . . . . . . . . . . . 744--750 W. W. Symes Erratum: ``Numerical Stability in an Inverse Scattering Problem'' [SIAM J. Numer. Anal. \bf 17 (1980), no. 5, 707--732, MR 81k:65135] . . . . . . . . 751--752
Reinhard Frank and Josef Schneid and Christoph W. Ueberhuber The Concept of $B$-Convergence . . . . . 753--780 Linda J. Hayes A modified backward time discretization for nonlinear parabolic equations using patch approximations . . . . . . . . . . 781--793 David S. Watkins Efficient initialization of stiff systems with one unknown initial condition . . . . . . . . . . . . . . . 794--800 Peter Wildenauer Construction of domains with all solutions, and the existence of extreme solutions . . . . . . . . . . . . . . . 801--807 J. R. Cash On the exponential fitting of composite, multiderivative linear multistep methods 808--821 Herbert B. Keller Geometrically isolated nonisolated solutions and their approximation . . . 822--838 Peter B. Geltner General Rayleigh Quotient Iteration . . 839--843 K. O. Geddes Block Structure in the Chebyshev--Padé Table . . . . . . . . . . . . . . . . . 844--861 G. Alefeld and J. G. Rokne On the evaluation of rational functions in interval arithmetic . . . . . . . . . 862--870 P. Van Der Cruyssen Stable Evaluation of Generalized Continued Fractions . . . . . . . . . . 871--881 Richard R. Gerber and Franklin T. Luk A generalized Broyden's method for solving simultaneous linear equations 882--890 A. Kroó Error estimations for deviation of best uniform, discrete and $ {L}_q$-approximations . . . . . . . . . 891--896 A. K. Varma An interpolatory rational trigonometric approximation . . . . . . . . . . . . . 897--899 David W. Kammler Differential approximation of completely monotonic functions . . . . . . . . . . 900--918 S. K. Burley and S. O. John and J. Nuttall Vector Orthogonal Polynomials . . . . . 919--924 C. den Heijer and W. C. Rheinboldt On Steplength Algorithms for a Class of Continuation Methods . . . . . . . . . . 925--948
J. E. Dennis, Jr. and Homer F. Walker Convergence Theorems for Least-Change Secant Update Methods . . . . . . . . . 949--987 Karl L. Nickel A Globally Convergent Ball Newton Method 988--1003 Leslie V. Foster Generalizations of Laguerre's method: higher order methods . . . . . . . . . . 1004--1018 Keith Miller and Robert N. Miller Moving Finite Elements. I . . . . . . . 1019--1032 Keith Miller Moving Finite Elements. II . . . . . . . 1033--1057 F. Kappel and K. Kunisch Spline approximations for neutral functional-differential equations . . . 1058--1080 P. J. van der Houwen Modified Nyström methods for semidiscrete hyperbolic differential equations . . . 1081--1097 E. Hairer and G. Wanner Algebraically Stable and Implementable Runge--Kutta Methods of High Order . . . 1098--1108 Bernd Güsmann Bounds of Galerkin Projections on Splines with Highly Nonuniform Meshes 1109--1119 N. I. Ioakimidis On the weighted Galerkin method of numerical solution of Cauchy type singular integral equations . . . . . . 1120--1127 Jean Descloux Essential numerical range of an operator with respect to a coercive form and the approximation of its spectrum by the Galerkin method . . . . . . . . . . . . 1128--1133 Corrado Corradi A note on the solution of separable nonlinear least-squares problems with separable nonlinear equality constraints 1134--1138 Noël de Villiers and David Glasser A Continuation Method for Nonlinear Regression . . . . . . . . . . . . . . . 1139--1154
Richard E. Ewing and Thomas F. Russell Efficient time-stepping methods for miscible displacement problems in porous media . . . . . . . . . . . . . . . . . 1--67 Peter H. Sammon Convergence estimates for semidiscrete parabolic equation approximations . . . 68--92 Mitchell Luskin and Rolf Rannacher On the smoothing property of the Galerkin method for parabolic equations 93--113 James F. Epperson An Error Estimate for Changing the Stefan Problem . . . . . . . . . . . . . 114--120 J. R. Kuttler Bounds for Stekloff Eigenvalues . . . . 121--125 D. Isaacson and E. L. Isaacson and D. Marchesin and P. J. Paes-Leme Numerical Analysis of the Spectral Properties of Coupled Oscillator Schrödinger Operators. II. Two-Coupled Anharmonic Oscillators . . . . . . . . . 126--141 Joseph E. Pasciak Spectral methods for a nonlinear initial value problem involving pseudodifferential operators . . . . . . 142--154 J. G. Verwer An analysis of Rosenbrock methods for nonlinear stiff initial value problems 155--170 Robert D. Skeel A theoretical framework for proving accuracy results for deferred corrections . . . . . . . . . . . . . . 171--196 A. Wassyng Solving $ A x = b $: A Method with Reduced Storage Requirements . . . . . . 197--204 R. Amit and C. Hall Storage requirements for profile and frontal elimination . . . . . . . . . . 205--218 D. W. Decker and C. T. Kelley Convergence acceleration for Newton's method at singular points . . . . . . . 219--229
T. J. Mahar Discrete Conservative Oscillators: Periodic and Asymptotically Periodic Solutions . . . . . . . . . . . . . . . 231--236 T. J. Mahar Discrete Almost-Linear Oscillators . . . 237--244 Kevin Burrage Efficiently Implementable Algebraically Stable Runge--Kutta Methods . . . . . . 245--258 Robert B. Feinberg $ {A}_0$-stable formulas of Adams type 259--262 K. E. Atkinson The numerical solution of Laplace's equation in three dimensions . . . . . . 263--274 John G. Heywood and Rolf Rannacher Finite element approximation of the nonstationary Navier--Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization . . . . . . . . . . . . . 275--311 V. Girault and P.-A. Raviart An analysis of upwind schemes for the Navier--Stokes equations . . . . . . . . 312--333 Edward W. Larsen and Paul Nelson Finite-difference approximations and superconvergence for the discrete-ordinate equations in slab geometry . . . . . . . . . . . . . . . . 334--348 R. A. Nicolaides Existence, uniqueness and approximation for generalized saddle point problems 349--357 Martin H. Gutknecht and Lloyd N. Trefethen Real polynomial Chebyshev approximation by the Carathéodory--Fejér method . . . . 358--371 R. K. Beatson Restricted range approximation by splines and variational inequalities . . 372--380 Zahari Zlatev Use of iterative refinement in the solution of sparse linear systems . . . 381--399 Ron S. Dembo and Stanley C. Eisenstat and Trond Steihaug Inexact Newton Methods . . . . . . . . . 400--408 D. C. Sorensen Newton's method with a model trust region modification . . . . . . . . . . 409--426 Ian H. Sloan and William E. Smith Properties of interpolatory product integration rules . . . . . . . . . . . 427--442 J. E. Dennis, Jr. and Homer F. Walker Erratum: ``Convergence Theorems for Least-Change Secant Update Methods'' [SIAM J. Numer. Anal. \bf 18 (1981), no. 6, 949--987] . . . . . . . . . . . . . . 443--443
Chandler Davis and W. M. Kahan and H. F. Weinberger Norm-preserving dilations and their applications to optimal error bounds . . 445--469 W. Kahan and B. N. Parlett and E. Jiang Residual bounds on approximate eigensystems of nonnormal matrices . . . 470--484 Y. Saad The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems . . . . . . . . . . . . . . . . 485--506 N. Dyn and G. G. Lorentz and S. D. Riemenschneider Continuity of the Birkhoff Interpolation 507--509 Hakop Hakopian Multivariate spline functions, $ {B}$-spline basis and polynomial interpolations . . . . . . . . . . . . . 510--517 Seymour V. Parter On the eigenvalues of second order elliptic difference operators . . . . . 518--530 I. N. Molchanov and \=E. F. Galba Difference methods for elliptic partial differential equations with nonunique solutions . . . . . . . . . . . . . . . 531--547 S. F. McCormick An Algebraic Interpretation of Multigrid Methods . . . . . . . . . . . . . . . . 548--560 Ragnar Winther A finite element method for a version of the Boussinesq equation . . . . . . . . 561--570 Miente Bakker Galerkin methods for even-order parabolic equations in one space variable . . . . . . . . . . . . . . . . 571--587 D. J. Evans and A. Danaee A new group hopscotch method for the numerical solution of partial differential equations . . . . . . . . . 588--598 Mingyou Huang and Vidar Thomee On the Backward Euler Method for Parabolic Equations with Rough Initial Data . . . . . . . . . . . . . . . . . . 599--603 W. Rümelin Numerical treatment of stochastic differential equations . . . . . . . . . 604--613 David Slepian Solution of certain integral equations with difference kernels . . . . . . . . 614--622 Kevin R. Hickey and Glenn R. Luecke Remarks on Marti's method for solving first kind equations [SIAM J. Numer. Anal. \bf 15 (1978), no. 6, 1071--1076, by J. T. Marti] . . . . . . . . . . . . 623--628 C. Canuto and A. Quarteroni Error estimates for spectral and pseudospectral approximations of hyperbolic equations . . . . . . . . . . 629--642 Michael Prüfer A Combinatorial Algorithm Providing Alternating Approximations for a Zero of an $ {M}$-Function . . . . . . . . . . . 643--652 Werner C. Rheinboldt Computation of critical boundaries on equilibrium manifolds . . . . . . . . . 653--669
David Gottlieb and Max Gunzburger and Eli Turkel On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods . . . . . . . 671--682 Andrew B. White, Jr. On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension . . . . . . . . . . . . 683--697 Richard B. Philips and Milton E. Rose Compact finite difference schemes for mixed initial-boundary value problems 698--720 Robert S. Fisk On an oscillation phenomenon in the numerical solution of the diffusion-convection equation . . . . . 721--724 Marie-Noëlle Le Roux Variable step size multistep methods for parabolic problems . . . . . . . . . . . 725--741 Douglas N. Arnold An interior penalty finite element method with discontinuous elements . . . 742--760 Y. Maday and A. Quarteroni Spectral and Pseudo-Spectral Approximations of the Navier--Stokes Equations . . . . . . . . . . . . . . . 761--780 Patricio Basso Iterative methods for the localization of the global maximum . . . . . . . . . 781--792 Kazuo Murota Global convergence of a modified Newton iteration for algebraic equations . . . 793--799 Francesco Zirilli The solution of nonlinear systems of equations by second order systems of O.D.E. and linearly implicit $ {A}$-stable techniques . . . . . . . . . 800--815 David Elliott The classical collocation method for singular integral equations . . . . . . 816--832 T. A. Manteuffel Optimal parameters for linear second-degree stationary iterative methods . . . . . . . . . . . . . . . . 833--839 J. P. Delahaye and B. Germain-Bonne The set of logarithmically convergent sequences cannot be accelerated . . . . 840--844 R. E. Moore and L. Qi A Successive Interval Test for Nonlinear Systems . . . . . . . . . . . . . . . . 845--850 L. Qi A Note on the Moore Test for Nonlinear Systems . . . . . . . . . . . . . . . . 851--857 David M. Gay Solving Interval Linear Equations . . . 858--870
Jim Douglas, Jr. and Thomas F. Russell Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures . . . . . . 871--885 Randolph E. Bank Analysis of a Multilevel Inverse Iteration Procedure for Eigenvalue Problems . . . . . . . . . . . . . . . . 886--898 A. K. Aziz and M. R. Dorr and R. B. Kellogg A new approximation method for the Helmholtz equation in an exterior domain 899--908 Ohannes A. Karakashian On a Galerkin--Lagrange multiplier method for the stationary Navier--Stokes equations . . . . . . . . . . . . . . . 909--923 S. F. McCormick and J. W. Ruge Multigrid Methods for Variational Problems . . . . . . . . . . . . . . . . 924--929 Theodore R. Hatcher An error bound for certain successive overrelaxation schemes . . . . . . . . . 930--941 Herbert B. Keller and Marianela Lentini Invariant imbedding, the box scheme and an equivalence between them . . . . . . 942--962 R. M. M. Mattheij The Conditioning of Linear Boundary Value Problems . . . . . . . . . . . . . 963--978 Leif Abrahamsson and Stanley Osher Monotone difference schemes for singular perturbation problems . . . . . . . . . 979--992 Wolfgang A. Dahmen and Charles A. Micchelli On the linear independence of multivariate $ {B}$-splines. I. Triangulations of simploids . . . . . . 993--1012 Klaus Höllig Multivariate Splines . . . . . . . . . . 1013--1031 J. I. Maeztu Divided Differences Associated with Reversible Systems in $ \mathbb {R}^2 $ 1032--1040 J. P. Thiran and P. Defert Weak minimal $ {H}$-sets for polynomials in two variables . . . . . . . . . . . . 1041--1050 Thomas R. Lucas Asymptotic expansions for interpolating periodic splines . . . . . . . . . . . . 1051--1066 Arnold Schönhage Rational Approximation to $ e^{-x} $ and Related $ \mathscr {L}^2$-Problems . . . 1067--1080 Kurt Jetter A new class of Gaussian quadrature formulas based on Birkhoff type data . . 1081--1089 Roger B. Lazarus Erratum: ``Self-Similar Solutions for Converging Shocks and Collapsing Cavities'' [SIAM J. Numer. Anal. \bf 18 (1981), no. 2, 316--371, MR 82i:76054] 1090--1090
Randall J. Leveque Large time step shock-capturing techniques for scalar conservation laws 1091--1109 Ronald H. W. Hoppe Discrete approximations of cosine operator functions. I . . . . . . . . . 1110--1128 R. E. White An Enthalpy Formulation of the Stefan Problem . . . . . . . . . . . . . . . . 1129--1157 R. E. White A numerical solution of the enthalpy formulation of the Stefan problem . . . 1158--1172 Seymour V. Parter and Michael Steuerwalt Block iterative methods for elliptic and parabolic difference equations . . . . . 1173--1195 Christine Bernardi Numerical approximation of a periodic linear parabolic problem . . . . . . . . 1196--1207 Jean Descloux and Mitchell Luskin On a finite element method to solve the criticality eigenvalue problem for the transport equation . . . . . . . . . . . 1208--1219 J. R. Cash On the Solution of Block Tridiagonal Systems of Linear Algebraic Equations having a Special Structure . . . . . . . 1220--1232 M. R. Li and B. Nour-Omid and B. N. Parlett A fast solver free of fill-in for finite element problems . . . . . . . . . . . . 1233--1242 Ahmed H. Sameh and John A. Wisniewski A trace minimization algorithm for the generalized eigenvalue problem . . . . . 1243--1259 Michael G. Duffy Quadrature over a pyramid or cube of integrands with a singularity at a vertex . . . . . . . . . . . . . . . . . 1260--1262 J. Barzilai and A. Ben-Tal Nonpolynomial and inverse interpolation for line search: synthesis and convergence rates . . . . . . . . . . . 1263--1277 R. K. Beatson Monotone and convex approximation by splines: error estimates and a curve fitting algorithm . . . . . . . . . . . 1278--1285 Paul Dierckx A fast algorithm for smoothing data on a rectangular grid while using spline functions . . . . . . . . . . . . . . . 1286--1304
P. Deift and T. Nanda and C. Tomei Ordinary differential equations and the symmetric eigenvalue problem . . . . . . 1--22 J. J. Dongarra and C. B. Moler and J. H. Wilkinson Improving the Accuracy of Computed Eigenvalues and Eigenvectors . . . . . . 23--45 Bertil Gustafsson and Heinz-Otto Kreiss Difference approximations of hyperbolic problems with different time scales. I. The reduced problem . . . . . . . . . . 46--58 Petter Bjòrstad Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles . . . . . . . . . . . . . . . 59--71 Murray Cantor Numerical Treatment of Potential Type Equations on $ \mathbb {R}^n $: Theoretical Considerations . . . . . . . 72--85 Zi Cai Li On the reduced rate of convergence for a nonconforming combined method . . . . . 86--93 Beny Neta and H. D. Victory, Jr. A new fourth-order finite-difference method for solving discrete-ordinates slab transport equations . . . . . . . . 94--105 Ira Bruce Schwartz Estimating regions of existence of unstable periodic orbits using computer-based techniques . . . . . . . 106--120 U. Ascher and S. Pruess and R. D. Russell On spline basis selection for solving differential equations . . . . . . . . . 121--142 S. McKee and A. Stokes Product integration methods for the nonlinear Basset equation . . . . . . . 143--160 William J. Layton Galerkin methods for two-point boundary value problems for first order systems 161--171 K. Atkinson and I. Graham and I. Sloan Piecewise continuous collocation for integral equations . . . . . . . . . . . 172--186 Thomas F. Coleman and Jorge J. Moré Estimation of sparse Jacobian matrices and graph coloring problems . . . . . . 187--209 G. Alefeld and L. Platzöder A Quadratically Convergent Krawczyk-Like Algorithm . . . . . . . . . . . . . . . 210--219
William J. Layton Stable Galerkin Methods for Hyperbolic Systems . . . . . . . . . . . . . . . . 221--233 Rainer Janssen A Generalization of Buchanan's Stability Criterion . . . . . . . . . . . . . . . 234--238 Tony F. Chan and Kenneth R. Jackson and Ben Ren Zhu Alternating-Direction Incomplete Factorizations . . . . . . . . . . . . . 239--257 H. I. El-Zorkany and R. Balasubramanian An Extension of the Alternating Direction Galerkin Method to More General Geometries . . . . . . . . . . . 258--278 Mitchell D. Smooke Error estimates for piecewise perturbation series solutions of the radial Schrödinger equation . . . . . . . 279--295 D. W. Decker and H. B. Keller and C. T. Kelley Convergence rates for Newton's method at singular points . . . . . . . . . . . . 296--314 George W. Johnson and Nieves H. Austria A quasi-Newton method employing direct secant updates of matrix factorizations 315--325 Alan George and Esmond Ng On row and column orderings for sparse least squares problems . . . . . . . . . 326--344 Stanley C. Eisenstat and Howard C. Elman and Martin H. Schultz Variational Iterative Methods for Nonsymmetric Systems of Linear Equations 345--357 Stanley C. Eisenstat A Note on the Generalized Conjugate Gradient Method . . . . . . . . . . . . 358--361 Olin G. Johnson and Charles A. Micchelli and George Paul Polynomial preconditioners for conjugate gradient calculations . . . . . . . . . 362--376 Nira Dyn and David Levin Iterative solution of systems originating from integral equations and surface interpolation . . . . . . . . . 377--390 William F. Moss The two-dimensional oscillating airfoil: a new implementation of the Galerkin method . . . . . . . . . . . . . . . . . 391--399 Avram Sidi and Doron S. Lubinsky On the zeros of some polynomials that arise in numerical quadrature and convergence acceleration . . . . . . . . 400--405 Patrick Keast and Julio C. Díaz Fully symmetric integration formulas for the surface of the sphere in $ {S} $ dimensions . . . . . . . . . . . . . . . 406--419 Lloyd N. Trefethen and Martin H. Gutknecht The Carathéodory--Fejér method for real rational approximation . . . . . . . . . 420--436
Peter Sammon Fully discrete approximation methods for parabolic problems with nonsmooth initial data . . . . . . . . . . . . . . 437--470 Pavol Sermer A Galerkin method for elliptic-hyperbolic type equations . . . 471--484 P. Ladev\`eze and D. Leguillon Error estimate procedure in the finite element method and applications . . . . 485--509 I. Babu\vska and J. E. Osborn Generalized finite element methods: their performance and their relation to mixed methods . . . . . . . . . . . . . 510--536 U. Ascher and R. Weiss Collocation for singular perturbation problems. I. First order systems with constant coefficients . . . . . . . . . 537--557 M. K. Horn Fourth- and fifth-order, scaled Runge--Kutta algorithms for treating dense output . . . . . . . . . . . . . . 558--568 E. Hairer and Ch. Lubich and S. P. Nòrsett Order of convergence of one-step methods for Volterra integral equations of the second kind . . . . . . . . . . . . . . 569--579 A. C. Genz and A. A. Malik An imbedded family of fully symmetric numerical integration rules . . . . . . 580--588 Avram Sidi and David Levin Prediction Properties of the $t$-Transformation . . . . . . . . . . . 589--598 James Demmel The condition number of equivalence transformations that block diagonalize matrix pencils . . . . . . . . . . . . . 599--610 Ji Guang Sun Perturbation analysis for the generalized singular value problem . . . 611--625 Trond Steihaug The conjugate gradient method and trust regions in large scale optimization . . 626--637 David M. Gay Computing Perturbation Bounds for Nonlinear Algebraic Equations . . . . . 638--651
K. P. Bube and J. C. Strikwerda Interior regularity estimates for elliptic systems of difference equations 653--670 M. Dryja A finite element - capacitance matrix method for the elliptic problem . . . . 671--680 Jim Douglas, Jr. Finite difference methods for two-phase incompressible flow in porous media . . 681--696 Karl Gustafson and Robert Hartman Divergence-free bases for finite element schemes in hydrodynamics . . . . . . . . 697--721 J. M. Boland and R. A. Nicolaides Stability of finite elements under divergence constraints . . . . . . . . . 722--731 James P. Fink and Werner C. Rheinboldt On the discretization error of parametrized nonlinear equations . . . . 732--746 A. Griewank and M. R. Osborne Analysis of Newton's method at irregular singularities . . . . . . . . . . . . . 747--773 N. Gaïtanos and A. Hadjidimos and A. Yeyios Optimum accelerated overrelaxation (AOR) method for systems with positive definite coefficient matrix . . . . . . 774--783 Youcef Saad Iterative solution of indefinite symmetric linear systems by methods using orthogonal polynomials over two disjoint intervals . . . . . . . . . . . 784--811 John D. Dixon Estimating extremal eigenvalues and condition numbers of matrices . . . . . 812--814 J. F. Andrus Automatic Integration of Systems of Second-Order ODE's Separated into Subsystems . . . . . . . . . . . . . . . 815--827 J. F. Andrus Convergence and accuracy properties of the method of quasilinearization . . . . 828--839 R. D. Skeel and L. W. Jackson The stability of variable-stepsize Nordsieck methods . . . . . . . . . . . 840--853 Larry L. Schumaker On Shape Preserving Quadratic Spline Interpolation . . . . . . . . . . . . . 854--864 Tien-Yien Li On Locating All Zeros of an Analytic Function within a Bounded Domain by a Revised Delves/Lyness Method . . . . . . 865--871 Alan George and Esmond Ng Erratum: ``On row and column orderings for sparse least squares problems'' [SIAM J. Numer. Anal. \bf 20 (1983), no. 2, 326--344] . . . . . . . . . . . . . . 872--872
Claudio Canuto and Hiroshi Fujii and Alfio Quarteroni Approximation of symmetry breaking bifurcations for the Rayleigh convection problem . . . . . . . . . . . . . . . . 873--884 A. B. Stephens and G. R. Shubin Existence and uniqueness for an exponentially derived switching scheme 885--889 Peter Markowich and Michael Renardy The numerical solution of a class of quasilinear parabolic Volterra equations arising in polymer rheology . . . . . . 890--908 David Gottlieb and Liviu Lustman The spectrum of the Chebyshev collocation operator for the heat equation . . . . . . . . . . . . . . . . 909--921 Juhani Pitkäranta and L. Ridgway Scott Error Estimates for the Combined Spatial and Angular Approximations of the Transport Equation for Slab Geometry . . 922--950 Claes Johnson and Juhani Pitkäranta Convergence of a fully discrete scheme for two-dimensional neutron transport 951--966 D. Braess and W. Hackbusch A new convergence proof for the multigrid method including the $ {V}$-cycle . . . . . . . . . . . . . . . 967--975 S. Z. Zhou The linear finite element method for a two-dimensional singular boundary value problem . . . . . . . . . . . . . . . . 976--984 Ricardo G. Durán On Polynomial Approximation in Sobolev Spaces . . . . . . . . . . . . . . . . . 985--988 S. W. Ellacott On the Faber transform and efficient numerical rational approximation . . . . 989--1000 C. T. Kelley and R. Suresh A new acceleration method for Newton's method at singular points . . . . . . . 1001--1009 Herbert Cornelius On the Acceleration of an Interval-Arithmetic Iteration Method . . 1010--1022 Charles W. Schelin Counting zeros of real polynomials within the unit disk . . . . . . . . . . 1023--1031 P. P. B. Eggermont Collocation for Volterra integral equations of the first kind with iterated kernel . . . . . . . . . . . . 1032--1048 P. H. M. Wolkenfelt On the relation between the repetition factor and numerical stability of direct quadrature methods for second kind Volterra integral equations . . . . . . 1049--1061 Narendra K. Jain and Kishore Singhal On Kublanovskaya's approach to the solution of the generalized latent value problem for functional $ \lambda $-matrices . . . . . . . . . . . . . . . 1062--1070 Germund G. Dahlquist and Werner Liniger and Olavi Nevanlinna Stability of two-step methods for variable integration steps . . . . . . . 1071--1085
Mario Ahués and Françoise Chatelin The Use of Defect Correction to Refine the Eigenelements of Compact Integral Operators . . . . . . . . . . . . . . . 1087--1093 Catherine Bandle Solutions of a nonlinear Dirichlet problem for nearly circular domains . . 1094--1098 C. Brezinski and J. P. Delahaye and B. Germain-Bonne Convergence acceleration by extraction of linear subsequences . . . . . . . . . 1099--1105 Hermann Brunner Nonpolynomial spline collocation for Volterra equations with weakly singular kernels . . . . . . . . . . . . . . . . 1106--1119 B. C. Carlson and John Todd The Degenerating Behavior of Elliptic Functions . . . . . . . . . . . . . . . 1120--1129 Germund Dahlquist On One-Leg Multistep Methods . . . . . . 1130--1138 C. de Boor and F. de Hoog and H. B. de Keller The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 1139--1146 Jean Descloux and Jacques Rappaz A Nonlinear Inverse Power Method with Shift . . . . . . . . . . . . . . . . . 1147--1152 Michael Eiermann and Wilhelm Niethammer On the Construction of Semiterative Methods . . . . . . . . . . . . . . . . 1153--1160 Irene Gargantini The Use of Linear Quadtrees in a Numerical Problem . . . . . . . . . . . 1161--1169 Walter Gautschi and Richard S. Varga Error bounds for Gaussian quadrature of analytic functions . . . . . . . . . . . 1170--1186 W. B. Gragg and D. D. Warner Two Constructive Results in Continued Fractions . . . . . . . . . . . . . . . 1187--1197 Martin H. Gutknecht On the computation of the conjugate trigonometric rational function and on a related splitting problem . . . . . . . 1198--1205 E. Hairer and G. Wanner On the Instability of the BDF Formulas 1206--1209 Rolf Jeltsch and Olavi Nevanlinna Stability of semidiscretizations of hyperbolic problems . . . . . . . . . . 1210--1218 William B. Jones and W. J. Thron and Haakon Waadeland Truncation error bounds for continued fractions $ {K}(a_n / 1) $ with parabolic element regions . . . . . . . 1219--1230 Werner Liniger The $ {A}$-contractive second-order multistep formulas with variable steps 1231--1238 J. T. Marti Evaluation of the least constant in Sobolev's inequality for $ H^1 (0, \, s) $ . . . . . . . . . . . . . . . . . . . 1239--1242 Jean Meinguet Refined Error Analyses of Cholesky Factorization . . . . . . . . . . . . . 1243--1250 Gilbert Strang and Arieh Iserles Barriers to Stability . . . . . . . . . 1251--1257 Lloyd N. Trefethen Circularity of the error curve and sharpness of the CF method in complex Chebyshev approximation . . . . . . . . 1258--1263 Jörg Waldvogel The Period in the Volterra--Lotka Predator-Prey Model . . . . . . . . . . 1264--1272 H. Werner and L. Wuytack On the Continuity of the Padé Operator 1273--1280 Garrett Birkhoff Salutation to Peter Henrici on his 60th Birthday: September 13, 1983 . . . . . . ??
Ami Harten and Peter D. Lax On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes . . . . . . . . . . . . . . . . 1--23 Peter Markowich and Michael Renardy Lax--Wendroff methods for hyperbolic history value problems . . . . . . . . . 24--51 G.-H. Cottet and P.-A. Raviart Particle methods for the one-dimensional Vlasov--Poisson equations . . . . . . . 52--76 J. M. Sanz-Serna and L. Abia Interpolation of the Coefficients in Nonlinear Elliptic Galerkin Procedures 77--83 E. C. Gartland, Jr. Computable pointwise error bounds and the Ritz method in one dimension . . . . 84--100 Miente Bakker One-dimensional Galerkin methods and superconvergence at interior nodal points . . . . . . . . . . . . . . . . . 101--110 E. H. Twizell and A. Q. M. Khaliq Multiderivative methods for periodic initial value problems . . . . . . . . . 111--122 E. Hairer and Ch. Lubich On the Stability of Volterra--Runge--Kutta Methods . . . . . 123--135 David Elliott Rates of convergence for the method of classical collocation for solving singular integral equations . . . . . . 136--148 Philip Rabinowitz and Ian H. Sloan Product Integration in the Presence of a Singularity . . . . . . . . . . . . . . 149--166 Martin Kütz Asymptotic Error Bounds for a Class of Interpolatory Quadratures . . . . . . . 167--175 A. Griewank and G. W. Reddien Characterization and computation of generalized turning points . . . . . . . 176--185 C. C. Paige A note on a result of Sun Ji Guang: sensitivity of the CS and GSV decompositions . . . . . . . . . . . . . 186--191 P. Albrecht and M. P. Klein Extrapolated Iterative Methods for Linear Systems . . . . . . . . . . . . . 192--201 J. D. Pryce A New Measure of Relative Error for Vectors . . . . . . . . . . . . . . . . 202--215
Stanley Osher Riemann solvers, the entropy condition, and difference approximations . . . . . 217--235 Craig C. Douglas Multi-grid algorithms with applications to elliptic boundary value problems . . 236--254 S. F. McCormick Multigrid methods for variational problems: further results . . . . . . . 255--263 R. Verfürth A Multilevel Algorithm for Mixed Problems . . . . . . . . . . . . . . . . 264--271 Tony F. Chan Stability analysis of finite difference schemes for the advection-diffusion equation . . . . . . . . . . . . . . . . 272--284 Anita Mayo The fast solution of Poisson's and the biharmonic equations on irregular regions . . . . . . . . . . . . . . . . 285--299 E. J. Doedel and G. W. Reddien Finite difference methods for singular two-point boundary value problems . . . 300--313 Graeme Fairweather and Patrick Keast and Julio César Díaz On the $ {H}^{-1}$-Galerkin method for second-order linear two-point boundary value problems . . . . . . . . . . . . . 314--326 C. A. Addison and W. H. Enright Properties of multistep formulas intended for a class of second order ODEs . . . . . . . . . . . . . . . . . . 327--339 Arieh Iserles Composite methods for numerical solution of stiff systems of ODEs . . . . . . . . 340--351 Vance Faber and Thomas Manteuffel Necessary and sufficient conditions for the existence of a conjugate gradient method . . . . . . . . . . . . . . . . . 352--362 G. Alefeld On the convergence of some interval-arithmetic modifications of Newton's method . . . . . . . . . . . . 363--372 Rolf E. Müller Computations of holomorphic multiparameter eigenvalue problems . . . 373--387 B. Werner and A. Spence The computation of symmetry-breaking bifurcation points . . . . . . . . . . . 388--399 Ronald A. DeVore and L. Ridgway Scott Error bounds for Gaussian quadrature and weighted-$ {L}^1 $ \ polynomial approximation . . . . . . . . . . . . . 400--412
Robert L. Higdon Boundary conditions for suppressing rapidly moving components in hyperbolic systems . . . . . . . . . . . . . . . . 413--432 J. R. Cash Two new finite difference schemes for parabolic equations . . . . . . . . . . 433--446 John C. Strikwerda An iterative method for solving finite difference approximations to the Stokes equations . . . . . . . . . . . . . . . 447--458 Douglas N. Arnold and Jukka Saranen On the asymptotic convergence of spline collocation methods for partial differential equations . . . . . . . . . 459--472 Anne Greenbaum Analysis of a multigrid method as an iterative technique for solving linear systems . . . . . . . . . . . . . . . . 473--485 Zdzis\law Jackiewicz One-Step Methods of any Order for Neutral Functional Differential Equations . . . . . . . . . . . . . . . 486--511 M. Crouzeix and F. J. Lisbona The convergence of variable-stepsize, variable-formula, multistep methods . . 512--534 George Majda Filtering techniques for systems of stiff ordinary differential equations. I 535--566 Françoise Chatelin and Willard L. Miranker Aggregation/Disaggregation for Eigenvalue Problems . . . . . . . . . . 567--582 T. J. Ypma Local Convergence of Inexact Newton Methods . . . . . . . . . . . . . . . . 583--590 A. Boja\'nczyk Complexity of solving linear systems in different models of computation . . . . 591--603 María-Cecilia Rivara Mesh Refinement Processes Based on the Generalized Bisection of Simplices . . . 604--613
P. Constantin and C. Foia\cs and R. Temam On the large time Galerkin approximation of the Navier--Stokes equations . . . . 615--634 P. J. van der Houwen Iterated Splitting Methods of High Order for Time-Dependent Partial Differential Equations . . . . . . . . . . . . . . . 635--656 Jean-François Maitre and François Musy Multigrid methods: convergence theory in a variational framework . . . . . . . . 657--671 Linda Kaufman and Daniel D. Warner High-order, fast-direct methods for separable elliptic equations . . . . . . 672--694 W. R. Dyksen and E. N. Houstis and R. E. Lynch and J. R. Rice The performance of the collocation and Galerkin methods with Hermite bicubics 695--715 C. W. Gear and L. R. Petzold ODE Methods for the Solution of Differential/Algebraic Systems . . . . . 716--728 Manfred R. Trummer A method for solving ill-posed linear operator equations . . . . . . . . . . . 729--737 Tony F. Chan Deflated decomposition of solutions of nearly singular systems . . . . . . . . 738--754 Thomas F. Coleman and Andrew R. Conn On the local convergence of a quasi-Newton method for the nonlinear programming problem . . . . . . . . . . 755--769 Stephen G. Nash Newton-type minimization via the Lánczos method . . . . . . . . . . . . . . . . . 770--788 Dennis D. Cox Multivariate Smoothing Spline Functions 789--813
Robert B. Schnabel and Paul D. Frank Tensor Methods for Nonlinear Equations 815--843 Alan Feldstein and Kenneth W. Neves High order methods for state-dependent delay differential equations with nonsmooth solutions . . . . . . . . . . 844--863 Christian Ringhofer On collocation schemes for quasilinear singularly perturbed boundary value problems . . . . . . . . . . . . . . . . 864--882 Peter C. Meek and John Norbury Nonlinear moving boundary problems and a Keller box scheme . . . . . . . . . . . 883--893 Irena Lasiecka Convergence estimates for semidiscrete approximations of nonselfadjoint parabolic equations . . . . . . . . . . 894--909 W. G. Szymczak and I. Babu\vska Adaptivity and error estimation for the finite element method applied to convection diffusion problems . . . . . 910--954 Stanley Osher and Sukumar Chakravarthy High Resolution Schemes and the Entropy Condition . . . . . . . . . . . . . . . 955--984 A. Y. Le Roux and P. Quesseveur Convergence of an Antidiffusion Lagrange--Euler Scheme for Quasi-Linear Equations . . . . . . . . . . . . . . . 985--994 P. K. Sweby High resolution schemes using flux limiters for hyperbolic conservation laws . . . . . . . . . . . . . . . . . . 995--1011
Yann Brenier Averaged multivalued solutions for scalar conservation laws . . . . . . . . 1013--1037 Jens Lorenz Analysis of difference schemes for a stationary shock problem . . . . . . . . 1038--1053 Joseph W. Jerome Fully discrete stability and invariant rectangular regions for reaction-diffusion systems . . . . . . . 1054--1065 James F. Epperson Finite element methods for a class of nonlinear evolution equations . . . . . 1066--1079 Anatoly M. Genis On finite element methods for the Euler--Poisson--Darboux equation . . . . 1080--1106 Per Erik Koch Collocation by $ {L}$-Splines at Transformed Gaussian Points . . . . . . 1107--1114 David R. Dellwo and Morton B. Friedman Accelerated Spectral Analysis of Compact Operators . . . . . . . . . . . . . . . 1115--1131 Hermann Brunner Iterated collocation methods and their discretizations for Volterra integral equations . . . . . . . . . . . . . . . 1132--1145 Paul T. Boggs and Jon W. Tolle A family of descent functions for constrained optimization . . . . . . . . 1146--1161 Andrew R. Conn and Nicholas I. M. Gould On the location of directions of infinite descent for nonlinear programming algorithms . . . . . . . . . 1162--1179 Milo R. Dorr The approximation theory for the $p$-version of the finite element method 1180--1207
Michael Brannigan Discrete Chebyshev approximation with linear constraints . . . . . . . . . . . 1--15 William W. Hager Approximations to the Multiplier Method 16--46 Gerald A. Shultz and Robert B. Schnabel and Richard H. Byrd A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties . . . . . . . . . 47--67 Jòrgen Hald and Kaj Madsen Combined LP and quasi-Newton methods for nonlinear $ {L}_1 $ optimization . . . . 68--80 Alexander Shapiro Optimal block diagonal $ {L}_2$-scaling of matrices . . . . . . . . . . . . . . 81--94 Peter Alfeld Multivariate Perpendicular Interpolation 95--106 J. R. Busch Osculatory Interpolation in $ \mathbb {R}^n $ . . . . . . . . . . . . . . . . 107--113 Suchitra Gupta An adaptive boundary value Runge--Kutta solver for first order boundary value problems . . . . . . . . . . . . . . . . 114--126 M. M. Chawla On the order and attainable intervals of periodicity of explicit Nyström methods for $ y = f(t, y) $ . . . . . . . . . . 127--131 Daniel S. Watanabe and Mitchell G. Roth The stability of difference formulas for delay differential equations . . . . . . 132--145 Seymour V. Parter and Michael Steuerwalt Block iterative methods for elliptic finite element equations . . . . . . . . 146--179 Bradley J. Lucier A stable adaptive numerical scheme for hyperbolic conservation laws . . . . . . 180--203 Peter Markowich and Michael Renardy Corrigenda: ``Lax--Wendroff Methods for Hyperbolic History Value Problems'' [SIAM J. Numer. Anal. \bf 21 (1984), no. 1, 24--51] . . . . . . . . . . . . . . . 204--204
R. E. White The binary alloy problem: existence, uniqueness, and numerical approximation 205--244 Jeffrey Rauch On convergence of the finite element method for the wave equation . . . . . . 245--249 George J. Fix and Milton E. Rose A comparative study of finite element and finite difference methods for Cauchy--Riemann type equations . . . . . 250--261 H. Weber Multigrid Bifurcation Iteration . . . . 262--279 Marianela Lentini and Michael R. Osborne and Robert D. Russell The close relationships between methods for solving two-point boundary value problems . . . . . . . . . . . . . . . . 280--309 T. Nanda Differential Equations and the $ {QR} $ Algorithm . . . . . . . . . . . . . . . 310--321 Eugene L. Allgower and Phillip H. Schmidt An algorithm for piecewise-linear approximation of an implicitly defined manifold . . . . . . . . . . . . . . . . 322--346 A. Jepson and A. Spence Folds in Solutions of Two Parameter Systems and Their Calculation. Part I 347--368 A. M. Erisman and R. G. Grimes and J. G. Lewis and W. G. Poole, Jr. A structurally stable modification of Hellerman--Rarick's $ P^4 $ algorithm for reordering unsymmetric sparse matrices . . . . . . . . . . . . . . . . 369--385 R. E. Carlson and F. N. Fritsch Monotone Piecewise Bicubic Interpolation 386--400 R. K. Beatson and Z. Ziegler Monotonicity Preserving Surface Interpolation . . . . . . . . . . . . . 401--411
Christopher Anderson and Claude Greengard On Vortex Methods . . . . . . . . . . . 413--440 Tony F. Chan and Tom Kerkhoven Fourier methods with extended stability intervals for the Korteweg--de Vries equation . . . . . . . . . . . . . . . . 441--454 Christine Bernardi and Genevi\`eve Raugel A conforming finite element method for the time-dependent Navier--Stokes equations . . . . . . . . . . . . . . . 455--473 J. M. Boland and R. A. Nicolaides Stable and semistable low order finite elements for viscous flows . . . . . . . 474--492 Luisa Donatella Marini An inexpensive method for the evaluation of the solution of the lowest order Raviart--Thomas mixed method . . . . . . 493--496 Reinhard Frank and Josef Schneid and Christoph W. Ueberhuber Stability properties of implicit Runge--Kutta methods . . . . . . . . . . 497--514 Reinhard Frank and Josef Schneid and Christoph W. Ueberhuber Order results for implicit Runge--Kutta methods applied to stiff systems . . . . 515--534 I. Gladwell and R. M. Thomas A qualitative analysis of two- and three-step methods for stable second order systems . . . . . . . . . . . . . 535--560 M. M. Chawla and C. P. Katti A uniform mesh finite difference method for a class of singular two-point boundary value problems . . . . . . . . 561--565 D. W. Decker and C. T. Kelley Broyden's method for a class of problems having singular Jacobian at the root . . 566--574 Avi Vardi A trust region algorithm for equality constrained minimization: convergence properties and implementation . . . . . 575--591 R. Farwig Multivariate truncated powers and $ {B}$-splines with coalescent knots . . . 592--603 R. Krawczyk and A. Neumaier Interval slopes for rational functions and associated centered forms . . . . . 604--616
Randolph E. Bank and Craig C. Douglas Sharp estimates for multigrid rates of convergence with general smoothing and acceleration . . . . . . . . . . . . . . 617--633 S. F. McCormick Multigrid methods for variational problems: general theory for the $ {V}$-cycle . . . . . . . . . . . . . . . 634--643 Alexander Bogomolny Fundamental solutions method for elliptic boundary value problems . . . . 644--669 Tzu Chu Lin The numerical solution of Helmholtz's equation for the exterior Dirichlet problem in three dimensions . . . . . . 670--686 David Hoff A scheme for computing solutions and interface curves for a doubly-degenerate parabolic equation . . . . . . . . . . . 687--712 Richard Sanders The moving grid method for nonlinear hyperbolic conservation laws . . . . . . 713--728 James P. Fink and Werner C. Rheinboldt Local error estimates for parametrized nonlinear equations . . . . . . . . . . 729--735 Allan D. Jepson and Alastair Spence The numerical solution of nonlinear equations having several parameters. I. Scalar equations . . . . . . . . . . . . 736--759 J. E. Dennis, Jr. and Homer F. Walker Least-change sparse secant update methods with inaccurate secant conditions . . . . . . . . . . . . . . . 760--778 Maharaja C. Pandian A convergence test and componentwise error estimates for Newton type methods 779--791 Hartmut Schwandt Krawczyk-like algorithms for the solution of systems of nonlinear equations . . . . . . . . . . . . . . . 792--810 Gary Herron A characterization of certain $ {C}^1 $ discrete triangular interpolants . . . . 811--819
Jorge Nocedal and Michael L. Overton Projected Hessian updating algorithms for nonlinearly constrained optimization 821--850 Charles Van Loan On the method of weighting for equality-constrained least-squares problems . . . . . . . . . . . . . . . . 851--864 Achiya Dax Successive Refinement of Large Multicell Models . . . . . . . . . . . . . . . . . 865--887 Patricio Basso Optimal search for the global maximum of functions with bounded seminorm . . . . 888--903 Tony F. Chan An approximate Newton method for coupled nonlinear systems . . . . . . . . . . . 904--913 A. Neumaier Residual inverse iteration for the nonlinear eigenvalue problem . . . . . . 914--923 Kenneth P. Bube Convergence of numerical inversion methods for discontinuous impedance profiles . . . . . . . . . . . . . . . . 924--946 Stanley Osher Convergence of Generalized MUSCL Schemes 947--961 Jim Douglas, Jr. Superconvergence in the pressure in the simulation of miscible displacement . . 962--969 Thomas F. Russell Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media . . . . . . . . . . . . 970--1013 Lawrence F. Shampine Interpolation for Runge--Kutta Methods 1014--1027 Graham F. Carey and Hung T. Dinh Grading Functions and Mesh Redistribution . . . . . . . . . . . . . 1028--1040
John B. Bell and Gregory R. Shubin and Mary Fanett Wheeler Analysis of a new method for computing the flow of miscible fluids in a porous medium . . . . . . . . . . . . . . . . . 1041--1050 Randall J. Leveque A large time step generalization of Godunov's method for systems of conservation laws . . . . . . . . . . . 1051--1073 Bradley J. Lucier Error bounds for the methods of Glimm, Godunov and LeVeque . . . . . . . . . . 1074--1081 I. Norman Katz and Douglas W. Wang The $p$-version of the finite element method for problems requiring $ {C}^1$-continuity . . . . . . . . . . . 1082--1106 John R. Baumgardner and Paul O. Frederickson Icosahedral Discretization of the Two-Sphere . . . . . . . . . . . . . . . 1107--1115 George Majda Filtering techniques for systems of stiff ordinary differential equations. II. Error estimates . . . . . . . . . . 1116--1134 Marino Zennaro One-step collocation: uniform superconvergence, predictor-corrector method, local error estimate . . . . . . 1135--1152 John R. Klauder and Wesley P. Petersen Numerical integration of multiplicative-noise stochastic differential equations . . . . . . . . . 1153--1166 S. Joe Discrete collocation methods for second kind Fredholm integral equations . . . . 1167--1177 C. R. Morrow and T. N. L. Patterson The construction of algebraic cubature formulae by the distribution of nodes along selected lines . . . . . . . . . . 1178--1190 Bruno Gabutti An asymptotic approximation for a class of oscillatory infinite integrals . . . 1191--1199 J. M. Shearer and M. A. Wolfe Some computable existence, uniqueness, and convergence tests for nonlinear systems . . . . . . . . . . . . . . . . 1200--1207 Stanis\law M. Grzegórski Orthogonal projections on convex sets for Newton-like methods . . . . . . . . 1208--1219 S. C. Eisenstat and K. R. Jackson and J. W. Lewis The Order of Monotone Piecewise Cubic Interpolation . . . . . . . . . . . . . 1220--1237 Daniel Lee On remainders and asymptotic error expansions in cardinal spline interpolation . . . . . . . . . . . . . 1238--1242 David L. Ragozin The discrete $k$-functional and spline smoothing of noisy data . . . . . . . . 1243--1254 Suchitra Gupta Corrigenda: ``An adaptive boundary value Runge--Kutta solver for first order boundary value problems'' [SIAM J. Numer. Anal. \bf 22 (1985), no. 1, 114--126] . . . . . . . . . . . . . . . 1255--1255
Eitan Tadmor The exponential accuracy of Fourier and Chebyshev differencing methods . . . . . 1--10 Hillel Tal-Ezer Spectral Methods in Time for Hyperbolic Equations . . . . . . . . . . . . . . . 11--26 Laurence A. Bales Higher order single step fully discrete approximations for second order hyperbolic equations with time dependent coefficients . . . . . . . . . . . . . . 27--43 Howard C. Elman and Martin H. Schultz Preconditioning by fast direct methods for nonselfadjoint nonseparable elliptic equations . . . . . . . . . . . . . . . 44--57 Milo R. Dorr The approximation of solutions of elliptic boundary-value problems via the $p$-version of the finite element method 58--77 H. D. Victory, Jr. and Keshab Ganguly On finite-difference methods for solving discrete-ordinates transport equations 78--108 C. R. Vogel Optimal choice of a truncation level for the truncated SVD solution of linear first kind integral equations when data are noisy . . . . . . . . . . . . . . . 109--117 Robert Whitley The stability of finite rank methods with applications to integral equations 118--134 George Miel On the Galerkin and collocation methods for a Cauchy singular integral equation 135--143 Mario Ahués and Mauricio Telias Refinement Methods of Newton Type for Approximate Eigenelements of Integral Operators . . . . . . . . . . . . . . . 144--159 E. L. Allgower and K. Böhmer and F.-A. Potra and W. C. Rheinboldt A mesh-independence principle for operator equations and their discretizations . . . . . . . . . . . . 160--169 J. L. Nazareth Analogues of Dixon's and Powell's theorems for unconstrained minimization with inexact line searches . . . . . . . 170--177 Avram Sidi and William F. Ford and David A. Smith Acceleration of Convergence of Vector Sequences . . . . . . . . . . . . . . . 178--196 Avram Sidi Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms . . . . . . . . 197--209 Patricia Hillhouse Finney and Thomas E. Price, Jr. Minimum norm quadratures which satisfy nonstandard interpolating conditions . . 210--216 J. Garloff and R. Krawczyk Optimal Inclusion of a Solution Set . . 217--226
Kenneth P. Bube Numerical methods for reflection inverse problems: convergence and nonimpulsive sources . . . . . . . . . . . . . . . . 227--258 Yann Brenier and Stanley Osher Approximate Riemann solvers and numerical flux functions . . . . . . . . 259--273 Tony F. Chan and Ding Lee and Long Jun Shen Stable explicit schemes for equations of the Schrödinger type . . . . . . . . . . 274--281 C. E. Greenwell-Yanik and G. Fairweather Analyses of Spline Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables . . . . . . . . . . 282--296 Warren E. Ferguson, Jr. The rate of convergence of a class of block Jacobi schemes . . . . . . . . . . 297--303 Hartmut Schwandt Almost globally convergent interval methods for discretizations of nonlinear elliptic partial differential equations 304--324 Heinz-Otto Kreiss and N. K. Nichols and David L. Brown Numerical methods for stiff two-point boundary value problems . . . . . . . . 325--368 Martin Stynes and Eugene O'Riordan A uniformly accurate finite element method for a singular perturbation problem in conservative form . . . . . . 369--375 John Paine and Robert D. Russell Conditioning of collocation matrices and discrete Green's functions . . . . . . . 376--392 Robert D. Skeel The order of accuracy for deferred corrections using uncentered end formulas . . . . . . . . . . . . . . . . 393--402 Kenneth Eriksson Some error estimates for the $p$-version of the finite element method . . . . . . 403--411 U. Ascher and G. Bader Stability of Collocation at Gaussian Points . . . . . . . . . . . . . . . . . 412--422 Zdzis\law Jackiewicz Quasilinear Multistep Methods and Variable Step Predictor-Corrector Methods for Neutral Functional Differential Equations . . . . . . . . . 423--452 Edwin H. Kaufman, Jr. The behavior of differential correction in difficult situations . . . . . . . . 453--460
P. Charrier and B. Tessieras On front-tracking methods applied to hyperbolic systems of nonlinear conservation laws . . . . . . . . . . . 461--472 A. Q. M. Khaliq and E. H. Twizell $ {L}_0$-Stable Splitting Methods for the Simple Heat Equation in Two Space Dimensions with Homogeneous Boundary Conditions . . . . . . . . . . . . . . . 473--484 J. A. C. Weideman and B. M. Herbst Split-step methods for the solution of the nonlinear Schrödinger equation . . . 485--507 Peter H. Sammon Numerical approximations for a miscible displacement process in porous media . . 508--542 Mohammad Asadzadeh Analysis of a fully discrete scheme for neutron transport in two-dimensional geometry . . . . . . . . . . . . . . . . 543--561 M. Lenoir Optimal isoparametric finite elements and error estimates for domains involving curved boundaries . . . . . . 562--580 Harry Yserentant On the Multi-Level Splitting of Finite Element Spaces for Indefinite Elliptic Boundary Value Problems . . . . . . . . 581--595 Uri Ascher Collocation for two-point boundary value problems revisited . . . . . . . . . . . 596--609 Peter N. Brown and Alan C. Hindmarsh Matrix-Free Methods for Stiff Systems of ODE's . . . . . . . . . . . . . . . . . 610--638 R. E. White A nonlinear parallel algorithm with application to the Stefan problem . . . 639--652 Rong Qing Jia Spline Interpolation at a Bi-Infinite Knot Sequence . . . . . . . . . . . . . 653--662 T. Lyche and K. Mòrken Making the OSLO Algorithm More Efficient 663--675 Johannes W. Wissmann and Thomas Becker Partially Symmetric Cubature Formulas for Even Degrees of Exactness . . . . . 676--685 Dragoslav Herceg and Ljiljana Cvetkovi\'c On a Numerical Differentiation . . . . . 686--691
James P. Fink and Werner C. Rheinboldt Folds on the solution manifold of a parametrized equation . . . . . . . . . 693--706 L. Grippo and F. Lampariello and S. Lucidi A nonmonotone line search technique for Newton's method . . . . . . . . . . . . 707--716 J. E. Dennis, Jr. and Trond Steihaug On the successive projections approach to least-squares problems . . . . . . . 717--733 Jaime Guerra and Bertil Gustafsson A semi-implicit method for hyperbolic problems with different time-scales . . 734--749 John G. Heywood and Rolf Rannacher Finite Element Approximation of the Nonstationary Navier--Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time . . . . 750--777 Slimane Adjerid and Joseph E. Flaherty A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations . . . . . . . . . 778--796 A. J. Wathen Mesh-Independent Spectra in the Moving Finite Element Equations . . . . . . . . 797--814 Claudio Canuto Boundary conditions in Chebyshev and Legendre methods . . . . . . . . . . . . 815--831 Rolf Dieter Grigorieff On the Convergence of Stability Constants . . . . . . . . . . . . . . . 832--836 L. R. Petzold Order Results for Implicit Runge--Kutta Methods Applied to Differential/Algebraic Systems . . . . . 837--852 Manfred R. Trummer An efficient implementation of a conformal mapping method based on the Szeg\Ho kernel . . . . . . . . . . . . . 853--872 W. G. Hawkins and H. H. Barrett A numerically stable circular harmonic reconstruction algorithm . . . . . . . . 873--890 Apostolos Gerasoulis Piecewise-polynomial quadratures for Cauchy singular integrals . . . . . . . 891--902 R. K. Beatson On the convergence of some cubic spline interpolation schemes . . . . . . . . . 903--912
Tony F. Chan and Diana C. Resasco Generalized Deflated Block-Elimination 913--924 C. de Boor and F. de Hoog Stability of Finite Difference Schemes for Two-Point Boundary Value Problems 925--935 C. de Boor and H.-O. Kreiss On the Condition of the Linear Systems Associated with Discretized BVPs of ODEs 936--939 Warren E. Ferguson, Jr. Analysis of a singularly-perturbed linear two-point boundary value problem 940--947 Thomas M. Hagstrom Asymptotic expansions and boundary conditions for time-dependent problems 948--958 A. D. Jepson and D. W. Decker Convergence Cones Near Bifurcation . . . 959--975 James P. Keener The Sarkovski\uì Sequence and Stable Periodic Orbits of Maps of the Interval 976--985 P. E. Kloeden and J. Lorenz Stable attracting sets in dynamical systems and in their one-step discretizations . . . . . . . . . . . . 986--995 Thomas A. Manteuffel and Andrew B. White, Jr. On the efficient numerical solution of systems of second order boundary value problems . . . . . . . . . . . . . . . . 996--1006 Hans D. Mittelmann A pseudo-arclength continuation method for nonlinear eigenvalue problems . . . 1007--1016 Paul Nelson Convergence of inner iterations for finite-difference approximations to the linear transport equation . . . . . . . 1017--1022 M. R. Osborne and R. D. Russell The Riccati transformation in the solution of boundary value problems . . 1023--1033 Michael B. Porter and Edward L. Reiss A note on the relationship between finite-difference and shooting methods for ODE eigenvalue problems . . . . . . 1034--1039 P. J. Rabier and G. W. Reddien Characterization and computation of singular points with maximum rank deficiency . . . . . . . . . . . . . . . 1040--1051 I. H. Sloan and V. Thomée Time discretization of an integro-differential equation of parabolic type . . . . . . . . . . . . . 1052--1061 Ewa Weinmüller Collocation for Singular Boundary Value Problems of Second Order . . . . . . . . 1062--1095 Eugene Isaacson Dedication . . . . . . . . . . . . . . . i--i
Petter E. Bjòrstad and Olof B. Widlund Iterative methods for the solution of elliptic problems on regions partitioned into substructures . . . . . . . . . . . 1097--1120 Thomas Kerkhoven A proof of convergence of Gummel's algorithm for realistic device geometries . . . . . . . . . . . . . . . 1121--1137 N. Bressan and A. Quarteroni Analysis of Chebyshev collocation methods for parabolic equations . . . . 1138--1154 Peter Monk Error estimates for a numerical method for an ill-posed Cauchy problem for the heat equation . . . . . . . . . . . . . 1155--1172 J. P. Vila Simplified Godunov schemes for $ 2 \times 2 $ systems of conservation laws 1173--1192 Liviu Lustman The time evolution of spectral discretizations of hyperbolic systems 1193--1198 Rudolf Wegmann On Fornberg's Numerical Method for Conformal Mapping . . . . . . . . . . . 1199--1213 G. A. Chandler Superconvergent approximations to the solution of a boundary integral equation on polygonal domains . . . . . . . . . . 1214--1229 P. D. Robinson and P. K. Yuen Bivariational methods for linear integral equations with nonsymmetric kernels . . . . . . . . . . . . . . . . 1230--1240 Alan E. Berger A conservative uniformly accurate difference method for a singular perturbation problem in conservation form . . . . . . . . . . . . . . . . . . 1241--1253 Maarten de Gee Asymptotic Expansions for the Midpoint Rule Applied to Delay Differential Equations . . . . . . . . . . . . . . . 1254--1272 Alan Genz Fully symmetric interpolatory rules for multiple integrals . . . . . . . . . . . 1273--1283 Catterina Dagnino Extensions of some results for interpolatory product integration rules to rules not necessarily of interpolatory type . . . . . . . . . . . 1284--1289 Graziano Vincenti On the computation of the coefficients of $s$-orthogonal polynomials . . . . . 1290--1294 W. Govaerts The Geodesics of Pryce's Relative Distance in $ \mathbb {R}^2_\infty $ . . 1295--1302
Rolf Jeltsch and J. H. Smit Accuracy barriers of two time level difference schemes for hyperbolic equations . . . . . . . . . . . . . . . 1--11 Kenneth Eriksson and Claes Johnson Error estimates and automatic time step control for nonlinear parabolic problems. I . . . . . . . . . . . . . . 12--23 C. V. Pao Numerical Methods for Semilinear Parabolic Equations . . . . . . . . . . 24--35 Kenneth L. Bowers and John Lund Numerical solution of singular Poisson problems via the sinc-Galerkin method 36--51 E. M. Harrell and W. J. Layton $ {L}^2 $ estimates for Galerkin methods for semilinear elliptic equations . . . 52--58 Wayne R. Dyksen Tensor product generalized ADI methods for separable elliptic problems . . . . 59--76 Ronghua Li Generalized Difference Methods for a Nonlinear Dirichlet Problem . . . . . . 77--88 F. R. de Hoog and R. M. M. Mattheij On Dichotomy and Well Conditioning in BVP . . . . . . . . . . . . . . . . . . 89--105 K. Burrage High order algebraically stable multistep Runge--Kutta methods . . . . . 106--115 Ian H. Sloan and Philip J. Kachoyan Lattice methods for multiple integration: theory, error analysis and examples . . . . . . . . . . . . . . . . 116--128 J. C. Alexander Average Intersection and Pivoting Densities . . . . . . . . . . . . . . . 129--146 Kurt Jetter Uniqueness of Gauss--Birkhoff Quadrature Formulas . . . . . . . . . . . . . . . . 147--154 Youcef Saad Least squares polynomials in the complex plane and their use for solving nonsymmetric linear systems . . . . . . 155--169 Vance Faber and Thomas A. Manteuffel Orthogonal Error Methods . . . . . . . . 170--187 Bradley N. Parsons General $k$-part stationary iterative solutions to linear systems . . . . . . 188--198 James Weldon Demmel The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems . . . . . . 199--206 A. Neumaier Overestimation in Linear Interval Equations . . . . . . . . . . . . . . . 207--214 Günter Mayer Comparison Theorems for Iterative Methods Based on Strong Splittings . . . 215--227 A. Cuyt A recursive computation scheme for multivariate rational interpolants . . . 228--239
David Gottlieb and Liviu Lustman and Eitan Tadmor Stability analysis of spectral methods for hyperbolic initial-boundary value systems . . . . . . . . . . . . . . . . 241--256 Richard S. Falk and Gerard R. Richter Analysis of a continuous finite element method for hyperbolic equations . . . . 257--278 Ami Harten and Stanley Osher Uniformly high-order accurate nonoscillatory schemes. I . . . . . . . 279--309 Georges H. Guirguis On the coupling boundary integral and finite element methods for the exterior Stokes problem in $3$-D . . . . . . . . 310--322 Alfio Quarteroni Fourier spectral methods for pseudoparabolic equations . . . . . . . 323--335 Tony F. Chan and Long Jun Shen Stability analysis of difference schemes for variable coefficient Schrödinger type equations . . . . . . . . . . . . . . . 336--349 Neil M. Wigley Stress intensity factors and improved convergence estimates at a corner . . . 350--354 R. A. Nicolaides Deflation of conjugate gradients with applications to boundary value problems 355--365 David Kamowitz and Seymour V. Parter On $ \mathrm {MGR} \lbrack \nu \rbrack $ Multigrid Methods . . . . . . . . . . . 366--381 Tony F. Chan Analysis of Preconditioners for Domain Decomposition . . . . . . . . . . . . . 382--390 Peter Albrecht A New Theoretical Approach to Runge--Kutta Methods . . . . . . . . . . 391--406 Peter N. Brown A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods . . . . . . . . . . . 407--434 Tien-Yien Li and Tim Sauer and James A. Yorke Numerical solution of a class of deficient polynomial systems . . . . . . 435--451 Eugene L. Allgower and Stefan Gnutzmann An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces . . . . . . . . 452--469 C. W. Clenshaw and F. W. J. Olver Level-Index Arithmetic Operations . . . 470--485
Zi-Cai Li and Rudolf Mathon and Pavol Sermer Boundary methods for solving elliptic problems with singularities and interfaces . . . . . . . . . . . . . . . 487--498 John R. Cannon and Salvador Pérez Esteva and John van der Hoek A Galerkin procedure for the diffusion equation subject to the specification of mass . . . . . . . . . . . . . . . . . . 499--515 C. T. Kelley and E. W. Sachs A quasi-Newton method for elliptic boundary value problems . . . . . . . . 516--531 David Gottlieb and Liviu Lustman and Eitan Tadmor Convergence of spectral methods for hyperbolic initial-boundary value systems . . . . . . . . . . . . . . . . 532--537 Ole H. Hald Convergence of vortex methods for Euler's equations. III . . . . . . . . . 538--582 W. H. Hundsdorfer and M. N. Spijker On the algebraic equations in implicit Runge--Kutta methods . . . . . . . . . . 583--594 P. J. van der Houwen and B. P. Sommeijer Explicit Runge--Kutta (-Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions . . . . . . . . . 595--617 James P. Fink and Werner C. Rheinboldt A geometric framework for the numerical study of singular points . . . . . . . . 618--633 S. Friedland and J. Nocedal and M. L. Overton The formulation and analysis of numerical methods for inverse eigenvalue problems . . . . . . . . . . . . . . . . 634--667 Ming Kui Chen On the Solution of Circulant Linear Systems . . . . . . . . . . . . . . . . 668--683 Andreas Griewank The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert spaces . . . . . . . . . . . . . 684--705 R. H. J. Gmelig Meyling An algorithm for constructing configurations of knots for bivariate $ {B}$-splines . . . . . . . . . . . . . . 706--724 Günter Baszenski and Larry L. Schumaker On a Method for Fitting an Unknown Function Based on Mean-Value Measurements . . . . . . . . . . . . . . 725--736
Peter Monk A mixed finite element method for the biharmonic equation . . . . . . . . . . 737--749 I. Babu\vska and Manil Suri The Optimal Convergence Rate of the $p$-Version of the Finite Element Method 750--776 Randolph E. Bank and Donald J. Rose Some Error Estimates for the Box Method 777--787 Donald A. French The finite element method for a degenerate elliptic equation . . . . . . 788--815 K. Ruotsalainen and J. Saranen Some boundary element methods using Dirac's distributions as trial functions 816--827 Christopher Beattie An extension of Aronszajn's rule: slicing the spectrum for intermediate problems . . . . . . . . . . . . . . . . 828--843 M. Calvo and F. Lisbona and J. Montijano On the stability of variable-stepsize Nordsieck BDF methods . . . . . . . . . 844--854 Terje O. Espelid On the construction of good fully symmetric integration rules . . . . . . 855--881 Thomas A. Grandine The evaluation of inner products of multivariate simplex splines . . . . . . 882--886 Thomas A. Grandine The Computational Cost of Simplex Spline Functions . . . . . . . . . . . . . . . 887--890 Peter Alfeld and Bruce Piper and L. L. Schumaker An explicit basis for $ {C}^1 $ quartic bivariate splines . . . . . . . . . . . 891--911 P. Deuflhard and B. Fiedler and P. Kunkel Efficient numerical pathfollowing beyond critical points . . . . . . . . . . . . 912--927 Joel Franklin Convergence in Karmarkar's algorithm for linear programming . . . . . . . . . . . 928--945 Stephen B. Haley Solution of Modified Matrix Equations 946--951 Moshe Haviv Aggregation/Disaggregation Methods for Computing the Stationary Distribution of a Markov Chain . . . . . . . . . . . . . 952--966
Marsha J. Berger On Conservation at Grid Interfaces . . . 967--984 Jan Mandel and Jind\vrich Ne\vcas Convergence of finite elements for transonic potential flows . . . . . . . 985--996 Òystein Pettersen The Random Choice Method: Structural Stability of a Conservation Equation in Reservoir Dynamics . . . . . . . . . . . 997--1007 Lloyd N. Trefethen and Manfred R. Trummer An Instability Phenomenon in Spectral Methods . . . . . . . . . . . . . . . . 1008--1023 Daniele Funaro A preconditioning matrix for the Chebyshev differencing operator . . . . 1024--1031 Seymour V. Parter On an estimate for the three-grid MGR multigrid method . . . . . . . . . . . . 1032--1045 Ronald H. W. Hoppe Multigrid Algorithms for Variational Inequalities . . . . . . . . . . . . . . 1046--1065 R. Beauwens and M. Ben Bouzid On Sparse Block Factorization Iterative Methods . . . . . . . . . . . . . . . . 1066--1076 M. C. Delfour and G. Payre and J.-P. Zolésio Approximation of nonlinear problems associated with radiating bodies in space . . . . . . . . . . . . . . . . . 1077--1094 W.-J. Beyn On the numerical approximation of phase portraits near stationary points . . . . 1095--1113 King-Wah Eric Chu Exclusion theorems and the perturbation analysis of the generalized eigenvalue problem . . . . . . . . . . . . . . . . 1114--1125 Chi Ming Ip On Least-Change Secant Updates in Factored Form . . . . . . . . . . . . . 1126--1132 Rodrigo Fontecilla and Trond Steihaug and Richard A. Tapia A convergence theory for a class of quasi-Newton methods for constrained optimization . . . . . . . . . . . . . . 1133--1151 Richard H. Byrd and Robert B. Schnabel and Gerald A. Shultz A trust region algorithm for nonlinearly constrained optimization . . . . . . . . 1152--1170 Richard H. Byrd and Jorge Nocedal and Ya Xiang Yuan Global convergence of a class of quasi-Newton methods on convex problems 1171--1190 H. Ratschek and J. G. Rokne Efficiency of a Global Optimization Algorithm . . . . . . . . . . . . . . . 1191--1201 R. Krawczyk Optimal enclosure of a generalized zero set of a function strip . . . . . . . . 1202--1211 William F. Ford and Avram Sidi An algorithm for a generalization of the Richardson extrapolation process . . . . 1212--1232
J. H. Ellison and C. A. Hall and T. A. Porsching An unconditionally stable convergent finite difference method for Navier--Stokes problems on curved domains . . . . . . . . . . . . . . . . 1233--1248 I. Babu\vska and J. E. Osborn Estimates for the errors in eigenvalue and eigenvector approximation by Galerkin methods, with particular attention to the case of multiple eigenvalues . . . . . . . . . . . . . . 1249--1276 T. A. Porsching and M. Lin Lee The Reduced Basis Method for Initial Value Problems . . . . . . . . . . . . . 1277--1287 Gunter H. Meyer Continuous orthonormalization for multipoint problems for linear ordinary differential equations . . . . . . . . . 1288--1300 I. Babu\vska and V. Majer The factorization method for the numerical solution of two-point boundary value problems for linear ODEs . . . . . 1301--1334 E. L. Allgower and K. Böhmer Application of the mesh independence principle to mesh refinement strategies 1335--1351 Kendall E. Atkinson and Florian A. Potra Projection and iterated projection methods for nonlinear integral equations 1352--1373 H. D. Mittelmann On Continuation for Variational Inequalities . . . . . . . . . . . . . . 1374--1381 Hubert Schwetlick and Jürgen Cleve Higher order predictors and adaptive steplength control in path following algorithms . . . . . . . . . . . . . . . 1382--1393 Eugene L. Poole and James M. Ortega Multicolor ICCG Methods for Vector Computers . . . . . . . . . . . . . . . 1394--1418 Rami Melhem Determination of stripe structures for finite element matrices . . . . . . . . 1419--1433 Paul H. Calamai and Jorge J. Moré Quasi-Newton Updates with Bounds . . . . 1434--1441
Randall J. LeVeque Second order accuracy of Brenier's time-discrete method for nonlinear systems of conservation laws . . . . . . 1--7 Yann Brenier and Stanley Osher The discrete one-sided Lipschitz condition for convex scalar conservation laws . . . . . . . . . . . . . . . . . . 8--23 C. Canuto and D. Funaro The Schwarz Algorithm for Spectral Methods . . . . . . . . . . . . . . . . 24--40 Gabriel N. Gatica A note on the a posteriori error analysis for the finite element method 41--45 Yonghoon Kwon and Fabio A. Milner $ {L}^\infty $-error estimates for mixed methods for semilinear second-order elliptic equations . . . . . . . . . . . 46--53 E. N. Houstis and E. A. Vavalis and J. R. Rice Convergence of $ {O}(h^4) $ Cubic Spline Collocation Methods for Elliptic Partial Differential Equations . . . . . . . . . 54--74 E. K. Blum and G. J. Reid On the numerical solution of three-dimensional boundary value problems by separation of variables . . 75--90 Jan Mandel and Steve F. McCormick and John W. Ruge An algebraic theory for multigrid methods for variational problems . . . . 91--110 Eugene C. Gartland, Jr. Strong stability of compact discrete boundary value problems via exact discretizations . . . . . . . . . . . . 111--123 Blair Swartz Conditioning Collocation . . . . . . . . 124--147 Carl de Boor The Condition of the B-Spline Basis for Polynomials . . . . . . . . . . . . . . 148--152 Thomas N. Gambill and Robert D. Skeel Logarithmic reduction of the wrapping effect with application to ordinary differential equations . . . . . . . . . 153--162 Kenneth R. Jackson The convergence of integrand-approximation formulas for the numerical solution of IVPs for ODEs . . 163--188 Robert Schreiber and Beresford N. Parlett Block Reflectors: Theory and Computation 189--205 Chi Ming Ip and Michael J. Todd Optimal conditioning and convergence in rank one quasi-Newton updates . . . . . 206--221 Jarle Berntsen and Terje O. Espelid On the construction of higher degree three-dimensional embedded integration rules . . . . . . . . . . . . . . . . . 222--234 R. D. Small The generating function method of nonlinear approximation . . . . . . . . 235--244
Pravir Dutt Stable boundary conditions and difference schemes for Navier--Stokes equations . . . . . . . . . . . . . . . 245--267 Jonathan B. Goodman and Randall J. LeVeque A geometric approach to high resolution TVD schemes . . . . . . . . . . . . . . 268--284 R. Verfürth Multilevel Algorithms for Mixed Problems. II. Treatment of the Mini-Element . . . . . . . . . . . . . . 285--293 Bernd Einfeldt On Godunov-Type Methods for Gas Dynamics 294--318 J. M. Sanz-Serna A Numerical Method for a Partial Integro-Differential Equation . . . . . 319--327 Sunil Kumar A discrete collocation-type method for Hammerstein equations . . . . . . . . . 328--341 Pei Xian Chen Convergence of SIP . . . . . . . . . . . 342--350 Alan Weiser and Mary Fanett Wheeler On convergence of block-centered finite differences for elliptic problems . . . 351--375 Craig C. Douglas and Willard L. Miranker Constructive Interference in Parallel Algorithms . . . . . . . . . . . . . . . 376--398 John Gregory and Marvin Zeman Spline matrices and their applications to some higher order methods for boundary value problems . . . . . . . . 399--410 Alfredo Bellen and Marino Zennaro Stability properties of interpolants for Runge--Kutta methods . . . . . . . . . . 411--432 A. R. Conn and N. I. M. Gould and Ph. L. Toint Global convergence of a class of trust region algorithms for optimization with simple bounds . . . . . . . . . . . . . 433--460 R. Günttner On asymptotics for the uniform norms of the Lagrange interpolation polynomials corresponding to extended Chebyshev nodes . . . . . . . . . . . . . . . . . 461--469 J. Kreimer and R. Y. Rubinstein Smoothed functionals and constrained stochastic approximation . . . . . . . . 470--487
John G. Heywood and Rolf Rannacher Finite Element Approximation of the Nonstationary Navier--Stokes Problem, Part III. Smoothing Property and Higher Order Error Estimates for Spatial Discretization . . . . . . . . . . . . . 489--512 Juan Enrique Santos and Jim Douglas, Jr. and Alberto Pedro Calderón Finite element methods for a composite model in elastodynamics . . . . . . . . 513--532 Noel J. Walkington Acoustic wave propagation through flows with vorticity . . . . . . . . . . . . . 533--549 N. Ramanujam and V. M. Sunanda Kumari Method of lines for elliptic differential equations with a small parameter . . . . . . . . . . . . . . . 550--563 R. C. Y. Chin and Thomas A. Manteuffel An analysis of block successive overrelaxation for a class of matrices with complex spectra . . . . . . . . . . 564--585 Stephen E. Cohn and Dick P. Dee Observability of discretized partial differential equations . . . . . . . . . 586--617 Paul A. Farrell Sufficient conditions for the uniform convergence of a difference scheme for a singularly perturbed turning point problem . . . . . . . . . . . . . . . . 618--643 Sòren Jensen and Ivo Babu\vska Dimensional reduction for nonlinear boundary value problems . . . . . . . . 644--669 David Voss A Fifth-Order Exponentially Fitted Formula . . . . . . . . . . . . . . . . 670--678 Carl D. Meyer and G. W. Stewart Derivatives and Perturbations of Eigenvectors . . . . . . . . . . . . . . 679--691 Rodrigo Fontecilla Local convergence of secant methods for nonlinear constrained optimization . . . 692--712 Giuliana Criscuolo and Giuseppe Mastroianni On the convergence of product formulas for the numerical evaluation of derivatives of Cauchy principal value integrals . . . . . . . . . . . . . . . 713--727
M. Lenoir and A. Tounsi The localized finite element method and its application to the two-dimensional sea-keeping problem . . . . . . . . . . 729--752 A. Bamberger and J. C. Guillot and P. Joly Numerical Diffraction by a Uniform Grid 753--783 Ricardo H. Nochetto and Claudio Verdi Approximation of Degenerate Parabolic Problems Using Numerical Integration . . 784--814 Joseph W. Jerome Convection-dominated nonlinear systems: analysis of the Douglas-Russell transport-diffusion algorithm based on approximate characteristics and invariant regions . . . . . . . . . . . 815--836 I. Babu\vska and B. Q. Guo The $h$-$p$ version of the finite element method for domains with curved boundaries . . . . . . . . . . . . . . . 837--861 J. R. Cash On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae . . . . . . . . . . 862--882 I. Lasiecka and A. Manitius Differentiability and convergence rates of approximating semigroups for retarded functional-differential equations . . . 883--907 Claes Johnson Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations . . . . . . . . . . . . . . . 908--926 M. A. Saunders and H. D. Simon and E. L. Yip Two conjugate-gradient-type methods for unsymmetric linear equations . . . . . . 927--940 Robert Beauwens and Mustapha Ben Bouzid Existence and conditioning properties of sparse approximate block factorizations 941--956 S. R. Vatsya Convergence of conjugate residual-like methods to solve linear equations . . . 957--964
Robert L. Pego and Denis Serre Instabilities in Glimm's scheme for two systems of mixed type . . . . . . . . . 965--988 Ricardo G. Durán On the approximation of miscible displacement in porous media by a method of characteristics combined with a mixed method . . . . . . . . . . . . . . . . . 989--1001 Eitan Tadmor Convenient total variation diminishing conditions for nonlinear difference schemes . . . . . . . . . . . . . . . . 1002--1014 J. T. Lin The numerical analysis of a phase field model in moving boundary problems . . . 1015--1031 Ricardo G. Durán A Note on the Convergence of Linear Finite Elements . . . . . . . . . . . . 1032--1036 R. England and R. M. M. Mattheij Boundary Value Problems and Dichotomic Stability . . . . . . . . . . . . . . . 1037--1054 Luca Dieci and Michael R. Osborne and Robert D. Russell A Riccati transformation method for solving linear BVPs. I. Theoretical aspects . . . . . . . . . . . . . . . . 1055--1073 Luca Dieci and Michael R. Osborne and Robert D. Russell A Riccati transformation method for solving linear BVPs. II. Computational aspects . . . . . . . . . . . . . . . . 1074--1092 Paul P. B. Eggermont On Galerkin methods for Abel-type integral equations . . . . . . . . . . . 1093--1117 I. G. Graham and G. A. Chandler High-order methods for linear functionals of solutions of second kind integral equations . . . . . . . . . . . 1118--1137 C. T. Kelley and J. I. Northrup A pointwise quasi-Newton method for integral equations . . . . . . . . . . . 1138--1155 Loyce M. Adams and Randall J. LeVeque and David M. Young Analysis of the SOR iteration for the $9$-point Laplacian . . . . . . . . . . 1156--1180 Guangye Li The Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations . . . . . . . . . . . . . . . 1181--1196 James V. Burke and Jorge J. Moré On the Identification of Active Constraints . . . . . . . . . . . . . . 1197--1211
Daniele Funaro and Alfio Quarteroni and Paola Zanolli An iterative procedure with interface relaxation for domain decomposition methods . . . . . . . . . . . . . . . . 1213--1236 Christine Bernardi and Claudio Canuto and Yvon Maday Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem . . . . . . . . . . . . . 1237--1271 John C. Strikwerda and Bruce A. Wade An Extension of the Kreiss Matrix Theorem . . . . . . . . . . . . . . . . 1272--1278 J. A. C. Weideman and Lloyd N. Trefethen The eigenvalues of second-order spectral differentiation matrices . . . . . . . . 1279--1298 Thomas Kerkhoven A spectral analysis of the decoupling algorithm for semiconductor simulation 1299--1312 Andreas Neubauer An a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates . . . . . . . . . . . . . . . . . 1313--1326 David R. Dellwo Accelerated refinement with applications to integral equations . . . . . . . . . 1327--1339 Jesse L. Barlow Error analysis and implementation aspects of deferred correction for equality constrained least squares problems . . . . . . . . . . . . . . . . 1340--1358 Lothar Reichel Polynomials by conformal mapping for the Richardson iteration method for complex linear systems . . . . . . . . . . . . . 1359--1368 Daniel B. Szyld Criteria for combining inverse and Rayleigh quotient iteration . . . . . . 1369--1375 R. A. Tapia and David L. Whitley The projected Newton method has order $ 1 + \sqrt 2 $ for the symmetric eigenvalue problem . . . . . . . . . . . 1376--1382 Moody T. Chu and Larry K. Norris Isospectral Flows and Abstract Matrix Factorizations . . . . . . . . . . . . . 1383--1391 P. Kunkel Quadratically convergent methods for the computation of unfolded singularities 1392--1408 Francis Conrad and Rapha\`ele Herbin and Hans D. Mittelmann Approximation of obstacle problems by continuation methods . . . . . . . . . . 1409--1431 R. Manohar and J. W. Stephenson and G. M. Trojan Nine-Node Triangular Cubic Elements . . 1432--1441 M. J. Shelley and G. R. Baker Order-preserving approximations to successive derivatives of periodic functions by iterated splines . . . . . 1442--1452 T. N. T. Goodman and K. Unsworth Shape-preserving interpolation by parametrically defined curves . . . . . 1453--1465
Hillel Tal-Ezer Spectral Methods in Time for Parabolic Problems . . . . . . . . . . . . . . . . 1--11 Todd Arbogast Analysis of the simulation of single phase flow through a naturally fractured reservoir . . . . . . . . . . . . . . . 12--29 Eitan Tadmor Convergence of spectral methods for nonlinear conservation laws . . . . . . 30--44 Hans Babovsky and Reinhard Illner A convergence proof for Nanbu's simulation method for the full Boltzmann equation . . . . . . . . . . . . . . . . 45--65 Mohammad Asadzadeh $ {L}_p $ and Eigenvalue Error Estimates for the Discrete Ordinates Method for Two-Dimensional Neutron Transport . . . 66--87 E. J. Allen and H. D. Victory, Jr. and K. Ganguly On the convergence of finite-differenced multigroup, discrete-ordinates methods for anisotropically scattering slab media . . . . . . . . . . . . . . . . . 88--106 Nicholas Ian Mark Gould On the convergence of a sequential penalty function method for constrained minimization . . . . . . . . . . . . . . 107--128 C.-C. Jay Kuo and Bernard C. Levy A Two-Level Four-Color $ \operatorname {SOR} $ Method . . . . . . . . . . . . . 129--151 M. Eiermann and X. Li and R. S. Varga On Hybrid Semi-Iterative Methods . . . . 152--168 V. Ervin and W. Layton An analysis of a defect-correction method for a model convection-diffusion equation . . . . . . . . . . . . . . . . 169--179 Ewa B. Weinmüller Stability of singular boundary value problems and their discretization by finite differences . . . . . . . . . . . 180--213 P. J. van der Houwen and B. P. Sommeijer Phase-Lag Analysis of Implicit Runge--Kutta Methods . . . . . . . . . . 214--229 R. E. Carlson and F. N. Fritsch An algorithm for monotone piecewise bicubic interpolation . . . . . . . . . 230--238 Zong Ben Xu A computational ball test for the existence of solutions to nonlinear operator equations . . . . . . . . . . . 239--248
Keshab Ganguly and H. D. Victory, Jr. On the convergence of particle methods for multidimensional Vlasov--Poisson systems . . . . . . . . . . . . . . . . 249--288 Björn Engquist and Thomas Y. Hou Particle Method Approximation of Oscillatory Solutions to Hyperbolic Differential Equations . . . . . . . . . 289--319 R. A. Renaut-Williamson Semidiscretisations of $ u_{tt} = u_{xx} $ and Rational Approximations to $ (\ln z)^2 $ . . . . . . . . . . . . . . . . . 320--337 R. A. Renaut-Williamson Full Discretisations of $ u_{tt} = u_{xx} $ and Rational Approximations to $ \cosh \mu z $ . . . . . . . . . . . . 338--347 Stig Larsson The long-time behavior of finite-element approximations of solutions to semilinear parabolic problems . . . . . 348--365 P. Lesaint and R. Touzani Approximation of the heat equation in a variable domain with application to the Stefan problem . . . . . . . . . . . . . 366--379 David E. Womble A front-tracking method for multiphase free boundary problems . . . . . . . . . 380--396 Kevin Burrage and Fred Chipman Construction of $ {A}$-stable diagonally implicit multivalue methods . . . . . . 397--413 P. J. van der Houwen and B. P. Sommeijer Diagonally Implicit Runge--Kutta--Nyström Methods for Oscillatory Problems . . . . 414--429 Apostolos Gerasoulis Nyström's iterative variant methods for the solution of Cauchy singular integral equations . . . . . . . . . . . . . . . 430--441 Martin Stynes An adaptive uniformly convergent numerical method for a semilinear singular perturbation problem . . . . . 442--455 Michael Lautsch A Spline Inversion Formula for the Radon Transform . . . . . . . . . . . . . . . 456--467 François Dubeau and Jean Savoie Développements Asymptotiques de Fonctions Splines avec Partage Uniforme de la Droite Réelle. (French) [Asymptotic expansions of spline functions with uniform partition of the real line] . . 468--479 R. K. Beatson and H. Wolkowicz Post-Processing Piecewise Cubics for Monotonicity . . . . . . . . . . . . . . 480--502 Raymond H. Chan The spectrum of a family of circulant preconditioned Toeplitz systems . . . . 503--506
C. Ringhofer and C. Schmeiser An approximate Newton method for the solution of the basic semiconductor device equations . . . . . . . . . . . . 507--516 Uri Ascher On numerical differential algebraic problems with application to semiconductor device simulation . . . . 517--538 Irene Martínez Gamba and Maria Cristina J. Squeff Simulation of the transient behavior of a one-dimensional semiconductor device. II . . . . . . . . . . . . . . . . . . . 539--552 Vidar Thomée and Jin Chao Xu and Nai Ying Zhang Superconvergence of the Gradient in Piecewise Linear Finite-Element Approximation to a Parabolic Problem . . 553--573 Y. Yan and I. H. Sloan Mesh grading for integral equations of the first kind with logarithmic kernel 574--587 W. H. Enright Analysis of error control strategies for continuous Runge--Kutta methods . . . . 588--599 Paul T. Boggs and Jon W. Tolle A strategy for global convergence in a sequential quadratic programming algorithm . . . . . . . . . . . . . . . 600--623 Steve Batterson and John Smillie The Dynamics of Rayleigh Quotient Iteration . . . . . . . . . . . . . . . 624--636 E. P. Papadopoulou and Y. G. Saridakis and T. S. Papatheodorou Block AOR iterative schemes for large-scale least-squares problems . . . 637--660 Hartmut Schwandt Cyclic reduction for tridiagonal systems of equations with interval coefficients on vector computers . . . . . . . . . . 661--680 Larkin B. Scott and L. Ridgway Scott Efficient Methods for Data Smoothing . . 681--692 Richard H. Bartels and Andrew R. Conn and Yuying Li Primal methods are better than dual methods for solving overdetermined linear systems in the $ {L}_\infty $ sense . . . . . . . . . . . . . . . . . 693--726 Richard H. Byrd and Jorge Nocedal A tool for the analysis of quasi-Newton methods with application to unconstrained minimization . . . . . . . 727--739 Miodrag S. Petkovi\'c On Halley-like algorithms for simultaneous approximation of polynomial complex zeros . . . . . . . . . . . . . 740--763 A. R. Conn and N. I. M. Gould and Ph. L. Toint Correction to the Paper on ``Global Convergence of a Class of Trust Region Algorithms for Optimization with Simple Bounds'' [SIAM J. Numer. Anal. \bf 25 (1988), no. 2, 433--460, MR 89h:90192] 764--767
Christine Bernardi and Yvon Maday Properties of some weighted Sobolev spaces and application to spectral approximations . . . . . . . . . . . . . 769--829 J. P. Vila An analysis of a class of second-order accurate Godunov-type schemes . . . . . 830--853 Yvon Maday and Eitan Tadmor Analysis of the spectral vanishing viscosity method for periodic conservation laws . . . . . . . . . . . 854--870 J. F. Colombeau and A. Y. LeRoux and A. Noussair and B. Perrot Microscopic profiles of shock waves and ambiguities in multiplications of distributions . . . . . . . . . . . . . 871--883 Charles M. Elliott and Donald A. French A nonconforming finite-element method for the two-dimensional Cahn--Hilliard equation . . . . . . . . . . . . . . . . 884--903 James H. Bramble and Richard E. Ewing and Gang Li Alternating direction multistep methods for parabolic problems --- iterative stabilization . . . . . . . . . . . . . 904--919 L. Greenberg and I. Babu\vska A continuous analogue of Sturm sequences in the context of Sturm--Liouville equations . . . . . . . . . . . . . . . 920--945 M. Calvo and F. Lisbona and J. Montijano On the stability of interpolatory variable-stepsize Adams methods in Nordsieck form . . . . . . . . . . . . . 946--962 Michel Roche Implicit Runge--Kutta methods for differential algebraic equations . . . . 963--975 Kathryn E. Brenan and Linda R. Petzold The Numerical Solution of Higher Index Differential/Algebraic Equations by Implicit Methods . . . . . . . . . . . . 976--996 Larry L. Schumaker On Super Splines and Finite Elements . . 997--1005 Donald Goldfarb and Sanjay Mehrotra A self-correcting version of Karmarkar's algorithm . . . . . . . . . . . . . . . 1006--1015 Werner Queck The convergence factor of preconditioned algorithms of the Arrow-Hurwicz type . . 1016--1030
Vitoriano Ruas Existence and stability of asymmetric finite-element approximations in nonlinear incompressible analysis . . . 1031--1059 Russel E. Caflisch and John S. Lowengrub Convergence of the Vortex Method for Vortex Sheets . . . . . . . . . . . . . 1060--1080 J. E. Lavery Solution of steady-state one-dimensional conservation laws by mathematical programming . . . . . . . . . . . . . . 1081--1089 C. I. Goldstein Analysis and application of multigrid preconditioners for singularly perturbed boundary value problems . . . . . . . . 1090--1123 Susanne C. Brenner An optimal-order nonconforming multigrid method for the biharmonic equation . . . 1124--1138 Martine Marion and Roger Temam Nonlinear Galerkin Methods . . . . . . . 1139--1157 K. Strehmel and R. Weiner and H. Claus Stability analysis of linearly implicit one-step interpolation methods for stiff retarded differential equations . . . . 1158--1174 Desmond J. Higham Robust Defect Control with Runge--Kutta Schemes . . . . . . . . . . . . . . . . 1175--1183 David R. Dellwo Accelerated spectral refinement with applications to integral operators . . . 1184--1193 Bernard Bialecki Sinc-Nyström method for numerical solution of a dominant system of Cauchy singular integral equations given on a piecewise smooth contour . . . . . . . . 1194--1211 Christine Bernardi Optimal finite-element interpolation on curved domains . . . . . . . . . . . . . 1212--1240 T. Y. Li and Tim Sauer and J. A. Yorke The cheater's homotopy: an efficient procedure for solving systems of polynomial equations . . . . . . . . . . 1241--1251 Nicholas J. Higham The Accuracy of Solutions to Triangular Systems . . . . . . . . . . . . . . . . 1252--1265 Richard H. Bartels and Andrew R. Conn and Yuying Li Erratum: ``Primal methods are better than dual methods for solving overdetermined linear systems in the $ {L}_\infty $ sense?'' [SIAM J. Numer. Anal. 26 (1989), no. 3, 693--726] . . . 1266--1266
James H. Bramble and Jin Chao Xu A local post-processing technique for improving the accuracy in mixed finite-element approximations . . . . . 1267--1275 Douglas N. Arnold and Richard S. Falk A uniformly accurate finite element method for the Reissner--Mindlin plate 1276--1290 Marie-Noëlle Le Roux and Vidar Thomée Numerical Solution of Semilinear Integrodifferential Equations of Parabolic Type with Nonsmooth Data . . . 1291--1309 San Yih Lin and Mitchell Luskin Relaxation Methods for Liquid Crystal Problems . . . . . . . . . . . . . . . . 1310--1324 Bernardo Cockburn Quasimonotone Schemes for Scalar Conservation Laws. Part I . . . . . . . 1325--1341 Franco Brezzi and Luisa Donatella Marini and Paola Pietra Two-dimensional exponential fitting and applications to drift-diffusion models 1342--1355 Claes G. L. Johnson and L. Ridgway Scott An analysis of quadrature errors in second-kind boundary integral methods 1356--1382 Randolph E. Bank and L. Ridgway Scott On the conditioning of finite element equations with highly refined meshes . . 1383--1394 Ricardo G. Durán and Ricardo H. Nochetto Pointwise accuracy of a stable Petrov--Galerkin approximation to the Stokes problem . . . . . . . . . . . . . 1395--1406 J.-C. Nédélec and S. Wolf Homogenization of the problem of eddy currents in a transformer core . . . . . 1407--1424 E. Magenes and C. Verdi and A. Visintin Theoretical and numerical results on the two-phase Stefan problem . . . . . . . . 1425--1438 Craig C. Douglas and Barry F. Smith Using symmetries and antisymmetries to analyze a parallel multigrid algorithm: the elliptic boundary value problem case 1439--1461 S. V. Krishnamachari and L. J. Hayes and T. F. Russell A finite element alternating-direction method combined with a modified method of characteristics for convection-diffusion problems . . . . . 1462--1473 Todd Arbogast and Fabio A. Milner A finite difference method for a two-sex model of population dynamics . . . . . . 1474--1486 C. N. Dawson and T. F. Russell and M. F. Wheeler Some improved error estimates for the modified method of characteristics . . . 1487--1512 Richard E. Ewing and Yi Rang Yuan and Gang Li Timestepping along characteristics for a mixed finite-element approximation for compressible flow of contamination from nuclear waste in porous media . . . . . 1513--1524 Joachim A. Nitsche Finite-Element Methods for Conformal Mappings . . . . . . . . . . . . . . . . 1525--1533 I. Babu\vska and B. Q. Guo and J. E. Osborn Regularity and numerical solution of eigenvalue problems with piecewise analytic data . . . . . . . . . . . . . 1534--1560
Qiang Du and Max D. Gunzburger Finite-Element Approximations of a Ladyzhenskaya Model for Stationary Incompressible Viscous Flow . . . . . . 1--19 J. C. López Marcos A Difference Scheme for a Nonlinear Partial Integrodifferential Equation . . 20--31 Christian Ringhofer A Spectral Method for the Numerical Simulation of Quantum Tunneling Phenomena . . . . . . . . . . . . . . . 32--50 Bernhard A. Schmitt An Algebraic Approximation for the Matrix Exponential in Singularly Perturbed Boundary Value Problems . . . 51--66 W. Auzinger and R. Frank and F. Macsek Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme . . 67--104 Andreas Frommer and Günter Mayer On the $ {R}$-order of Newton-like methods for enclosing solutions of nonlinear equations . . . . . . . . . . 105--116 S. Ghaderpanah and S. Klasa Polynomial Scaling . . . . . . . . . . . 117--135 Didier El Baz $ {M}$-Functions and Parallel Asynchronous Algorithms . . . . . . . . 136--140 Richard H. Byrd On the Convergence of Constrained Optimization Methods with Accurate Hessian Information on a Subspace . . . 141--153 Rodrigo Fontecilla Inexact Secant Methods for Nonlinear Constrained Optimization . . . . . . . . 154--165 Paul Levrie and Adhemar Bultheel Convergence Acceleration for the Numerical Solution of Second-Order Linear Recurrence Relations . . . . . . 166--177 Naoki Osada A Convergence Acceleration Method for Some Logarithmically Convergent Sequences . . . . . . . . . . . . . . . 178--189 F. Wesley Wilson and R. Kent Goodrich and Wendy Spratte Lawson's Triangulation is Nearly Optimal for Controlling Error Bounds . . . . . . 190--197 M. Nooijen and G. te Velde and E. J. Baerends Symmetric Numerical Integration Formulas for Regular Polygons . . . . . . . . . . 198--218 Walter Gautschi and E. Tychopoulos and R. S. Varga A Note on the Contour Integral Representation of the Remainder Term for a Gauss--Chebyshev Quadrature Rule . . . 219--224 Elias Masry and Stamatis Cambanis Trapezoidal Monte Carlo Integration . . 225--246 Bernardo Cockburn Quasimonotone Schemes for Scalar Conservation Laws. Part II . . . . . . . 247--258 Bernardo Cockburn Quasimonotone Schemes for Scalar Conservation Laws. Part III . . . . . . 259--276
Claes Johnson and Yi-Yong Nie and Vidar Thomée An A Posteriori Error Estimate and Adaptive Timestep Control for a Backward Euler Discretization of a Parabolic Problem . . . . . . . . . . . . . . . . 277--291 John C. Strikwerda and Bruce A. Wade and Kenneth P. Bube Regularity Estimates up to the Boundary for Elliptic Systems of Difference Equations . . . . . . . . . . . . . . . 292--322 Alain Bamberger and Patrick Joly and Jean E. Roberts Second-Order Absorbing Boundary Conditions for the Wave Equation: A Solution for the Corner Problem . . . . 323--352 John G. Heywood and Rolf Rannacher Finite-Element Approximation of the Nonstationary Navier--Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization . . . . . . . . . . 353--384 Stephen L. Keeling On Lipschitz Continuity of Nonlinear Differential Operators . . . . . . . . . 385--393 Stephen L. Keeling Galerkin/Runge--Kutta Discretizations for Semilinear Parabolic Equations . . . 394--418 Donald A. French On the Convergence of Finite-Element Approximations of a Relaxed Variational Problem . . . . . . . . . . . . . . . . 419--436 Rui-Xiu Dai and Werner C. Rheinboldt On the Computation of Manifolds of Foldpoints for Parameter-Dependent Problems . . . . . . . . . . . . . . . . 437--446 Kevin Burrage and Linda Petzold On Order Reduction for Runge--Kutta Methods Applied to Differential/Algebraic Systems and to Stiff Systems of ODEs . . . . . . . . . 447--456 Wilson C. Obi Error Analysis of a Laplace Transform Inversion Procedure . . . . . . . . . . 457--469 John Gregory and R. S. Wang Discrete Variable Methods for the $m$-Dependent Variable, Nonlinear Extremal Problem in the Calculus of Variations . . . . . . . . . . . . . . . 470--487 Paolo Costantini and Ferruccio Fontanella Shape-Preserving Bivariate Interpolation 488--506 Rembert Reemtsen Modifications of the First Remez Algorithm . . . . . . . . . . . . . . . 507--518 Rui J. P. de Figueiredo and Guanrong Chen $ \operatorname {PDL}_g $ Splines Defined by Partial Differential Operators with Initial and Boundary Value Conditions . . . . . . . . . . . . 519--528 J. E. Romate Local error analysis of three-dimensional panel methods in terms of curvilinear surface coordinates . . . 529--542 Dwight Diener Instability in the Dimension of Spaces of Bivariate Piecewise Polynomials of Degree $ 2 r $ and Smoothness Order $r$ 543--551
P. N. Childs and K. W. Morton Characteristic Galerkin Methods for Scalar Conservation Laws in One Dimension . . . . . . . . . . . . . . . 553--594 J. R. Cannon and Yanping Lin A priori $ {L}^2 $ error estimates for finite-element methods for nonlinear diffusion equations with memory . . . . 595--607 Yanping Lin Galerkin Methods for Nonlinear Parabolic Integrodifferential Equations with Nonlinear Boundary Conditions . . . . . 608--621 V. Vanaja and R. B. Kellogg Iterative Methods for a Forward-Backward Heat Equation . . . . . . . . . . . . . 622--635 Zhi Qiang Cai and Steve McCormick On the Accuracy of the Finite Volume Element Method for Diffusion Equations on Composite Grids . . . . . . . . . . . 636--655 Thomas A. Manteuffel and Seymour V. Parter Preconditioning and Boundary Conditions 656--694 Daniele Funaro A Variational Formulation for the Chebyshev Pseudospectral Approximation of Neumann Problems . . . . . . . . . . 695--703 Douglas H. Irvine and Michael A. Savageau Efficient Solution of Nonlinear Ordinary Differential Equations Expressed in S-System Canonical Form . . . . . . . . 704--735 Roger K. Alexander and James J. Coyle Runge--Kutta Methods and Differential-Algebraic Systems . . . . . 736--752 J. C. Butcher and J. R. Cash Towards Efficient Runge--Kutta Methods for Stiff Systems . . . . . . . . . . . 753--761 Jesse Barlow and James Demmel Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices . . 762--791 Lalita N. Deshpande and Balmohan V. Limaye On the Stability of Singular Finite Rank Methods . . . . . . . . . . . . . . . . 792--803 R. Baker Kearfott Preconditioners for the Interval Gauss--Seidel Method . . . . . . . . . . 804--822 Timothy N. Phillips and Andreas Karageorghis On the Coefficients of Integrated Expansions of Ultraspherical Polynomials 823--830
Robert L. Higdon Radiation Boundary Conditions for Elastic Wave Propagation . . . . . . . . 831--869 Eduard Harabetian A Numerical Method for Viscous Perturbations of Hyperbolic Conservation Laws . . . . . . . . . . . . . . . . . . 870--884 P. Dutt Spectral Methods for Initial Boundary Value Problems --- An Alternative Approach . . . . . . . . . . . . . . . . 885--903 Bengt Fornberg High-Order Finite Differences and the Pseudospectral Method on Staggered Grids 904--918 Stanley Osher and Leonid I. Rudin Feature-Oriented Image Enhancement Using Shock Filters . . . . . . . . . . . . . 919--940 Michael Mascagni The Backward Euler Method for Numerical Solution of the Hodgkin--Huxley Equations of Nerve Conduction . . . . . 941--962 Christoph Börgers and Olof B. Widlund On Finite Element Domain Imbedding Methods . . . . . . . . . . . . . . . . 963--978 D. Braess and R. Verfürth Multigrid Methods for Nonconforming Finite Element Methods . . . . . . . . . 979--986 Hermann Brunner On the Numerical Solution of Nonlinear Volterra--Fredholm Integral Equations by Collocation Methods . . . . . . . . . . 987--1000 M. Lentini and R. März The Conditioning of Boundary Value Problems in Transferable Differential-Algebraic Equations . . . . 1001--1015 John C. Clements Convexity-Preserving Piecewise Rational Cubic Interpolation . . . . . . . . . . 1016--1023 R. Hettich and P. Zencke An Algorithm for General Restricted Rational Chebyshev Approximation . . . . 1024--1033 José Mario Martínez A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix Factorizations . . . . 1034--1049 Moody T. Chu and Kenneth R. Driessel The Projected Gradient Method for Least Squares Matrix Approximations with Spectral Constraints . . . . . . . . . . 1050--1060 William W. Hager Multiplier Methods for Nonlinear Optimal Control . . . . . . . . . . . . . . . . 1061--1080 Jim Burke On the Identification of Active Constraints II: The Nonconvex Case . . . 1081--1102
François Dubois Discrete Vector Potential Representation of a Divergence-Free Vector Field in Three-Dimensional Domains: Numerical Analysis of a Model Problem . . . . . . 1103--1141 S. Schochet The Rate of Convergence of Spectral-Viscosity Methods for Periodic Scalar Conservation Laws . . . . . . . . 1142--1159 Giovanni Sacchi Landriani and Hervé Vandeven Error Estimates for the Spectral Approximation of the Nonstationary Stokes Problem . . . . . . . . . . . . . 1160--1186 Christoph Börgers A Triangulation Algorithm for Fast Elliptic Solvers Based on Domain Imbedding . . . . . . . . . . . . . . . 1187--1196 Ching-Lung Chang and Max D. Gunzburger A Subdomain Galerkin/Least Squares Method for First-Order Elliptic Systems in the Plane . . . . . . . . . . . . . . 1197--1211 Martin Costabel and Ernst P. Stephan Coupling of Finite and Boundary Element Methods for an Elastoplastic Interface Problem . . . . . . . . . . . . . . . . 1212--1226 Homer F. Walker and Layne T. Watson Least-Change Secant Update Methods for Underdetermined Systems . . . . . . . . 1227--1262 Samih K. Bourji and Homer F. Walker Least-Change Secant Updates of Nonsquare Matrices . . . . . . . . . . . . . . . . 1263--1294 D. W. Lozier and F. W. J. Olver Closure and Precision in Level-Index Arithmetic . . . . . . . . . . . . . . . 1295--1304 A. K. Cline and R. J. Renka A Constrained Two-Dimensional Triangulation and the Solution of Closest Node Problems in the Presence of Barriers . . . . . . . . . . . . . . . . 1305--1321 P. Vértesi Optimal Lebesgue Constant for Lagrange Interpolation . . . . . . . . . . . . . 1322--1331 J. H. Verner A Contrast of Some Runge--Kutta Formula Pairs . . . . . . . . . . . . . . . . . 1332--1344 Davis K. Cope Convergence of Piessens' Method for Numerical Inversion of the Laplace Transform on the Real Line . . . . . . . 1345--1354 Y. Ritov The Convergence of an Algorithm for Finding the Distance Between a Ball in a Subspace and a Sum of Subspaces . . . . 1355--1367 King-Wah Eric Chu On Multiple Eigenvalues of Matrices Depending on Several Parameters . . . . 1368--1385
Thomas Y. Hou Convergence of a Variable Blob Vortex Method for the Euler and Navier--Stokes Equations . . . . . . . . . . . . . . . 1387--1404 B. Perthame Boltzmann Type Schemes for Gas Dynamics and the Entropy Property . . . . . . . . 1405--1421 Peter K. Moore and Joseph E. Flaherty A Local Refinement Finite-Element Method for One-Dimensional Parabolic Systems 1422--1444 Jukka Saranen Projection Methods for a Class of Hammerstein Equations . . . . . . . . . 1445--1449 P. Peisker and W. Rust and E. Stein Iterative Solution Methods for Plate Bending Problems: Multigrid and Preconditioned cg Algorithm . . . . . . 1450--1465 Garth A. Baker and Wadi N. Jureidini and Ohannes A. Karakashian Piecewise Solenoidal Vector Fields and the Stokes Problem . . . . . . . . . . . 1466--1485 Richard S. Falk and Mary E. Morley Equivalence of Finite Element Methods for Problems in Elasticity . . . . . . . 1486--1505 L. F. Shampine and W. Zhang Rate of Convergence of Multistep Codes Started by Variation of Order and Stepsize . . . . . . . . . . . . . . . . 1506--1518 M. Lentini and R. März Conditioning and Dichotomy in Differential Algebraic Equations . . . . 1519--1526 C. W. Gear Differential algebraic equations, indices, and integral algebraic equations . . . . . . . . . . . . . . . 1527--1534 Q. Lin and I. H. Sloan and R. Xie Extrapolation of the Iterated-Collocation Method for Integral Equations of the Second Kind . . . . . . 1535--1541 Steven F. Ashby and Thomas A. Manteuffel and Paul E. Saylor A Taxonomy for Conjugate Gradient Methods . . . . . . . . . . . . . . . . 1542--1568 O. Axelsson and P. S. Vassilevski Algebraic Multilevel Preconditioning Methods, II . . . . . . . . . . . . . . 1569--1590 O. Axelsson and L. Kolotilina Monotonicity and Discretization Error Estimates . . . . . . . . . . . . . . . 1591--1611 Lois Mansfield On the Conjugate Gradient Solution of the Schur Complement System Obtained from Domain Decomposition . . . . . . . 1612--1620 Cristina Gígola and Susana Gómez A Regularization Method for Solving the Finite Convex Min-Max Problem . . . . . 1621--1634 Finbarr O'Sullivan Convergence Characteristics of Methods of Regularization Estimators for Nonlinear Operator Equations . . . . . . 1635--1649
Robert Glassey and Jack Schaeffer Convergence of a Particle Method for the Relativistic Vlasov--Maxwell System . . 1--25 F. Coron and B. Perthame Numerical Passage from Kinetic to Fluid Equations . . . . . . . . . . . . . . . 26--42 Kenneth Eriksson and Claes Johnson Adaptive Finite Element Methods for Parabolic Problems. I: A Linear Model Problem . . . . . . . . . . . . . . . . 43--77 Roger Zarnowski and David Hoff A Finite-Difference Scheme for the Navier--Stokes Equations of One-Dimensional, Isentropic, Compressible Flow . . . . . . . . . . . 78--112 Ben-Yu Guo and He-Ping Ma A Pseudospectral Finite-Element Method for Solving Two-Dimensional Vorticity Equations . . . . . . . . . . . . . . . 113--132 Todd E. Peterson A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation . . . . . . . 133--140 John E. Lavery Solution of Steady-State, Two-Dimensional Conservation Laws by Mathematical Programming . . . . . . . . 141--155 A. K. Aziz and J.-L. Liu A Weighted Least Squares Method for the Backward-Forward Heat Equation . . . . . 156--167 Jeffrey S. Scroggs A physically motivated domain decomposition for singularly perturbed equations . . . . . . . . . . . . . . . 168--178 Lori Badea On the Schwarz Alternating Method with More than Two Subdomains for Nonlinear Monotone Problems . . . . . . . . . . . 179--204 B. Leimkuhler and L. R. Petzold and C. W. Gear Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations . . . . . . . . . . . . . . . 205--226 Peter Linz Bounds and Estimates for Condition Numbers of Integral Equations . . . . . 227--235 David R. Dellwo and Morton B. Friedman Accelerated Projection and Iterated Projection Methods with Applications to Nonlinear Integral Equations . . . . . . 236--250 Richard G. Carter On the Global Convergence of Trust Region Algorithms Using Inexact Gradient Information . . . . . . . . . . . . . . 251--265 Mahmoud El-Alem A Global Convergence Theory for the Celis--Dennis--Tapia Trust-Region Algorithm for Constrained Optimization 266--290
Georges-Henri Cottet and Jonathan Goodman and Thomas Y. Hou Convergence of the Grid-Free Point Vortex Method for the Three-Dimensional Euler Equations . . . . . . . . . . . . 291--307 Thomas Y. Hou and John Lowengrub and Robert Krasny Convergence of a Point Vortex Method for Vortex Sheets . . . . . . . . . . . . . 308--320 Charles Collins and David Kinderlehrer and Mitchell Luskin Numerical Approximation of the Solution of a Variational Problem with a Double Well Potential . . . . . . . . . . . . . 321--332 Christine Bernardi and Claudio Canuto and Yvon Maday Spectral Approximations of the Stokes Equations with Boundary Conditions on the Pressure . . . . . . . . . . . . . . 333--362 Lucia Gastaldi and Ricardo H. Nochetto Quasi-Optimal Pointwise Error Estimates for the Reissner--Mindlin Plate . . . . 363--377 Tony F. Chan and Thomas Y. Hou and P. L. Lions Geometry Related Convergence Results for Domain Decomposition Algorithms . . . . 378--391 Zhiqiang Cai and Jan Mandel and Steve McCormick The Finite Volume Element Method for Diffusion Equations on General Triangulations . . . . . . . . . . . . . 392--402 Joseph W. Jerome and Thomas Kerkhoven A Finite Element Approximation Theory for the Drift Diffusion Semiconductor Model . . . . . . . . . . . . . . . . . 403--422 Endre Süli and Antony Ware A Spectral Method of Characteristics for Hyperbolic Problems . . . . . . . . . . 423--445 Zi-Cai Li On Nonconforming Combinations of Various Finite Element Methods for Solving Elliptic Boundary Value Problems . . . . 446--475 M. Lescrenier Convergence of Trust Region Algorithms for Optimization with Bounds when Strict Complementarity Does Not Hold . . . . . 476--495 J. H. Verner Some Runge--Kutta Formula Pairs . . . . 496--511 Meei-Yow Lin Lee Estimation of the Error in the Reduced Basis Method Solution of Differential Algebraic Equation Systems . . . . . . . 512--528 Sanjay Mehrotra and Jie Sun A Method of Analytic Centers for Quadratically Constrained Convex Quadratic Programs . . . . . . . . . . . 529--544 Andrew R. Conn and Nicholas I. M. Gould and Philippe L. Toint A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds . . . . . . . . . . . . . . . . . 545--572 L. Brutman Polynomial Extrapolation from $ \lbrack - 1, 1 \rbrack $ to the Unit Disc . . . 573--579
Franco Brezzi and Richard S. Falk Stability of Higher-Order Hood-Taylor Methods . . . . . . . . . . . . . . . . 581--590 Randolph E. Bank and Bruno D. Welfert \em A Posteriori Error Estimates for the Stokes Problem . . . . . . . . . . . . . 591--623 I. Babu\vska and A. Craig and J. Mandel and J. Pitkäranta Efficient preconditioning for the $p$-version finite element method in two dimensions . . . . . . . . . . . . . . . 624--661 D. L. Hicks and K. L. Kuttler Error Bounds for Numerical Solutions to Hydrodynamical Problems Involving Shocks 662--684 Yann Brenier and Jérôme Jaffré Upstream Differencing for Multiphase Flow in Reservoir Simulation . . . . . . 685--696 H. P. Urbach Convergence of the Galerkin Method for Two-Dimensional Electromagnetic Problems 697--710 K. D. Cooper and P. M. Prenter Alternating Direction Collocation for Separable Elliptic Partial Differential Equations . . . . . . . . . . . . . . . 711--727 M. Bourlard and S. Nicaise and L. Paquet An Adapted Boundary Element Method for the Dirichlet Problem in Polygonal Domains . . . . . . . . . . . . . . . . 728--743 Gerard R. Richter An Explicit Finite Element Method for Convection-Dominated Steady State Convection-Diffusion Equations . . . . . 744--759 Ralph C. Smith and Gary A. Bogar and Kenneth L. Bowers and John Lund The Sinc--Galerkin Method for Fourth-Order Differential Equations . . 760--788 Mark J. Friedman and Eusebius J. Doedel Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points . . . . . . . . . . . . . . . . . 789--808 A. D. Jepson and A. Spence and K. A. Cliffe The numerical solution of nonlinear equations having several parameters. Part III. Equations with $ {Z}_2$-symmetry . . . . . . . . . . . . 809--832 J. B. Keiper and C. W. Gear The Analysis of Generalized Backwards Difference Formula Methods Applied to Hessenberg Form Differential-Algebraic Equations . . . . . . . . . . . . . . . 833--858 Nancy S. Ellner and Eugene L. Wachspress Alternating Direction Implicit Iteration for Systems with Complex Spectra . . . . 859--870 Raymond H. Chan and Xiao-Qing Jin and Man-Chung Yeung The Spectra of Super-Optimal Circulant Preconditioned Toeplitz Systems . . . . 871--879 Klaus-Jürgen Förster and Knut Petras Error Estimates in Gaussian Quadrature for Functions of Bounded Variation . . . 880--889
Eitan Tadmor Local Error Estimates for Discontinuous Solutions of Nonlinear Hyperbolic Equations . . . . . . . . . . . . . . . 891--906 Stanley Osher and Chi-Wang Shu High-Order Essentially Nonoscillatory Schemes for Hamilton--Jacobi Equations 907--922 K. Ito and F. Kappel and G. Peichl A fully discretized approximation scheme for size-structured population models 923--954 H. D. Victory, Jr. and Garry Tucker and Keshab Ganguly The Convergence Analysis of Fully Discretized Particle Methods for Solving Vlasov--Poisson Systems . . . . . . . . 955--989 P. K. Jimack and A. J. Wathen Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids . . . . . . . . . . . . 990--1003 Ricardo Durán and Adriana Ghioldi and Noemí Wolanski A Finite Element Method for the Mindlin--Reissner Plate Model . . . . . 1004--1014 R. E. Ewing and R. D. Lazarov and J. Wang Superconvergence of the Velocity Along the Gauss Lines in Mixed Finite Element Methods . . . . . . . . . . . . . . . . 1015--1029 P. Lesaint and J. Pousin Existence and Approximation Results for Thermal Boundary Layer Equations of Reactive Flows . . . . . . . . . . . . . 1030--1046 Yan Ping Lin and Vidar Thomée and Lars B. Wahlbin Ritz-Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations . . . . . . . . . . . . . . . 1047--1070 L. Greengard Spectral Integration and Two-Point Boundary Value Problems . . . . . . . . 1071--1080 J. M. Sanz-Serna and L. Abia Order Conditions for Canonical Runge--Kutta Schemes . . . . . . . . . . 1081--1096 Uri M. Ascher and Linda R. Petzold Projected Implicit Runge--Kutta Methods for Differential-Algebraic Equations . . 1097--1120 K. Ito and H. T. Tran and A. Manitius A Fully-Discrete Spectral Method for Delay-Differential Equations . . . . . . 1121--1140 Denis Talay Approximation of Upper Lyapunov Exponents of Bilinear Stochastic Differential Systems . . . . . . . . . . 1141--1164 Z. Jackiewicz and R. Renaut and A. Feldstein Two-Step Runge--Kutta Methods . . . . . 1165--1182 Eliane R. Panier and André L. Tits Avoiding the Maratos Effect by Means of a Nonmonotone Line Search I. General Constrained Problems . . . . . . . . . . 1183--1195 Sotirios E. Notaris Some New Formulae for the Stieltjes Polynomials Relative to Classical Weight Functions . . . . . . . . . . . . . . . 1196--1206
H. D. Victory, Jr. and Edward J. Allen The Convergence Theory of Particle-in-Cell Methods for Multidimensional Vlasov--Poisson Systems 1207--1241 Gunilla Kreiss The Dependence on the Outflow Boundary Condition of the Solution of Steady, Incompressible Euler Equations . . . . . 1242--1264 Ryan I. Fernandes and Graeme Fairweather An Alternating Direction Galerkin Method for a Class of Second-Order Hyperbolic Equations in Two Space Variables . . . . 1265--1281 Clint N. Dawson Godunov-Mixed Methods for Advective Flow Problems in One Space Dimension . . . . 1282--1309 Qiang Du and R. A. Nicolaides Numerical Analysis of a Continuum Model of Phase Transition . . . . . . . . . . 1310--1322 M. J. Baines An Analysis of the Moving Finite-Element Procedure . . . . . . . . . . . . . . . 1323--1349 M. Kroller and K. Kunisch Convergence Rates for the Feedback Operators Arising in the Linear Quadratic Regulator Problem Governed by Parabolic Equations . . . . . . . . . . 1350--1385 C. I. Goldstein Preconditioning Singularity Perturbed Elliptic and Parabolic Problems . . . . 1386--1418 Endre Süli Convergence of Finite Volume Schemes for Poisson's Equation on Nonuniform Meshes 1419--1430 Gerhard Starke Optimal Alternating Direction Implicit Parameters for Nonsymmetric Systems of Linear Equations . . . . . . . . . . . . 1431--1445 Thomas F. Fairgrieve and Allan D. Jepson O. K. Floquet Multipliers . . . . . . . 1446--1462 Percy Deift and James Demmel and Luen Chau Li and Carlos Tomei The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics 1463--1516 Geir Nævdal A Comment on Parrott's Theorem . . . . . 1517--1522
Bertil Gustafsson and Hans Stoor Navier--Stokes Equations for Almost Incompressible Flow . . . . . . . . . . 1523--1547 T. Gallouët and J.-P. Vila Finite Volume Schemes for Conservation Laws of Mixed Type . . . . . . . . . . . 1548--1573 Keshab Ganguly and J. Todd Lee and H. D. Victory, Jr. On Simulation Methods for Vlasov--Poisson Systems with Particles Initially Asymptotically Distributed . . 1574--1609 Peter B. Monk A Mixed Method for Approximating Maxwell's Equations . . . . . . . . . . 1610--1634 Prabir Daripa A New Theory for One-Dimensional Adaptive Grid Generation and Its Applications . . . . . . . . . . . . . . 1635--1660 D. B. Duncan and M. A. M. Lynch Jacobi Iteration in Implicit Difference Schemes for the Wave Equation . . . . . 1661--1679 Leopoldo P. Franca and Rolf Stenberg Error analysis of some Galerkin least squares methods for the elasticity equations . . . . . . . . . . . . . . . 1680--1697 Kazufumi Ito and Janos Turi Numerical Methods for a Class of Singular Integro-Differential Equations Based on Semigroup Approximation . . . . 1698--1722 A. Iserles and A. T. Peplow and A. M. Stuart A Unified Approach to Spurious Solutions Introduced by Time Discretisation. Part I: Basic Theory . . . . . . . . . . . . 1723--1751 D. C. Sorensen and Ping Tak Peter Tang On the Orthogonality of Eigenvectors Computed by Divide and Conquer Techniques . . . . . . . . . . . . . . . 1752--1775 A. T. Chronopoulos s-Step Iterative Methods for (Non)symmetric (In)definite Linear Systems . . . . . . . . . . . . . . . . 1776--1789 Masaharu Nakashima Embedded Pseudo-Runge--Kutta Methods . . 1790--1802 G. Myerson On Ignoring the Singularity . . . . . . 1803--1807
B. Perthame Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions . . . . . . . . . . 1--19 N. Anders Petersson A Numerical Method to Calculate the Two-Dimensional Flow Around an Underwater Obstacle . . . . . . . . . . 20--31 R. A. Nicolaides Direct Discretization of Planar Div-Curl Problems . . . . . . . . . . . . . . . . 32--56 Jie Shen On Error Estimates of Projection Methods for Navier--Stokes Equations: First-Order Schemes . . . . . . . . . . 57--77 Ricardo Durán and María Amelia Muschietti and Rodolfo Rodríguez Asymptotically Exact Error Estimators for Rectangular Finite Elements . . . . 78--88 Keith Miller On the Mass Matrix Spectrum Bounds of Wathen and the Local Moving Finite Elements of Baines . . . . . . . . . . . 89--106 Henner Eisen and Wilhelm Heinrichs A New Method of Stabilization for Singular Perturbation Problems with Spectral Methods . . . . . . . . . . . . 107--122 Hung Ju Kuo and Neil S. Trudinger Discrete Methods for Fully Nonlinear Elliptic Equations . . . . . . . . . . . 123--135 Maryse Bourlard and Monique Dauge and Mbaro-Saman Lubuma and Serge Nicaise Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points III. Finite Element Methods on Polygonal Domains . . 136--155 Bernard Bialecki and Graeme Fairweather and Karin R. Bennett Fast Direct Solvers for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations . . . . . . . . . 156--173 Wei Zhong Dai An unconditionally stable three-level explicit difference scheme for the Schrödinger equation with a variable coefficient . . . . . . . . . . . . . . 174--181 Francine Catté and Pierre-Louis Lions and Jean-Michel Morel and Tomeu Coll Image Selective Smoothing and Edge Detection by Nonlinear Diffusion . . . . 182--193 Christophe Fresnel and Marie-Noëlle Le Roux Numerical Solution of an Interdiffusion Problem . . . . . . . . . . . . . . . . 194--208 Y. Saad Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator . . . . . . . . . . . . . . . . 209--228 T. Y. Li and Zhong Gang Zeng and Luan Cong Solving Eigenvalue Problems of Real Nonsymmetric Matrices with Real Homotopies . . . . . . . . . . . . . . . 229--248 Jesse L. Barlow and Udaya B. Vemulapati A Note on Deferred Correction for Equality Constrained Least Squares Problems . . . . . . . . . . . . . . . . 249--256 Shmuel Rippa Long and Thin Triangles Can Be Good For Linear Interpolation . . . . . . . . . . 257--270 H. L. Gray and Suojin Wang A New Method for Approximating Improper Integrals . . . . . . . . . . . . . . . 271--283 Stamatis Cambanis and Elias Masry Trapezoidal Stratified Monte Carlo Integration . . . . . . . . . . . . . . 284--301
Jinchao Xu A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems 303--319 Mitchell Luskin and Ling Ma Analysis of the Finite Element Approximation of Microstructure in Micromagnetics . . . . . . . . . . . . . 320--331 R. P. Beyer and R. J. Leveque Analysis of a One-Dimensional Model for the Immersed Boundary Method . . . . . . 332--364 Manfred Dobrowolski A Mixed Finite Element Method for Approximating Incompressible Materials 365--389 Max D. Gunzburger and Steven L. Hou Treating Inhomogeneous Essential Boundary Conditions in Finite Element Methods and the Calculation of Boundary Stresses . . . . . . . . . . . . . . . . 390--424 Chichia Chiu and David A. Kopriva An Optimal Runge--Kutta Method for Steady-State Solutions of Hyperbolic Systems . . . . . . . . . . . . . . . . 425--438 Vladimir Veliov Second-Order Discrete Approximation to Linear Differential Inclusions . . . . . 439--451 Ching Lung Chang Finite Element Approximation for Grad-Div Type Systems in the Plane . . . 452--461 Christophe Devulder and Martine Marion A Class of Numerical Algorithms for Large Time Integration: The Nonlinear Galerkin Methods . . . . . . . . . . . . 462--483 Dongming Wei Existence, Uniqueness, and Numerical Analysis of Solutions of a Quasilinear Parabolic Problem . . . . . . . . . . . 484--497 Vladimír Janovský and Petr Plechá\vc Computer-aided analysis of imperfect bifurcation diagrams. I. Simple bifurcation point and isola formation centre . . . . . . . . . . . . . . . . . 498--512 Michal K\vrí\vzek On the Maximum Angle Condition for Linear Tetrahedral Elements . . . . . . 513--520 Daniel Okunbor and Robert D. Skeel An explicit Runge--Kutta--Nyström method is canonical if and only if its adjoint is explicit . . . . . . . . . . . . . . 521--527 Jörg Peters and Meera Sitharam Stability of interpolation from $ {C}^1 $ cubics at the vertices of an underlying triangulation . . . . . . . . 528--533 Eugene L. Allgower and Klaus Böhmer and Kurt Georg and Rick Miranda Exploiting Symmetry in Boundary Element Methods . . . . . . . . . . . . . . . . 534--552 E. T. Y. Lee Corners, Cusps, and Parametrizations: Variations on a Theorem of Epstein . . . 553--565 Shaun Disney and Ian H. Sloan Lattice Integration Rules of Maximal Rank Formed by Copying Rank 1 Rules . . 566--577 Knut Petras Error Bounds for Gaussian and Related Quadrature and Applications to R-Convex Functions . . . . . . . . . . . . . . . 578--585 William E. Smith and David Paget Optimal Nodes for Interpolatory Product Integration . . . . . . . . . . . . . . 586--600 Carsten Carstensen On Grau's Method for Simultaneous Factorization of Polynomials . . . . . . 601--613
Thomas Y. Hou and Brian T. R. Wetton Convergence of a Finite Difference Scheme for the Navier--Stokes Equations Using Vorticity Boundary Conditions . . 615--639 Heinz-Otto Kreiss and Godela Scherer Method of Lines for Hyperbolic Differential Equations . . . . . . . . . 640--646 Susanne C. Brenner A Multigrid Algorithm for the Lowest-Order Raviart--Thomas Mixed Triangular Finite Element Method . . . . 647--678 Christian Ringhofer A Spectral Collocation Technique for the Solution of the Wigner--Poisson Problem 679--700 J. M. Beckers Analytical Linear Numerical Stability Conditions for an Anisotropic Three-Dimensional Advection-Diffusion Equation . . . . . . . . . . . . . . . . 701--713 Peter Monk Analysis of a Finite Element Method for Maxwell's Equations . . . . . . . . . . 714--729 Richard S. Falk and Gerard R. Richter Local Error Estimates for a Finite Element Method for Hyperbolic and Convection-Diffusion Equations . . . . . 730--754 Yi Yan and Graeme Fairweather Orthogonal Spline Collocation Methods for Some Partial Integrodifferential Equations . . . . . . . . . . . . . . . 755--768 S. Chow Finite Element Error Estimates for a Blast Furnace Gas Flow Problem . . . . . 769--780 Luca Dieci Numerical Integration of the Differential Riccati Equation and Some Related Issues . . . . . . . . . . . . . 781--815 M. von Golitschek and W. A. Light Approximation by Solutions of the Planar Wave Equation . . . . . . . . . . . . . 816--830 Eugene L. Allgower and Kurt Georg and Rick Miranda The Method of Resultants for Computing Real Solutions of Polynomial Systems . . 831--844 Luis Alvarez and Pierre-Louis Lions and Jean-Michel Morel Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II . . 845--866 Elisabeth Rouy and Agn\`es Tourin A Viscosity Solutions Approach to Shape-From-Shading . . . . . . . . . . . 867--884 Moody T. Chu Numerical Methods for Inverse Singular Value Problems . . . . . . . . . . . . . 885--903
Wei Cai and David Gottlieb and Chi-Wang Shu On One-Sided Filters for Spectral Fourier Approximations of Discontinuous Functions . . . . . . . . . . . . . . . 905--916 Alfio Quarteroni and Elena Zampieri Finite Element Preconditioning for Legendre Spectral Collocation Approximations to Elliptic Equations and Systems . . . . . . . . . . . . . . . . 917--936 Lars B. Wahlbin On Superconvergence Up to Boundaries in Finite Element Methods: A Counterexample 937--946 Ivo Babu\vska and Ricardo Durán and Rodolfo Rodríguez Analysis of the Efficiency of an A Posteriori Error Estimator for Linear Triangular Finite Elements . . . . . . . 947--964 Stéphane Jaffard Wavelet Methods for Fast Resolution of Elliptic Problems . . . . . . . . . . . 965--986 Jun Ping Wang Convergence Analysis Without Regularity Assumptions for Multigrid Algorithms Based on SOR Smoothing . . . . . . . . . 987--1001 Michel Chipot and Charles Collins Numerical Approximations in Variational Problems with Potential Wells . . . . . 1002--1019 Zhen Huan Teng Particle Method and Its Convergence for Scalar Conservation Laws . . . . . . . . 1020--1042 Bill Semper Conforming Finite Element Approximations for a Fourth-Order Singular Perturbation Problem . . . . . . . . . . . . . . . . 1043--1058 Hachmi Bendhia Numerical Analysis of a Bidimensional Hencky Problem Approximated by a Discontinuous Finite Element Method . . 1059--1073 Julián López-Gómez and Marcela Molina-Meyer and Mónica Villarreal Numerical Computation of Coexistence States . . . . . . . . . . . . . . . . . 1074--1092 Raymond H. Chan and Man-Chung Yeung Circulant Preconditioners Constructed from Kernels . . . . . . . . . . . . . . 1093--1103 T. Y. Li and Xiao Shen Wang Nonlinear Homotopies for Solving Deficient Polynomial Systems with Parameters . . . . . . . . . . . . . . . 1104--1118 Stephen Joe and Ian H. Sloan Imbedded Lattice Rules for Multidimensional Integration . . . . . . 1119--1135 Erlend Arge and Morten Dæhlen Grid point interpolation on finite regions using $ {C}^1 $ box splines . . 1136--1153 Hiroshi Sugiura and Tatsuo Torii Polynomial Interpolation on Quasi-Equidistributed Nodes on the Unit Disk . . . . . . . . . . . . . . . . . . 1154--1165 Thomas F. Coleman and Yuying Li A global and quadratically convergent method for linear $ {L}_\infty $ problems . . . . . . . . . . . . . . . . 1166--1186 J. Frédéric Bonnans and Eliane R. Panier and André L. Tits and Jian L. Zhou Avoiding the Maratos effect by means of a nonmonotone line search. II. Inequality constrained problems --- feasible iterates . . . . . . . . . . . 1187--1202
Christine Bernardi and Frédéric Laval and Brigitte Métivet and Bernadette Pernaud-Thomas Finite Element Approximation of Viscous Flows with Varying Density . . . . . . . 1203--1243 D. F. Griffiths and A. M. Stuart and H. C. Yee Numerical Wave Propagation in an Advection Equation with a Nonlinear Source Term . . . . . . . . . . . . . . 1244--1260 Ivo Babu\vska and Manil Suri On Locking and Robustness in the Finite Element Method . . . . . . . . . . . . . 1261--1293 Sòren Jensen Adaptive Dimensional Reduction Numerical Solution of Monotone Quasilinear Boundary Value Problems . . . . . . . . 1294--1320 Thomas A. Manteuffel and Andrew B. White, Jr. A Calculus of Difference Schemes for the Solution of Boundary-Value Problems on Irregular Meshes . . . . . . . . . . . . 1321--1346 Jean-Luc Guermond Numerical Quadratures for Layer Potentials Over Curved Domains in $ \mathbb {R}^3 $ . . . . . . . . . . . . 1347--1369 Per Lötstedt Grid Independent Convergence of the Multigrid Method for First-Order Equations . . . . . . . . . . . . . . . 1370--1394 Peter Deuflhard and Florian A. Potra Asymptotic Mesh Independence of Newton--Galerkin Methods via a Refined Mysovski\uì theorem . . . . . . . . . . . 1395--1412 José Mario Martínez Fixed-Point Quasi-Newton Methods . . . . 1413--1434 M. Neamtu Multivariate Divided Differences I: Basic Properties . . . . . . . . . . . . 1435--1445 Markus Hegland An Optimal Order Regularization Method Which Does Not Use Additional Smoothness Assumptions . . . . . . . . . . . . . . 1446--1461 Mu Sheng Wei Perturbation Theory for the Rank-Deficient Equality Constrained Least Squares Problem . . . . . . . . . 1462--1481 Elliot Linzer On the Stability of Transform-Based Circular Deconvolution . . . . . . . . . 1482--1492 E. R. Hansen Bounding the Solution of Interval Linear Equations . . . . . . . . . . . . . . . 1493--1503
Haim Nessyahu and Eitan Tadmor The Convergence Rate of Approximate Solutions for Nonlinear Scalar Conservation Laws . . . . . . . . . . . 1505--1519 Weinan E Convergence of Spectral Methods for Burgers' Equation . . . . . . . . . . . 1520--1541 P. L. Roe and D. Sidilkover Optimum Positive Linear Schemes for Advection in Two and Three Dimensions 1542--1568 Arnold Reusken On Maximum Norm Convergence of Multigrid Methods for Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 1569--1578 R. A. Nicolaides Analysis and Convergence of the MAC Scheme I. The Linear Problem . . . . . . 1579--1591 S. Karni Viscous Shock Profiles and Primitive Formulations . . . . . . . . . . . . . . 1592--1609 P. Oswald Hierarchical Conforming Finite Element Methods for the Biharmonic Equation . . 1610--1625 Wei Zhang Huang and David M. Sloan The Pseudospectral Method for Third-Order Differential Equations . . . 1626--1647 M. C. Delfour and A. Ouansafi Noniterative Approximations to the Solution of the Matrix Riccati Differential Equation . . . . . . . . . 1648--1693 Michael Knorrenschild Differential/Algebraic Equations as Stiff Ordinary Differential Equations 1694--1715 G. Beylkin On the Representation of Operators in Bases of Compactly Supported Wavelets 1716--1740 Anne C. Morlet and Jens Lorenz Numerical Solution of a Functional Equation on a Circle . . . . . . . . . . 1741--1768 M. Heinkenschloß and C. T. Kelley and H. T. Tran Fast Algorithms for Nonsmooth Compact Fixed-Point Problems . . . . . . . . . . 1769--1792 K. Kunisch and E. W. Sachs Reduced SQP Methods for Parameter Identification Problems . . . . . . . . 1793--1820
Randolph E. Bank and Rafael F. Santos Analysis of Some Moving Space-Time Finite Element Methods . . . . . . . . . 1--18 Wilhelm Heinrichs Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations . . . . . . . 19--39 Martin H. Gutknecht Changing the Norm in Conjugate Gradient Type Algorithms . . . . . . . . . . . . 40--56 Hung T. Huynh Accurate Monotone Cubic Interpolation 57--100 Uri M. Ascher and Paul M. Carter A Multigrid Method for Shape-from-Shading . . . . . . . . . . . 102--115 Susanne C. Brenner A Nonconforming Mixed Multigrid Method for the Pure Displacement Problem in Planar Linear Elasticity . . . . . . . . 116--135 Craig C. Douglas and Jim Douglas, Jr. A Unified Convergence Theory for Abstract Multigrid or Multilevel Algorithms, Serial and Parallel . . . . 136--158 Charles I. Goldstein Multigrid Methods for Elliptic Problems in Unbounded Domains . . . . . . . . . . 159--183 M. R. Hanisch Multigrid Preconditioning for the Biharmonic Dirichlet Problem . . . . . . 184--214 Naomi H. Naik and John Van Rosendale The Improved Robustness of Multigrid Elliptic Solvers Based on Multiple Semicoarsened Grids . . . . . . . . . . 215--229 Ulrich Rüde Fully Adaptive Multigrid Methods . . . . 230--248 David Sidilkover and Achi Brandt Multigrid Solution to Steady-State Two-Dimensional Conservation Laws . . . 249--274 Jun Ping Wang Convergence Analysis of Multigrid Algorithms for Nonselfadjoint and Indefinite Elliptic Problems . . . . . . 275--285 Stefan Vandewalle and Robert Piessens On Dynamic Iteration Methods for Solving Time-Periodic Differential Equations . . 286--303
Werner C. Rheinboldt On the Sensitivity of Solutions of Parameterized Equations . . . . . . . . 305--320 Yvon Maday and Sidi M. Ould Kaber and Eitan Tadmor Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws . . . . 321--342 C. I. Goldstein and Thomas A. Manteuffel and Seymour V. Parter Preconditioning and boundary conditions without $ {H}_2 $ estimates: $ {L}_2 $ condition numbers and the distribution of the singular values . . . . . . . . . 343--376 Ohannes Karakashian and Georgios D. Akrivis and Vassilios A. Dougalis On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation . . . . . 377--400 Aslak Tveito and Ragnar Winther An Error Estimate for a Finite Difference Scheme Approximating a Hyperbolic System of Conservation Laws 401--424 Bernard Bialecki A Fast Domain Decomposition Poisson Solver on a Rectangle for Hermite Bicubic Orthogonal Spline Collocation 425--434 Wilhelm Heinrichs Domain Decomposition for Fourth-Order Problems . . . . . . . . . . . . . . . . 435--453 François Rogier Mathematical and Numerical Study of a Magnetostatic Problem Around a Thin Shield . . . . . . . . . . . . . . . . . 454--477 Ping Lee A Lagrange Multiplier Method for the Interface Equations from Electromagnetic Applications . . . . . . . . . . . . . . 478--506 Wolfgang Dahmen and Charles A. Micchelli Using the Refinement Equation for Evaluating Integrals of Wavelets . . . . 507--537 V. Brasey and E. Hairer Half-explicit Runge--Kutta methods for differential-algebraic systems of index $2$ . . . . . . . . . . . . . . . . . . 538--552 Jeng Yen Constrained Equations of Motion in Multibody Dynamics as ODEs on Manifolds 553--568 S. Joe and S. A. R. Disney Intermediate Rank Lattice Rules for Multidimensional Integration . . . . . . 569--582 Jan Verschelde and Ann Haegemans The $ {GBQ}$-algorithm for constructing start systems of homotopies for polynomial systems . . . . . . . . . . . 583--594 Roger Delbourgo Accurate $ {C}^2 $ rational interpolants in tension . . . . . . . . . . . . . . . 595--607
Thomas Y. Hou and Brian T. R. Wetton Second-Order Convergence of a Projection Scheme for the Incompressible Navier--Stokes Equations with Boundaries 609--629 Andrew Wathen and David Silvester Fast Iterative Solution of Stabilised Stokes Systems. Part I: Using Simple Diagonal Preconditioners . . . . . . . . 630--649 E. Weinan Convergence of Fourier Methods for the Navier--Stokes Equations . . . . . . . . 650--674 Frédéric Coquel and Philippe Le Floch Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: A General Theory . . . . . . 675--700 Xu-Dong Liu A Maximum Principle Satisfying Modification of Triangle Based Adaptive Stencils for the Solution of Scalar Hyperbolic Conservation Laws . . . . . . 701--716 Robert L. Doucette A Collocation Method for the Numerical Solution of Laplace's Equation with Nonlinear Boundary Conditions on a Polygon . . . . . . . . . . . . . . . . 717--732 T. N'Kaoua and R. Sentis A New Time Discretization for the Radiative Transfer Equations: Analysis and Comparison with the Classical Discretization . . . . . . . . . . . . . 733--748 Eugene C. Gartland, Jr. On the Uniform Convergence of the Scharfetter-Gummel Discretization in One Dimension . . . . . . . . . . . . . . . 749--758 Wei Dong Chen A Regularization Method for the Numerical Inversion of the Laplace Transform . . . . . . . . . . . . . . . 759--773 Florian A. Potra Implementation of Linear Multistep Methods for Solving Constrained Equations of Motion . . . . . . . . . . 774--789 Thomas Manteuffel and James Otto Optimal Equivalent Preconditioners . . . 790--812 P. Amodio and L. Brugnano and T. Politi Parallel Factorizations for Tridiagonal Matrices . . . . . . . . . . . . . . . . 813--823 Ta-Kang Ku and C.-C. Jay Kuo Preconditioned Iterative Methods for Solving Toeplitz-Plus-Hankel Systems . . 824--845 Albrecht Böttcher and Hartmut Wolf Galerkin--Petrov Methods for Bergman Space Toeplitz Operators . . . . . . . . 846--863 J. Rohn Inverse Interval Matrix . . . . . . . . 864--870 John Gregory and Cantian Lin Discrete Variable Methods for the m-Dependent Variable Nonlinear, Extremal Problem in the Calculus of Variations II 871--881 K. Atkinson and E. Venturino Numerical Evaluation of Line Integrals 882--888 Peter Alfeld and Larry L. Schumaker and Walter Whiteley The generic dimension of the space of $ {C}^1 $ splines of degree $ d \geq 8 $ on tetrahedral decompositions . . . . . 889--920
Randolph E. Bank and R. Kent Smith \em A Posteriori Error Estimates Based on Hierarchical Bases . . . . . . . . . 921--935 Xiao-Chuan Cai and Olof B. Widlund Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems . . . . . . . . . . . . . . . . 936--952 Jun Ping Wang Convergence analysis of the Schwarz algorithm and multilevel decomposition iterative methods. II. Nonselfadjoint and indefinite elliptic problems . . . . 953--970 M. Farhloul and M. Fortin A New Mixed Finite Element for the Stokes and Elasticity Problems . . . . . 971--990 R. H. Nochetto and M. Paolini and C. Verdi A Fully Discrete Adaptive Nonlinear Chernoff Formula . . . . . . . . . . . . 991--1014 Andreas Kirmse Bending-Dominated Deformation of Thin Spherical Shells: Analysis and Finite-Element Approximation . . . . . . 1015--1040 G. A. Chandler and I. G. Graham The Computation of Water Waves Modelled by Nekrasov's Equation . . . . . . . . . 1041--1065 Ben Yu Guo and He Ping Ma Combined Finite Element and Pseudospectral Method for the Two-Dimensional Evolutionary Navier--Stokes Equations . . . . . . . . 1066--1083 A. Ostermann and M. Roche Rosenbrock Methods for Partial Differential Equations and Fractional Orders of Convergence . . . . . . . . . 1084--1098 Gautam M. Shroff and Herbert B. Keller Stabilization of Unstable Procedures: The Recursive Projection Method . . . . 1099--1120 W. Govaerts Computation of Takens--Bogdanov Type Bifurcations with Arbitrary Codimension 1121--1133 Bin Hong On the Computation of Multiple Bifurcations with Multiple Parameters and Symmetry . . . . . . . . . . . . . . 1134--1154 Stephen Schecter Numerical Computation of Saddle-Node Homoclinic Bifurcation Points . . . . . 1155--1178 Hon-Wah Tam and Robert D. Skeel Stability of Parallel Explicit ODE Methods . . . . . . . . . . . . . . . . 1179--1192 Raymond H. Chan and Man-Chung Yeung Circulant Preconditioners for Complex Toeplitz Matrices . . . . . . . . . . . 1193--1207 Martin Hanke An $ \epsilon $-free a posteriori stopping rule for certain iterative regularization methods . . . . . . . . . 1208--1228
Jing Hua Wang and Gerald Warnecke On entropy consistency of large time step schemes. I. The Godunov and Glimm schemes . . . . . . . . . . . . . . . . 1229--1251 Jing Hua Wang and Gerald Warnecke On entropy consistency of large time step schemes. II. Approximate Riemann solvers . . . . . . . . . . . . . . . . 1252--1267 Howard C. Elman and Michael P. Chernesky Ordering Effects on Relaxation Methods Applied to the Discrete One-Dimensional Convection-Diffusion Equation . . . . . 1268--1290 John E. Dennis, Jr. and H. Wolkowicz Sizing and Least-Change Secant Methods 1291--1314 Clint Dawson Godunov-Mixed Methods for Advection-Diffusion Equations in Multidimensions . . . . . . . . . . . . 1315--1332 Kazufumi Ito and Sungkwon Kang A Dissipative Pseudospectral Method for the Two-Dimensional Navier--Stokes Equations . . . . . . . . . . . . . . . 1333--1350 Dietmar Berthold and Peter Junghanns New Error Bounds for the Quadrature Method for the Solution of Cauchy Singular Integral Equations . . . . . . 1351--1372 C. Palencia A Stability Result for Sectorial Operators in Banach Spaces . . . . . . . 1373--1384 Yonghoon Kwon and Chung-Ki Cho Second-Order Accurate Difference Methods for a One-Sex Model of Population Dynamics . . . . . . . . . . . . . . . . 1385--1399 Relja Vulanovi\'c and Paul A. Farrell Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem 1400--1418 W. H. Enright The Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge--Kutta Formulas . . . . 1419--1445 J. H. Verner Differentiable Interpolants for High-Order Runge--Kutta Methods . . . . 1446--1466 Edda Eich Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints . . . 1467--1482 P. L. de Angelis and G. Toraldo On the Identification Property of a Projected Gradient Method . . . . . . . 1483--1497 Hari Krishna and Yunbiao Wang The Split Levinson Algorithm is Weakly Stable . . . . . . . . . . . . . . . . . 1498--1508 Heinz W. Engl and Gerhard Landl Convergence Rates for Maximum Entropy Regularization . . . . . . . . . . . . . 1509--1536
Richard E. Ewing and Raytcho D. Lazarov and Joseph E. Pasciak and Panayot S. Vassilevski Domain Decomposition Type Iterative Techniques for Parabolic Problems on Locally Refined Grids . . . . . . . . . 1537--1557 William J. Morokoff and Russel E. Caflisch A Quasi-Monte Carlo Approach to Particle Simulation of the Heat Equation . . . . 1558--1573 H. T. Banks and H. T. Tran and D. E. Woodward Estimation of Variable Coefficients in the Fokker--Planck Equations Using Moving Node Finite Elements . . . . . . 1574--1602 John G. Heywood and Rolf Rannacher On the Question of Turbulence Modeling by Approximate Inertial Manifolds and the Nonlinear Galerkin Method . . . . . 1603--1621 C. M. Elliott and A. M. Stuart The Global Dynamics of Discrete Semilinear Parabolic Equations . . . . . 1622--1663 Daniele Funaro A New Scheme for the Approximation of Advection-Diffusion Equations by Collocation . . . . . . . . . . . . . . 1664--1676 Todd Arbogast and Mandri Obeyesekere and Mary F. Wheeler Numerical Methods for the Simulation of Flow in Root-Soil Systems . . . . . . . 1677--1702 J. Ka\vcur and A. Handlovi\vcová and M. Ka\vcurová Solution of Nonlinear Diffusion Problems by Linear Approximation Schemes . . . . 1703--1722 M. E. Kramer and R. M. M. Mattheij Application of Global Methods in Parallel Shooting . . . . . . . . . . . 1723--1739 Raymond H. Chan and James G. Nagy and Robert J. Plemmons FFT-Based Preconditioners for Toeplitz-Block Least Squares Problems 1740--1768 J. Saranen and L. Schroderus Quadrature Methods for Strongly Elliptic Equations of Negative Order on Smooth Closed Curves . . . . . . . . . . . . . 1769--1795 O. Scherzer and H. W. Engl and K. Kunisch Optimal A Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-posed Problems . . . . . . 1796--1838
Haim Nessyahu and Eitan Tadmor and Tamir Tassa The Convergence Rate of Godunov Type Schemes . . . . . . . . . . . . . . . . 1--16 C. D. Munz On Godunov-type schemes for Lagrangian gas dynamics . . . . . . . . . . . . . . 17--42 Zhen Huan Teng On the Accuracy of Fractional Step Methods for Conservation Laws in Two Dimensions . . . . . . . . . . . . . . . 43--63 Robert L. Higdon Radiation Boundary Conditions for Dispersive Waves . . . . . . . . . . . . 64--100 Vladimir Kozlov and Vladimir Maz'ya and Leonid Rozin On Certain Hybrid Iterative Methods for Solving Boundary Value Problems . . . . 101--110 Pierre-Alain Gremaud Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions . . . . . 111--127 Bernard Brighi and Michel Chipot Approximated Convex Envelope of a Function . . . . . . . . . . . . . . . . 128--148 Peter K. Moore \em A Posteriori Error Estimation with Finite Element Semi- and Fully-Discrete Methods for Non-linear Parabolic Equations in One Space Dimension . . . . 149--169 Marie-Noëlle Le Roux Semidiscretization in Time of Nonlinear Parabolic Equations with Blowup of the Solution . . . . . . . . . . . . . . . . 170--195 J. J. H. Miller and S. Wang A Tetrahedral Mixed Finite Element Method for the Stationary Semiconductor Continuity Equations . . . . . . . . . . 196--216 José Mario Martínez SOR-Secant Methods . . . . . . . . . . . 217--226 Imad M. Jaimoukha and Ebrahim M. Kasenally Krylov Subspace Methods for Solving Large Lyapunov Equations . . . . . . . . 227--251 G. Alefeld and A. Gienger and F. Potra Efficient Numerical Validation of Solutions of Nonlinear Systems . . . . . 252--260 Luca Dieci and Robert D. Russell and Erik S. Van Vleck Unitary Integrators and Applications to Continuous Orthonormalization Techniques 261--281 G. Koepfler and C. Lopez and J. M. Morel A Multiscale Algorithm for Image Segmentation by Variational Method . . . 282--299
R. H. W. Hoppe and R. Kornhuber Adaptive Multilevel Methods for Obstacle Problems . . . . . . . . . . . . . . . . 301--323 Dietmar Kröner and Mirko Rokyta Convergence of Upwind Finite Volume Schemes for Scalar Conservation Laws in Two Dimensions . . . . . . . . . . . . . 324--343 Lung An Ying and Ping Wen Zhang Fully Discrete Convergence Estimates for Vortex Methods in Bounded Domains . . . 344--361 Dominique Sandri Finite Element Approximation of Viscoelastic Fluid Flow: Existence of Approximate Solutions and Error Bounds. Continuous Approximation of the Stress 362--377 Arnold Reusken On Maximum Norm Convergence of Multigrid Methods for Elliptic Boundary Value Problems . . . . . . . . . . . . . . . . 378--392 Peter Monk and Endre Süli A Convergence Analysis of Yee's Scheme on Nonuniform Grids . . . . . . . . . . 393--412 John W. Barrett and W. B. Liu Finite Element Approximation of the Parabolic $p$-Laplacian . . . . . . . . 413--428 I. Gohberg and M. Hanke and I. Koltracht Fast Preconditioned Conjugate Gradient Algorithms for Wiener--Hopf Integral Equations . . . . . . . . . . . . . . . 429--443 Graeme Fairweather Spline Collocation Methods for a Class of Hyperbolic Partial Integro-Differential Equations . . . . . 444--460 Youngmok Jeon An Indirect Boundary Integral Equation Method for the Biharmonic Equation . . . 461--476 Yi Yan A Fast Numerical Solution for a Second Kind Boundary Integral Equation with a Logarithmic Kernel . . . . . . . . . . . 477--498 A. Bellen and Z. Jackiewicz and M. Zennaro Contractivity of Waveform Relaxation Runge--Kutta Iterations and Related Limit Methods for Dissipative Systems in the Maximum Norm . . . . . . . . . . . . 499--523 K.-w. E. Chu and W. Govaerts and A. Spence Matrices with Rank Deficiency Two in Eigenvalue Problems and Dynamical Systems . . . . . . . . . . . . . . . . 524--539 R. Scherer and W. Wendler Complete Algebraic Characterization of A-Stable Runge--Kutta Methods . . . . . 540--551 P. Chartier $ {L}$-stable parallel one-block methods for ordinary differential equations . . 552--571 V. Martínez and A. Marquina and R. Donat Shooting Methods for One-Dimensional Diffusion-Absorption Problems . . . . . 572--589 Luis Alvarez and Luis Mazorra Signal and Image Restoration Using Shock Filters and Anisotropic Diffusion . . . 590--605
Bernardo Cockburn and Chi-Wang Shu Nonlinearly Stable Compact Schemes for Shock Calculations . . . . . . . . . . . 607--627 Haim Nessyahu and Tamir Tassa Convergence Rate of Approximate Solutions to Conservation Laws with Initial Rarefactions . . . . . . . . . . 628--654 Rosa Donat Studies on Error Propagation for Certain Nonlinear Approximations to Hyperbolic Equations: Discontinuities in Derivatives . . . . . . . . . . . . . . 655--679 George C. Hsiao and Shangyou Zhang Optimal Order Multigrid Methods for Solving Exterior Boundary Value Problems 680--694 Th. Apel and B. Heinrich Mesh Refinement and Windowing Near Edges for Some Elliptic Problem . . . . . . . 695--708 Weizhang Huang and Yuhe Ren and Robert D. Russell Moving Mesh Partial Differential Equations (MMPDEs) Based on the Equidistribution Principle . . . . . . . 709--730 Jiang Zhu and Hong Wei Wu and Yuan Ming Wang A Mixed Method for the Mixed Initial Boundary Value Problems of Equations of Semiconductor Devices . . . . . . . . . 731--744 Bodo Heise Analysis of a Fully Discrete Finite Element Method for a Nonlinear Magnetic Field Problem . . . . . . . . . . . . . 745--759 Pedro C. Espinoza Positive Ordered Solutions of a Discrete Analogue of a Nonlinear Elliptic Eigenvalue Problem . . . . . . . . . . . 760--767 Vicente F. Candela Computation of Shift Operators in Orthonormal Compactly Supported Wavelet Bases . . . . . . . . . . . . . . . . . 768--787 Thomas K. DeLillo The Accuracy of Numerical Conformal Mapping Methods: A Survey of Examples and Results . . . . . . . . . . . . . . 788--812 M. Benassi and R. E. White Parallel Numerical Solution of Variational Inequalities . . . . . . . . 813--830 Mohammad Asadzadeh and Kenneth Eriksson On Adaptive Finite Element Methods for Fredholm Integral Equations of the Second Kind . . . . . . . . . . . . . . 831--855 Penny J. Davies Numerical Stability and Convergence of Approximations of Retarded Potential Integral Equations . . . . . . . . . . . 856--875 K. Burrage and F. H. Chipman and P. H. Muir Order Results for Mono-Implicit Runge--Kutta Methods . . . . . . . . . . 876--891 R. Baker Kearfott and Zhaoyun Xing An Interval Step Control for Continuation Methods . . . . . . . . . . 892--914 Jan Verschelde and Pierre Verlinden and Ronald Cools Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems 915--930 John L. Spouge Computation of the Gamma, Digamma, and Trigamma Functions . . . . . . . . . . . 931--944
Ivo Babu\vska and Gabriel Caloz and John E. Osborn Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients . . . . . . . . 945--981 C. N. Dawson and C. J. Van Duijn and M. F. Wheeler Characteristic-Galerkin Methods for Contaminant Transport with Nonequilibrium Adsorption Kinetics . . . 982--999 S. Larsson and J. M. Sanz-Serna The Behavior of Finite Element Solutions of Semilinear Parabolic Problems Near Stationary Points . . . . . . . . . . . 1000--1018 Randall J. LeVeque and Zhi Lin Li The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources . . . 1019--1044 Clint N. Dawson and Todd F. Dupont Explicit/Implicit, Conservative Domain Decomposition Procedures for Parabolic Problems Based on Block-Centered Finite Differences . . . . . . . . . . . . . . 1045--1061 Zhangxin Chen and Bernardo Cockburn Error Estimates for a Finite Element Method for the Drift-Diffusion Semiconductor Device Equations . . . . . 1062--1089 C. I. Draghicescu An Efficient Implementation of Particle Methods for the Incompressible Euler Equations . . . . . . . . . . . . . . . 1090--1108 O. Coulaud and A. Henrot Numerical Approximation of a Free Boundary Problem Arising in Electromagnetic Shaping . . . . . . . . 1109--1127 Bernard Bialecki and Xiao-Chuan Cai $ {H}^1$-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems . . . . . . . . 1128--1146 Roger K. Alexander Stability of Runge--Kutta Methods for Stiff Ordinary Differential Equations 1147--1168 P. W. Sharp and J. H. Verner Completely Imbedded Runge--Kutta Pairs 1169--1190 Ami Harten and Itai Yad-Shalom Fast Multiresolution Algorithms for Matrix-Vector Multiplication . . . . . . 1191--1218 Kurt S. Riedel Generalized Epsilon-Pseudospectra . . . 1219--1225 Andrew V. Knyazev and Alexander L. Skorokhodov Preconditioned Gradient-Type Iterative Methods in a Subspace for Partial Generalized Symmetric Eigenvalue Problems . . . . . . . . . . . . . . . . 1226--1239 Wim Sweldens and Robert Piessens Quadrature Formulae and Asymptotic Error Expansions for Wavelet Approximations of Smooth Functions . . . . . . . . . . . . 1240--1264
I. Babu\vska and T. von Petersdorff and B. Andersson Numerical treatment of vertex singularities and intensity factors for mixed boundary value problems for the Laplace equation in $ {\bf R}^3 $ . . . 1265--1288 Jing Zhao and David Hoff A Convergent Finite-Difference Scheme for the Navier--Stokes Equations of One-Dimensional, Nonisentropic, Compressible Flow . . . . . . . . . . . 1289--1311 Petr Klou\vcek and Franz S. Rys Stability of the fractional step $ {\Theta } $-scheme for the nonstationary Navier--Stokes equations . . . . . . . . 1312--1335 Kalman Z. Meth Stable Numerical Boundary Conditions for Stokes Equations . . . . . . . . . . . . 1336--1351 David Silvester and Andrew Wathen Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners . . . . . . . . . 1352--1367 A. I. Pehlivanov and G. F. Carey and R. D. Lazarov Least-Squares Mixed Finite Elements for Second-Order Elliptic Problems . . . . . 1368--1377 M. Ganesh and I. G. Graham and J. Sivaloganathan A Pseudospectral Three-Dimensional Boundary Integral Method Applied to a Nonlinear Mode Problem from Finite Elasticity . . . . . . . . . . . . . . . 1378--1414 Dá\vsa Janovská Numerical Treatment of Subspace-Breaking Takens--Bogdanov Points with Nonlinear Degeneracies . . . . . . . . . . . . . . 1415--1433 K. Burrage and P. W. Sharp A Class of Variable-Step Explicit Nordsieck Multivalue Methods . . . . . . 1434--1451 A. R. Humphries and A. M. Stuart Runge--Kutta Methods for Dissipative and Gradient Dynamical Systems . . . . . . . 1452--1485 Jun Liu A Sensitivity Analysis for Least-Squares Ill-Posed Problems Using the Haar Basis 1486--1496 J. A. C. Weideman Computation of the Complex Error Function . . . . . . . . . . . . . . . . 1497--1518
Wai-Sun Don and David Gottlieb The Chebyshev--Legendre Method: Implementing Legendre Methods on Chebyshev Points . . . . . . . . . . . . 1519--1534 Alfred S. Carasso Overcoming Hölder continuity in ill-posed continuation problems . . . . . . . . . 1535--1557 S.-K. Tin and N. Kopell and C. K. R. T. Jones Invariant Manifolds and Singularly Perturbed Boundary Value Problems . . . 1558--1576 Gunilla Kreiss and Heinz-Otto Kreiss and N. Anders Petersson On the Convergence to Steady State of Solutions of Nonlinear Hyperbolic-Parabolic Systems . . . . . . 1577--1604 Richard E. Ewing and Raytcho D. Lazarov and Apostol T. Vassilev Finite Difference Scheme for Parabolic Problems on Composite Grids with Refinement in Time and Space . . . . . . 1605--1622 Charles I. Goldstein Preconditioning Nonconforming Finite Element Methods . . . . . . . . . . . . 1623--1644 Howard C. Elman and Gene H. Golub Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems . . 1645--1661 Maksymilian Dryja and Barry F. Smith and Olof B. Widlund Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions . . . . . . 1662--1694 Achi Brandt Rigorous Quantitative Analysis of Multigrid, I: Constant Coefficients Two-Level Cycle with $ {L}_2$-Norm . . . 1695--1730 Stephen F. McCormick Multilevel Adaptive Methods for Elliptic Eigenproblems: A Two-Level Convergence Theory . . . . . . . . . . . . . . . . . 1731--1745 James H. Bramble and Do Y. Kwak and Joseph E. Pasciak Uniform Convergence of Multigrid V-Cycle Iterations for Indefinite and Nonsymmetric Problems . . . . . . . . . 1746--1763 S. Zeng and P. Wesseling Multigrid Solution of the Incompressible Navier--Stokes Equations in General Coordinates . . . . . . . . . . . . . . 1764--1784 Z. Cai and R. Lazarov and T. A. Manteuffel and S. F. McCormick First-Order System Least Squares for Second-Order Partial Differential Equations: Part I . . . . . . . . . . . 1785--1799 Thomas A. Manteuffel and Michael Steuerwalt and Burton Wendroff Dedication to Seymour V. Parter on the occasion of his 65th birthday . . . . . vii--ix
Donald Estep \em A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations . . . . 1--48 K. R. Jackson and S. P. Nòrsett The Potential for Parallelism in Runge--Kutta Methods. Part 1: RK Formulas in Standard Form . . . . . . . 49--82 X. C. Hu and T. A. Manteuffel and S. McCormick and T. F. Russell Accurate Discretization for Singular Perturbations: The One-Dimensional Case 83--109 Tao Tang and Zhen Huan Teng Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms 110--127 S. F. Ashby and P. N. Brown and M. R. Dorr and A. C. Hindmarsh A Linear Algebraic Analysis of Diffusion Synthetic Acceleration for the Boltzmann Transport Equation . . . . . . . . . . . 128--178 Peter N. Brown A Linear Algebraic Development of Diffusion Synthetic Acceleration for Three-Dimensional Transport Equations 179--214 Jie Shen and Roger Temam Nonlinear Galerkin method using Chebyshev and Legendre polynomials. I. The one-dimensional case . . . . . . . . 215--234 Panayot S. Vassilevski and Junping Wang An Application of the Abstract Multilevel Theory to Nonconforming Finite Element Methods . . . . . . . . . 235--248 M.-P. Istace and J.-P. Thiran On the Third and Fourth Zolotarev Problems in the Complex Plane . . . . . 249--259 Mario Büttner and Bernhard A. Schmitt and Rüdiger Weiner $ {W}$-methods with automatic partitioning by Krylov techniques for large stiff systems . . . . . . . . . . 260--284 Richard J. Charron and Min Hu $ {A}$-contractivity of linearly implicit multistep methods . . . . . . . 285--295 Jean-Pierre Dussault Numerical Stability and Efficiency of Penalty Algorithms . . . . . . . . . . . 296--317 Patrick J. Rabier and Werner C. Rheinboldt On the Numerical Solution of the Euler--Lagrange Equations . . . . . . . 318--329 J. A. C. Weideman Erratum: ``Computation of the complex error function'' [SIAM J. Numer. Anal. \bf 7 (1970), no. 1, 187--198] . . . . . 330--331
Seymour V. Parter and Ernest E. Rothman Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems . . . . . . . . . . . . . . . . 333--385 Jie Shen On Error Estimates of the Penalty Method for Unsteady Navier--Stokes Equations 386--403 Todd Arbogast and Mary F. Wheeler A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems . . . . . . . . . . . . . . . . 404--424 Rodolfo Bermejo A Galerkin-Characteristic Algorithm for Transport-Diffusion Equations . . . . . 425--454 Zhangxin Chen Finite Element Analysis of the One-Dimensional Full Drift-Diffusion Semiconductor Model . . . . . . . . . . 455--483 Guy Barles and Christine Georgelin A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature . . . . . . . 484--500 C. T. Kelley A Fast Multilevel Algorithm for Integral Equations . . . . . . . . . . . . . . . 501--513 I. G. Rosen and Chunming Wang A Multilevel Technique for the Approximate Solution of Operator Lyapunov and Algebraic Riccati Equations 514--541 Lung An Ying Convergence of Vortex Methods for Three-Dimensional Euler Equations in Bounded Domains . . . . . . . . . . . . 542--559 Adam Zem\la On the Fundamental Solutions for the Difference Helmholtz Operator . . . . . 560--570 Baruch Cahlon and Devadatta M. Kulkarni and Peter Shi Stepwise Stability for the Heat Equation with a Nonlocal Constraint . . . . . . . 571--593 Andrew T. Peplow and Simon N. Chandler-Wilde Approximate Solution of Second Kind Integral Equations on Infinite Cylindrical Surfaces . . . . . . . . . . 594--609 Sergey P. Shary On Optimal Solution of Interval Linear Equations . . . . . . . . . . . . . . . 610--630 M. A. H. Dempster and R. R. Merkovsky A Practical Geometrically Convergent Cutting Plane Algorithm . . . . . . . . 631--644 Jörg Peters $ {C}^1$-surface splines . . . . . . . . 645--666 Mark Taylor Cubature for the Sphere and the Discrete Spherical Harmonic Transform . . . . . . 667--670 P. Köhler Order-Preserving Mesh Spacing for Compound Quadrature Formulas and Functions with Endpoint Singularities 671--686
B. Cockburn and F. Coquel and P. G. LeFloch Convergence of the Finite Volume Method for Multidimensional Conservation Laws 687--705 Kenneth Eriksson and Claes Johnson Adaptive finite element methods for parabolic problems. II. Optimal error estimates in $ {L}_\infty {L}_2 $ and $ {L}_\infty {L}_\infty $ . . . . . . . . 706--740 Heinrich Freistühler and E. Bruce Pitman A Numerical Study of a Rotationally Degenerate Hyperbolic System. Part II. The Cauchy Problem . . . . . . . . . . . 741--753 Zhen Huan Teng and Lung An Ying and Ping Wen Zhang Convergence of the Variable-Elliptic-Vortex Method for Euler Equations . . . . . . . . . . . . 754--774 S. Benharbit and A. Chalabi and J. P. Vila Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions . . . . . 775--796 Uri M. Ascher and Steven J. Ruuth and Brian T. R. Wetton Implicit-Explicit Methods for Time-Dependent Partial Differential Equations . . . . . . . . . . . . . . . 797--823 L. Lin and J. B. Temple and J. Wang A Comparison of Convergence Rates for Godunov's Method and Glimm's Method in Resonant Nonlinear Systems of Conservation Laws . . . . . . . . . . . 824--840 Long Wei Lin and Blake Temple and Jing Hua Wang Suppression of Oscillations in Godunov's Method for a Resonant Non-Strictly Hyperbolic System . . . . . . . . . . . 841--864 Eun-Jae Park Mixed Finite Element Methods for Nonlinear Second-Order Elliptic Problems 865--885 Pedro Martins Girão Convergence of a Crystalline Algorithm for the Motion of a Simple Closed Convex Curve by Weighted Curvature . . . . . . 886--899 Ling Ma and Noel J. Walkington On Algorithms for Nonconvex Optimization in the Calculus of Variations . . . . . 900--923 A. Rathsfeld Nyström's Method and Iterative Solvers for the Solution of the Double-Layer Potential Equation Over Polyhedral Boundaries . . . . . . . . . . . . . . . 924--951 Fu Ming Ma Numerical Calculation of Center Manifolds for a Class of Infinite-Dimensional Systems with Applications . . . . . . . . . . . . . . 952--968 Yajun Yang and Kendall E. Atkinson Two-Dimensional Quadrature for Functions with a Point Singularity on a Triangular Region . . . . . . . . . . . . . . . . . 969--983
Y. Achdou and O. Pironneau A Fast Solver for Navier--Stokes Equations in the Laminar Regime Using Mortar Finite Element and Boundary Element Methods . . . . . . . . . . . . 985--1016 E. Weinan and Jian-Guo Liu Projection method. I. Convergence and numerical boundary layers . . . . . . . 1017--1057 Claes Johnson and Rolf Rannacher and Mats Boman Numerics and Hydrodynamic Stability: Toward Error Control in Computational Fluid Dynamics . . . . . . . . . . . . . 1058--1079 Y. Brenier and G.-H. Cottet Convergence of Particle Methods with Random Rezoning for the Two-Dimensional Euler and Navier--Stokes Equations . . . 1080--1097 S. Mas-Gallic Particle Approximation of a Linear Convection-Diffusion Problem with Neumann Boundary Conditions . . . . . . 1098--1125 Irad Yavneh Multigrid Smoothing Factors for Red-Black Gauss--Seidel Relaxation Applied to a Class of Elliptic Operators 1126--1138 Fabienne Berger and Jean-François Colombeau Numerical Solutions of One-Pressure Models in Multifluid Flows . . . . . . . 1139--1154 Gang Bao Finite Element Approximation of Time Harmonic Waves in Periodic Structures 1155--1169 Martine Marion and Jinchao Xu Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements . . . . . . . . . . . . . . . . 1170--1184 Richard S. Falk and Jian-Ming Xu Convergence of a Second-Order Scheme for the Nonlinear Dynamical Equations of Elastic Rods . . . . . . . . . . . . . . 1185--1209 Roger Pierre Optimal selection of the bubble function in the stabilization of the $ {\rm P}1 $-$ {\rm P}1 $ element for the Stokes problem . . . . . . . . . . . . . . . . 1210--1224 Philip T. Keenan Thermal Simulation of Pipeline Flow . . 1225--1262 Anne-Sophie Bonnet-Bendhia and Nabil Gmati Spectral Approximation of a Boundary Condition for an Eigenvalue Problem . . 1263--1279 A. Bermúdez and R. Durán and M. A. Muschietti and R. Rodríguez and J. Solomin Finite Element Vibration Analysis of Fluid-Solid Systems Without Spurious Modes . . . . . . . . . . . . . . . . . 1280--1295 Ch. Lubich and K. Nipp and D. Stoffer Runge--Kutta Solutions of Stiff Differential Equations Near Stationary Points . . . . . . . . . . . . . . . . . 1296--1307 Alexander P. Morgan and Andrew J. Sommese and Charles W. Wampler A Product-Decomposition Bound for Bezout Numbers . . . . . . . . . . . . . . . . 1308--1325
Bracy H. Elton and C. David Levermore and Garry H. Rodrigue Convergence of Convective-Diffusive Lattice Boltzmann Methods . . . . . . . 1327--1354 V. S. Ryaben'ki\uì and S. V. Tsynkov Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems . . . . . . . . . . . . . 1355--1389 Z. Jackiewicz and S. Tracogna A General Class of Two-Step Runge--Kutta Methods for Ordinary Differential Equations . . . . . . . . . . . . . . . 1390--1427 Yingkang Hu and Xiang Ming Yu Discrete Modulus of Smoothness of Splines with Equally Spaced Knots . . . 1428--1435 Luca Dieci and Jens Lorenz Computation of Invariant Tori by the Method of Characteristics . . . . . . . 1436--1474 Anne C. Morlet Convergence of the Sinc Method for a Fourth-Order Ordinary Differential Equation with an Application . . . . . . 1475--1503 Maurice H. P. M. van Putten A Two-Dimensional Numerical Implementation of Magnetohydrodynamics in Divergence Form . . . . . . . . . . . 1504--1518 P. E. Kloeden and E. Platen and N. Hofmann Extrapolation Methods for the Weak Approximation of Ito Diffusions . . . . 1519--1534 J. Saranen and L. Schroderus Some Discrete Methods for Boundary Integral Equations on Smooth Closed Curves . . . . . . . . . . . . . . . . . 1535--1564 H. T. Huynh Accurate Upwind Methods for the Euler Equations . . . . . . . . . . . . . . . 1565--1619 Zhen Yue Zhang An Inverse Extreme Eigenpair Problem and Its Parallel Iterative Solution for Symmetric Tridiagonal Matrices . . . . . 1620--1634 Uri M. Ascher and Linda R. Petzold The Numerical Solution of Delay-Differential-Algebraic Equations of Retarded and Neutral Type . . . . . . 1635--1657 Steven Pruess and Charles T. Fulton and Yuantao Xie An Asymptotic Numerical Method for a Class of Singular Sturm--Liouville Problems . . . . . . . . . . . . . . . . 1658--1676 De Kang Mao A Shock Tracking Technique Based on Conservation in One Space Dimension . . 1677--1703 Randall J. LeVeque and Zhi Lin Li Erratum: ``The immersed interface method for elliptic equations with discontinuous coefficients and singular sources'' [SIAM J. Numer. Anal. \bf 31 (1994), no. 4, 1019--1044, MR 95g:65139] 1704--1704
B. D. Reddy and J. C. Simo Stability and Convergence of a Class of Enhanced Strain Methods . . . . . . . . 1705--1728 Kenneth Eriksson and Claes Johnson Adaptive finite element methods for parabolic problems. IV. Nonlinear problems . . . . . . . . . . . . . . . . 1729--1749 Kenneth Eriksson and Claes Johnson Adaptive Finite Element Methods for Parabolic Problems V: Long-Time Integration . . . . . . . . . . . . . . 1750--1763 Ben Yu Guo and Wei Ming Cao A Spectral Method for the Fluid Flow with Low Mach Number on the Spherical Surface . . . . . . . . . . . . . . . . 1764--1777 Weimin Han and B. Daya Reddy On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity . . . . . . . . . . . . 1778--1807 J.-D. Benamou A Domain Decomposition Method for the Polar Factorization of Vector-Valued Mappings . . . . . . . . . . . . . . . . 1808--1838 S. Li and L. Vu-Quoc Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein--Gordon Equation . . 1839--1875 Anton Arnold and Christian Ringhofer Operator Splitting Methods Applied to Spectral Discretizations of Quantum Transport Equations . . . . . . . . . . 1876--1894 Francine Catté and Françoise Dibos and Georges Koepfler A Morphological Scheme for Mean Curvature Motion and Applications to Anisotropic Diffusion and Motion of Level Sets . . . . . . . . . . . . . . . 1895--1909 V. D. Didenko and S. Roch and B. Silbermann Approximation Methods for Singular Integral Equations with Conjugation on Curves with Corners . . . . . . . . . . 1910--1939 A. M. Stuart and A. R. Humphries The Essential Stability of Local Error Control for Dynamical Systems . . . . . 1940--1971 Stanley C. Eisenstat and Ilse C. F. Ipsen Relative Perturbation Techniques for Singular Value Problems . . . . . . . . 1972--1988 M. E. Hosea A New Recurrence for Computing Runge--Kutta Truncation Error Coefficients . . . . . . . . . . . . . . 1989--2001
J. M. Greenberg and A. Y. Leroux A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations . . . . . . . . . . . . . . . 1--16 W. Layton and H. W. J. Lenferink A Multilevel Mesh Independence Principle for the Navier--Stokes Equations . . . . 17--30 R. D. Lazarov and Ilya D. Mishev and P. S. Vassilevski Finite Volume Methods for Convection-Diffusion Problems . . . . . 31--55 Jim Rulla and Noel J. Walkington Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions . . . . . . . . . . . . . . . 56--67 Jim Rulla Error Analysis for Implicit Approximations to Solutions to Cauchy Problems . . . . . . . . . . . . . . . . 68--87 W. B. Liu and John W. Barrett Finite Element Approximation of Some Degenerate Monotone Quasilinear Elliptic Systems . . . . . . . . . . . . . . . . 88--106 Lutz Tobiska and Rüdiger Verfürth Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier--Stokes Equations . . . . . . . . 107--127 Michael Shub and Steve Smale Complexity of Bezout's theorem. IV. Probability of success and extensions 128--148 Sônia M. Gomes and Elsa Cortina Convergence Estimates for the Wavelet Galerkin Method . . . . . . . . . . . . 149--161 Thomas I. Seidman Optimal Filtering for the Backward Heat Equation . . . . . . . . . . . . . . . . 162--170 Carsten Carstensen Coupling of FEM and BEM for Interface Problems in Viscoplasticity and Plasticity with Hardening . . . . . . . 171--207 Qiya Hu Stieltjes derivatives and $ \beta $-polynomial spline collocation for Volterra integrodifferential equations with singularities . . . . . . . . . . . 208--220 I. Babu\vska and C. Schwab \em A Posteriori Error Estimation for Hierarchic Models of Elliptic Boundary Value Problems on Thin Domains . . . . . 221--246 Wing Kwong Yeung and Kenneth P. Bube \em A Priori Estimates and Convergence for the Discrete Forward and Inverse Problems of Reflection Seismology . . . 247--279 David Gottlieb and Chi-Wang Shu On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a Sub-Interval From a Spectral Partial Sum of a Piecewise Analytic Function . . . . . . 280--290 Karl J. Havlak and Harold Dean Victory, Jr. The Numerical Analysis of Random Particle Methods Applied to Vlasov--Poisson--Fokker--Planck Kinetic Equations . . . . . . . . . . . . . . . 291--317 Richard E. Ewing and Hong Wang An Optimal-Order Estimate for Eulerian--Lagrangian Localized Adjoint Methods for Variable-Coefficient Advection-Reaction Problems . . . . . . 318--348 Daniel Goldman and Tasso J. Kaper $ {N} $ th-order operator splitting schemes and nonreversible systems . . . 349--367 Laurent Jay Symplectic Partitioned Runge--Kutta Methods for Constrained Hamiltonian Systems . . . . . . . . . . . . . . . . 368--387 Yingkang Hu and Xiang Ming Yu The Degree of Copositive Approximation and a Computer Algorithm . . . . . . . . 388--398 James S. Otto Multigrid Convergence for Discretizations of Singular Perturbation Problems with Grid-Aligned Flow . . . . 399--416
Francesc Ar\`andiga and Vicente F. Candela Multiresolution Standard Form of a Matrix . . . . . . . . . . . . . . . . . 417--434 Bodo Werner Computation of Hopf Bifurcation with Bordered Matrices . . . . . . . . . . . 435--455 Jan Janssen and Stefan Vandewalle Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Continuous-Time Case . . . . . . . . . . 456--474 Sebastian Reich Symplectic Integration of Constrained Hamiltonian Systems by Composition Methods . . . . . . . . . . . . . . . . 475--491 Lawrence C. Cowsar and Todd F. Dupont and Mary F. Wheeler \em A Priori Estimates for Mixed Finite Element Approximations of Second-Order Hyperbolic Equations with Absorbing Boundary Conditions . . . . . . . . . . 492--504 A. H. Schatz and I. H. Sloan and L. B. Wahlbin Superconvergence in Finite Element Methods and Meshes That Are Locally Symmetric with Respect to a Point . . . 505--521 Bernardo Cockburn and Pierre-Alain Gremaud Error Estimates for Finite Element Methods for Scalar Conservation Laws . . 522--554 Xuejun Zhang Two-level Schwarz methods for the biharmonic problem discretized conforming $ {C}^1 $ elements . . . . . 555--570 Peter Alfeld Upper and Lower Bounds on the Dimension of Multivariate Spline Spaces . . . . . 571--588 W. Sun Block Iterative Algorithms for Solving Hermite Bicubic Collocation Equations 589--601 B. Dubuc and S. Dubuc Error Bounds on the Estimation of Fractal Dimension . . . . . . . . . . . 602--626 Randall J. LeVeque High-Resolution Conservative Algorithms for Advection in Incompressible Flow . . 627--665 Miloslav Feistauer and George C. Hsiao and Ralph E. Kleinman Asymptotic and A Posteriori Error Estimates for Boundary Element Solutions of Hypersingular Integral Equations . . 666--685 Jian Shen A Block Finite Difference Scheme for Second-Order Elliptic Problems with Discontinuous Coefficients . . . . . . . 686--706 Alain Largillier and Balmohan V. Limaye Finite-Rank Methods and Their Stability for Coupled Systems of Operator Equations . . . . . . . . . . . . . . . 707--728 Christoph Schwab and Manil Suri The optimal $p$-version approximation of singularities on polyhedra in the boundary element method . . . . . . . . 729--759 Xu-Dong Liu and Stanley Osher Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I . . 760--779 R. Bruce Kellogg and Biyue Liu A Finite Element Method for the Compressible Stokes Equations . . . . . 780--788 Benqi Guo and Norbert Heuer and Ernst P. Stephan The $h$-$p$ version of the boundary element method for transmission problems with piecewise analytic data . . . . . . 789--808 Y. Li and I. Babu\vska A convergence analysis of a $p$-version finite element method for one-dimensional elastoplasticity problem with constitutive laws based on the gauge function method . . . . . . . . . 809--842
J. O. Langseth and A. Tveito and R. Winther On the Convergence of Operator Splitting Applied to Conservation Laws with Source Terms . . . . . . . . . . . . . . . . . 843--863 Mimmo Iannelli and Roberto Loro and Fabio A. Milner and Andrea Pugliese and Guglielmo Rabbiolo Numerical Analysis of a Model for the Spread of HIV/AIDS . . . . . . . . . . . 864--882 Hong-Jiong Tian and Jiao-Xun Kuang The Numerical Stability of Linear Multistep Methods for Delay Differential Equations with Many Delays . . . . . . . 883--889 Stephen A. Vavasis Stable Finite Elements for Problems with Wild Coefficients . . . . . . . . . . . 890--916 S. N. Papakostas and Ch Tsitouras and G. Papageorgiou A General Family of Explicit Runge--Kutta Pairs of Orders 6(5) . . . 917--936 Wei Cai and Jianzhong Wang Adaptive Multiresolution Collocation Methods for Initial Boundary Value Problems of Nonlinear PDEs . . . . . . . 937--970 J. Ma and V. Rokhlin and S. Wandzura Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions . . . 971--996 H. J. Schroll Convergence of Implicit Finite Difference Methods Applied to Nonlinear Mixed Systems . . . . . . . . . . . . . 997--1013 Smadar Karni Far-Field Filtering Operators for Suppression of Reflections from Artificial Boundaries . . . . . . . . . 1014--1047 Hideaki Kaneko and Yuesheng Xu Superconvergence of the Iterated Galerkin Methods for Hammerstein Equations . . . . . . . . . . . . . . . 1048--1064 Márcio A. Murad and Vidar Thomée and Abimael F. D. Loula Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot's Consolidation Problem . . . . . . . . . 1065--1083 Amiya K. Pani and Todd E. Peterson Finite Element Methods with Numerical Quadrature for Parabolic Integrodifferential Equations . . . . . 1084--1105 Willy Dörfler A Convergent Adaptive Algorithm for Poisson's Equation . . . . . . . . . . . 1106--1124 K. J. in 't Hout A Note on Unconditional Maximum Norm Contractivity of Diagonally Split Runge--Kutta Methods . . . . . . . . . . 1125--1134 Paul A. Farrell and John J. H. Miller and Eugene O'Riordan and Grigori I. Shishkin A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation . . . . . . . . . . 1135--1149 Vladimír Janovský and Petr Plechá\vc Local Numerical Analysis of Hopf Bifurcation . . . . . . . . . . . . . . 1150--1168 Ben-Yu Guo and Jian Li Fourier--Chebyshev Spectral Method for the Two-Dimensional Navier--Stokes Equations . . . . . . . . . . . . . . . 1169--1187 Folkmar A. Bornemann and Bodo Erdmann and Ralf Kornhuber \em A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions . . . . . . . . . . . . . . . 1188--1204 Ami Harten Multiresolution Representation of Data: A General Framework . . . . . . . . . . 1205--1256
Domingo Alberto Tarzia Numerical Analysis for the Heat Flux in a Mixed Elliptic Problem to Obtain a Discrete Steady-State Two-Phase Stefan Problem . . . . . . . . . . . . . . . . 1257--1265 Gary Cohen and Patrick Joly Construction and Analysis of Fourth-Order Finite Difference Schemes for the Acoustic Wave Equation in Nonhomogeneous Media . . . . . . . . . . 1266--1302 Luca F. Pavarino and Olof B. Widlund A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions . . . . . . 1303--1335 Zi-Niu Wu Uniqueness of Steady-State Solutions for Difference Equations on Overlapping Grids . . . . . . . . . . . . . . . . . 1336--1357 Mark Ainsworth A Preconditioner Based on Domain Decomposition for $h$-$p$ Finite-Element Approximation on Quasi-Uniform Meshes 1358--1376 Stephen Wollman and Ercument Ozizmir Numerical Approximation of the One-Dimensional Vlasov--Poisson System with Periodic Boundary Conditions . . . 1377--1409 Olli Jokinen On Monotone Solutions of an Integrodifferential Equation in Linear Viscoelasticity . . . . . . . . . . . . 1410--1424 Ibrahim Bless Ranero and Tomás Chacón Rebello An Efficient Two-Dimensional Vortex Method with Long Time Accuracy . . . . . 1425--1450 Yin Yan Attractors and Error Estimates for Discretizations of Incompressible Navier--Stokes Equations . . . . . . . . 1451--1472 Riccardo Fazio A Novel Approach to the Numerical Solution of Boundary Value Problems on Infinite Intervals . . . . . . . . . . . 1473--1483 Thanh Tran Local Error Estimates for the Galerkin Method Applied to Strongly Elliptic Integral Equations on Open Curves . . . 1484--1493 P. Joly and C. Poirier and J. E. Roberts and P. Trouve A New Nonconforming Finite Element Method for the Computation of Electromagnetic Guided Waves I: Mathematical Analysis . . . . . . . . . 1494--1525 Lixin Wu Dufort--Frankel-type methods for linear and nonlinear Schrödinger equations . . . 1526--1533 Lucilla Corrias Fast Legendre--Fenchel Transform and Applications to Hamilton--Jacobi Equations and Conservation Laws . . . . 1534--1558 Christopher T. H. Baker and Christopher A. H. Paul A Global Convergence Theorem for a Class of Parallel Continuous Explicit Runge--Kutta Methods and Vanishing Lag Delay Differential Equations . . . . . . 1559--1576 J. Saranen and G. Vainkko Trigonometric Collocation Methods with Product Integration for Boundary Integral Equations on Closed Curves . . 1577--1596 Weinan E and Jian-Guo Liu Projection method. II. Godunov--Ryabenki analysis . . . . . . . . . . . . . . . . 1597--1621 Anton Arnold and Christian Ringhofer An Operator Splitting Method for the Wigner--Poisson Problem . . . . . . . . 1622--1643 Masaki Utumi and Ryuji Takaki and Toshio Kawai Optimal Time Step Control for the Numerical Solution of Ordinary Differential Equations . . . . . . . . . 1644--1653 C. Palencia Maximum Norm Analysis of Completely Discrete Finite Element Methods for Parabolic Problems . . . . . . . . . . . 1654--1668 Todd Arbogast and Mary F. Wheeler and Nai-Ying Zhang A Nonlinear Mixed Finite Element Method for a Degenerate Parabolic Equation Arising in Flow in Porous Media . . . . 1669--1687
A. Dutt and M. Gu and V. Rokhlin Fast Algorithms for Polynomial Interpolation, Integration, and Differentiation . . . . . . . . . . . . 1689--1711 Peter Albrecht The Runge--Kutta Theory in a Nutshell 1712--1735 Barry Bernstein and Kathleen A. Feigl and Elwood T. Olsen A First-Order Exactly Incompressible Finite Element for Axisymmetric Fluid Flow . . . . . . . . . . . . . . . . . . 1736--1758 Jinchao Xu Two-Grid Discretization Techniques for Linear and Nonlinear PDEs . . . . . . . 1759--1777 David Gottlieb and Bertil Gustafsson and Pelle Olsson and Bo Strand On the Superconvergence of Galerkin Methods for Hyperbolic IBVP . . . . . . 1778--1796 J. Thomas Beale and Thomas Y. Hou and John Lowengrub Convergence of a Boundary Integral Method for Water Waves . . . . . . . . . 1797--1843 L. Vozovoi and M. Israeli and A. Averbuch Analysis and Application of Fourier--Gegenbauer Method to Stiff Differential Equations . . . . . . . . . 1844--1863 Thomas Kerkhoven Piecewise Linear Petrov--Galerkin Error Estimates for the Box Method . . . . . . 1864--1884 Bernd Heinrich The Fourier-Finite-Element Method for Poisson's Equation in Axisymmetric Domains with Edges . . . . . . . . . . . 1885--1911 A. Griewank and G. W. Reddien The Approximate Solution of Defining Equations for Generalized Turning Points 1912--1920 Uri M. Ascher and Ping Lin Sequential Regularization Methods for Higher Index DAEs with Constraint Singularities: The Linear Index-$2$ Case 1921--1940 Peter Kunkel and Volker Mehrmann A New Class of Discretization Methods for the Solution of Linear Differential-Algebraic Equations with Variable Coefficients . . . . . . . . . 1941--1961 Mark C. Haase Extra Smoothness Requirements for Galerkin Methods for the Wave Equation 1962--1968 J. Bahi and E. Griepentrog and J. C. Miellou Parallel Treatment of a Class of Differential-Algebraic Systems . . . . . 1969--1980 N. André and M. Chipot Uniqueness and Nonuniqueness for the Approximation of Quasilinear Elliptic Equations . . . . . . . . . . . . . . . 1981--1994 Fred J. Hickernell Quadrature Error Bounds with Applications to Lattice Rules . . . . . 1995--2016 Ching-Yih Tseng A Multiple-Exchange Algorithm for Complex Chebyshev Approximation by Polynomials on the Unit Circle . . . . . 2017--2049 J. L. Estivalezes and P. Villedieu High-Order Positivity-Preserving Kinetic Schemes for the Compressible Euler Equations . . . . . . . . . . . . . . . 2050--2067 Vladimír Janovský and Viktor Seige Qualitative Analysis of Newton's Flow 2068--2097
D. Issautier Convergence of a Weighted Particle Method for Solving the Boltzmann (B.G.K.) Equation . . . . . . . . . . . 2099--2119 Ulrich Tautenhahn Error Estimates for Regularization Methods in Hilbert Scales . . . . . . . 2120--2130 Kurt Otto Analysis of Preconditioners for Hyperbolic Partial Differential Equations . . . . . . . . . . . . . . . 2131--2165 Carsten Carstensen and Ernst P. Stephan Adaptive Boundary Element Methods for Some First Kind Integral Equations . . . 2166--2183 Zhimin Zhang and Ivo Babu\vska A Numerical Method for Steady State Free Boundary Problems . . . . . . . . . . . 2184--2214 Noel J. Walkington Algorithms for Computing Motion by Mean Curvature . . . . . . . . . . . . . . . 2215--2238 G. Larcher and A. Lauss and H. Niederreiter and W. Ch. Schmid Optimal Polynomials for $ (t, m, s)$-Nets and Numerical Integration of Multivariate Walsh Series . . . . . . . 2239--2253 Yoshihiro Saito and Taketomo Mitsui Stability Analysis of Numerical Schemes for Stochastic Differential Equations 2254--2267 Weiwei Sun and Weizhang Huang and Robert D. Russell Finite Difference Preconditioning for Solving Orthogonal Collocation Equations for Boundary Value Problems . . . . . . 2268--2285 P. K. Jimack A Best Approximation Property of the Moving Finite Element Method . . . . . . 2286--2302 Z. Jackiewicz and M. Kwapisz Convergence of Waveform Relaxation Methods for Differential-Algebraic Systems . . . . . . . . . . . . . . . . 2303--2317 Katalin Balla and Roswitha März Transfer of Boundary Conditions for DAEs of Index $1$ . . . . . . . . . . . . . . 2318--2332 Gerald Moore Computation and Parametrisation of Invariant Curves and Tori . . . . . . . 2333--2358 O. Axelsson and W. Layton A Two-Level Method for the Discretization of Nonlinear Boundary Value Problems . . . . . . . . . . . . . 2359--2374 Sang Dong Kim and Seymour V. Parter Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations . . . . . . . . . 2375--2400 Jean-David Benamou A Domain Decomposition Method with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations 2401--2416 Xuzhou Chen and Moody T. Chu On the Least Squares Solution of Inverse Eigenvalue Problems . . . . . . . . . . 2417--2430 D. Braess and R. Verfürth \em A Posteriori Error Estimators for the Raviart--Thomas Element . . . . . . 2431--2444 V. Caselles and B. Coll Snakes in Movement . . . . . . . . . . . 2445--2456 C. Lovadina A New Class of Mixed Finite Element Methods for Reissner--Mindlin Plates . . 2457--2467 G. E. Sneddon Second-Order Spectral Differentiation Matrices . . . . . . . . . . . . . . . . 2468--2487 G. D. Akrivis and V. A. Dougalis and G. E. Zouraris Error Estimates for Finite Difference Methods for a Wide-Angle ``Parabolic'' Equation . . . . . . . . . . . . . . . . 2488--2509
John Guckenheimer and Mark Myers and Bernd Sturmfels Computing Hopf bifurcations. I . . . . . 1--21 S. N. Papakostas and Ch. Tsitouras Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge--Kutta Methods . . 22--47 Ebrahim M. Kasenally and Valeria Simoncini Analysis of a Minimum Perturbation Algorithm for Nonsymmetric Linear Systems . . . . . . . . . . . . . . . . 48--66 Keith Miller A Geometrical-Mechanical Interpretation of Gradient-Weighted Moving Finite Elements . . . . . . . . . . . . . . . . 67--90 K. Kunisch and X.-C. Tai Sequential and Parallel Splitting Methods for Bilinear Control Problems in Hilbert Spaces . . . . . . . . . . . . . 91--118 A. T. Hill Global Dissipativity for $A$-Stable Methods . . . . . . . . . . . . . . . . 119--142 Weimin Han and B. Daya Reddy and Gregory C. Schroeder Qualitative and Numerical Analysis of Quasi-Static Problems in Elastoplasticity . . . . . . . . . . . . 143--177 Zhiqiang Cai and Jan Mandel and Steve McCormick Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems 178--200 John W. Barrett and Peter Knabner Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part $1$: Error Estimates for Nonequilibrium Adsorption Processes . . 201--227 Mark Ainsworth and J. Tinsley Oden \em A Posteriori Error Estimators for the Stokes and Oseen Equations . . . . . 228--245 Russel E. Caflisch and Shi Jin and Giovanni Russo Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation . . . 246--281 Rafael Muñoz-Sola Polynomial Liftings on a Tetrahedron and Applications to the $h$-$p$ Version of the Finite Element Method in Three Dimensions . . . . . . . . . . . . . . . 282--314 Frank Ihlenburg and Ivo Babu\vska Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The $h$-$p$ Version of the FEM . . . . . 315--358 Pablo Martín and José M. Ferrándiz Multistep Numerical Methods Based on the Scheifele $G$-Functions with Application to Satellite Dynamics . . . . . . . . . 359--375 J. G. Verwer and B. P. Sommeijer Stability Analysis of an Odd-Even-Line Hopscotch Method for Three-Dimensional Advection-Diffusion Problems . . . . . . 376--388 Ch. G. Makridakis and I. Babu\vska On the Stability of the Discontinuous Galerkin Method for the Heat Equation 389--401 Luca Dieci and Robert D. Russell and Erik S. Van Vleck On the Computation of Lyapunov Exponents for Continuous Dynamical Systems . . . . 402--423
Zhiqiang Cai and Thomas A. Manteuffel and Stephen F. McCormick First-Order System Least Squares for Second-Order Partial Differential Equations: Part II . . . . . . . . . . . 425--454 John W. Barrett and Peter Knabner Finite Element Approximation of The Transport of Reactive Solutes in Porous Media. Part II: Error Estimates for Equilibrium Adsorption Processes . . . . 455--479 C. L. Chang and John J. Nelson Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation . . . . . . . . . . . 480--489 Ricardo H. Nochetto and Claudio Verdi Convergence Past Singularities for a Fully Discrete Approximation of Curvature-Driven Interfaces . . . . . . 490--512 Igor Moret A Note on the Superlinear Convergence of GMRES . . . . . . . . . . . . . . . . . 513--516 Andreas Neubauer On Converse and Saturation Results for Tikhonov Regularization of Linear Ill-Posed Problems . . . . . . . . . . . 517--527 A. Bellen and L. Torelli Unconditional Contractivity in the Maximum Norm of Diagonally Split Runge--Kutta Methods . . . . . . . . . . 528--543 Rolf Stenberg and Manil Suri An $h$-$p$ Error Analysis of MITC Plate Elements . . . . . . . . . . . . . . . . 544--568 Lu Han and Larry L. Schumaker Fitting Monotone Surfaces to Scattered Data Using $ C^1 $ Piecewise Cubics . . 569--585 J. N. Lyness and I. H. Sloan Cubature Rules of Prescribed Merit . . . 586--602 Alain Bamberger and Roland Glowinski and Quang Huy Tran A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change . . . . . . . . . . . . . . . . . 603--639 Zhimin Zhang Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity . . . . . . . 640--663 Daniele Boffi Three-Dimensional Finite Element Methods for the Stokes Problem . . . . . . . . . 664--670 Patrick Joly and Jukka Tuomela A New Theoretical Approach to Absorbing Layers . . . . . . . . . . . . . . . . . 671--698 Michael Holst and Stefan Vandewalle Schwarz Methods: To Symmetrize or Not to Symmetrize . . . . . . . . . . . . . . . 699--722 Brian R. Wetton Analysis of the Spatial Error for a Class of Finite Difference Methods for Viscous Incompressible Flow . . . . . . 723--755 Mark A. Aves and David F. Griffiths and Desmond J. Higham Does Error Control Suppress Spuriosity? 756--778 Peixiong Lin and K. W. Morton and E. Süli Characteristic Galerkin Schemes for Scalar Conservation Laws in Two and Three Space Dimensions . . . . . . . . . 779--796 Pascal Van Hentenryck and David McAllester and Deepak Kapur Solving Polynomial Systems Using a Branch and Prune Approach . . . . . . . 797--827 Todd Arbogast and Mary F. Wheeler and Ivan Yotov Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences . . . . 828--852 Fred J. Hickernell Erratum: ``Quadrature error bounds with applications to lattice rules'' [SIAM J. Numer. Anal. \bf 33 (1996), no. 5, 1995--2016; MR 1 411 860] . . . . . . . 853--866
W. Govaerts Computation of Singularities in Large Nonlinear Systems . . . . . . . . . . . 867--880 Zhangxin Chen and Richard E. Ewing Stability and Convergence of a Finite Element Method for Reactive Transport in Ground Water . . . . . . . . . . . . . . 881--904 Ming-Jun Lai and Larry L. Schumaker Scattered Data Interpolation Using $ C^2 $ Supersplines of Degree Six . . . . . . 905--921 T. Csendes and D. Ratz Subdivision Direction Selection in Interval Methods for Global Optimization 922--938 Sang Dong Kim and Seymour V. Parter Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators . . . . . . . . . . . . . . . 939--958 Zhen-huan Teng and Pingwen Zhang Optimal $ L^1 $-Rate of Convergence for The Viscosity Method and Monotone Scheme to Piecewise Constant Solutions with Shocks . . . . . . . . . . . . . . . . . 959--978 Randolph E. Bank and R. Kent Smith Mesh Smoothing Using A Posteriori Error Estimates . . . . . . . . . . . . . . . 979--997 Yiwei Li and Ivo Babu\vska A Convergence Analysis of an $H$-Version Finite-Element Method with High-Order Elements for Two-Dimensional Elasto-Plasticity Problems . . . . . . . 998--1036 Xiaonan Wu and Houde Han A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities . . . . . . . . . . . 1037--1050 Ping Lin A Sequential Regularization Method for Time-Dependent Incompressible Navier--Stokes Equations . . . . . . . . 1051--1071 James H. Bramble and Joseph E. Pasciak and Apostol T. Vassilev Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems . . . . . . . 1072--1092 R. Bruce Kellogg and Biyue Liu A Penalized Finite-Element Method for a Compressible Stokes System . . . . . . . 1093--1105 Weizhang Huang and Robert D. Russell Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing . . . . . . . . . . . . . . . 1106--1126 Philippe Balland and Endre Süli Analysis of the Cell-Vertex Finite Volume Method for Hyperbolic Problems with Variable Coefficients . . . . . . . 1127--1151 Hans Joachim Schroll and Aslak Tveito and Ragnar Winther An $ L^1 $-Error Bound for a Semi-Implicit Difference Scheme Applied to a Stiff System of Conservation Laws 1152--1166 François Dubeau and Jean Savoie Best Error Estimates for Odd and Even Degree Deficient Splines . . . . . . . . 1167--1184 Chichia Chiu and Noel Walkington An ADI Method for Hysteretic Reaction-Diffusion Systems . . . . . . . 1185--1206 W.-J. Beyn and J.-M. Kleinkauf The Numerical Computation of Homoclinic Orbits for Maps . . . . . . . . . . . . 1207--1236 S. Shaw and M. K. Warby and J. R. Whiteman Error Estimates with Sharp Constants for a Fading Memory Volterra Problem in Linear Solid Viscoelasticity . . . . . . 1237--1254 Nilotpal Ghosh and William W. Hager and Purandar Sarmah The Application of Eigenpair Stability to Block Diagonalization . . . . . . . . 1255--1268 W. Govaerts and J. Guckenheimer and A. Khibnik Defining Functions for Multiple Hopf Bifurcations . . . . . . . . . . . . . . 1269--1288
S. Ning and R. B. Kearfott A Comparison of Some Methods for Solving Linear Interval Equations . . . . . . . 1289--1305 Philippe Guillaume and Mohamed Masmoudi Solution to the Time-Harmonic Maxwell's Equations in a Waveguide; Use of Higher-Order Derivatives for Solving the Discrete Problem . . . . . . . . . . . . 1306--1330 Sharad Kapur and Vladimir Rokhlin High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions 1331--1356 Karen A. Ames and James F. Epperson A Kernel-Based Method for the Approximate Solution of Backward Parabolic Problems . . . . . . . . . . . 1357--1390 B. Cano and J. M. Sanz-Serna Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems . . . . . . . . . . . 1391--1417 Fu-Rong Lin and Michael K. Ng and Raymond H. Chan Preconditioners for Wiener--Hopf Equations with High-Order Quadrature Rules . . . . . . . . . . . . . . . . . 1418--1431 Patricia K. Lamm and Lars Eldén Numerical Solution of First-Kind Volterra Equations by Sequential Tikhonov Regularization . . . . . . . . 1432--1450 L. Vozovoi and A. Weill and M. Israeli Spectrally Accurate Solution of Nonperiodic Differential Equations by the Fourier--Gegenbauer Method . . . . . 1451--1471 Charles K. Chui and Dong Hong Swapping Edges of Arbitrary Triangulations to Achieve the Optimal Order of Approximation . . . . . . . . . 1472--1482 Gabriel James Lord Attractors and Inertial Manifolds for Finite-Difference Approximations of the Complex Ginzburg--Landau Equation . . . 1483--1512 Marc Garbey and Hans G. Kaper Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems . . . . . . . . . . . . . 1513--1544 Zakaria Belhachmi Nonconforming Mortar Element Methods for the Spectral Discretization of Two-Dimensional Fourth-Order Problems 1545--1573 J. B. Burie and M. Marion Multilevel Methods in Space and Time for the Navier--Stokes Equations . . . . . . 1574--1599 Claudio Padra \em A Posteriori Error Estimators for Nonconforming Approximation of Some Quasi-Newtonian Flows . . . . . . . . . 1600--1615 P. Gervasio and E. Ovtchinnikov and A. Quarteroni The Spectral Projection Decomposition Method for Elliptic Equations in Two Dimensions . . . . . . . . . . . . . . . 1616--1639 Bruno D. Welfert Generation of Pseudospectral Differentiation Matrices I . . . . . . . 1640--1657 Ronald H. W. Hoppe and Barbara Wohlmuth Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems . . . . 1658--1681
Brian R. Wetton Error Analysis for Chorin's Original Fully Discrete Projection Method and Regularizations in Space and Time . . . 1683--1697 Qi Ya Hu Superconvergence of Numerical Solutions to Volterra Integral Equations with Singularities . . . . . . . . . . . . . 1698--1707 François Alouges A New Algorithm for Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case . . . . . . . . . 1708--1726 Z. Cai and T. A. Manteuffel and S. F. McCormick First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity . . . . . . . . . . . 1727--1741 D. B. Duncan Symplectic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation . . . . . . . . . 1742--1760 Avram Sidi A Complete Convergence and Stability Theory for a Generalized Richardson Extrapolation Process . . . . . . . . . 1761--1778 David C. Dobson and Curtis R. Vogel Convergence of an Iterative Method for Total Variation Denoising . . . . . . . 1779--1791 Todd R. Littell and Robert D. Skeel and Meiqing Zhang Error Analysis of Symplectic Multiple Time Stepping . . . . . . . . . . . . . 1792--1807 R. Bruce Kellogg and Martin Stynes Optimal Approximability of Solutions of Singularly Perturbed Two-Point Boundary Value Problems . . . . . . . . . . . . . 1808--1816 Pavel B. Bochev Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations 1817--1844 Carsten Carstensen and Joachim Gwinner FEM and BEM Coupling for a Nonlinear Transmission Problem with Signorini Contact . . . . . . . . . . . . . . . . 1845--1864 Andrzej Palczewski and Jacques Schneider and Alexandre V. Bobylev A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation . . . . . . . . . . . . . . . . 1865--1883 Art B. Owen Monte Carlo variance of scrambled net quadrature . . . . . . . . . . . . . . . 1884--1910 Marlis Hochbruck and Christian Lubich On Krylov Subspace Approximations to the Matrix Exponential Operator . . . . . . 1911--1925 A. L. Araújo and A. Murua and J. M. Sanz-Serna Symplectic Methods Based on Decompositions . . . . . . . . . . . . . 1926--1947 Gilles Aubert and Luminita Vese A Variational Method in Image Recovery 1948--1979 J. M. Greenberg and A. Y. LeRoux and R. Baraille and A. Noussair Analysis and Approximation of Conservation Laws with Source Terms . . 1980--2007 Bryan D. Davidson Large-Scale Continuation and Numerical Bifurcation for Partial Differential Equations . . . . . . . . . . . . . . . 2008--2027 Peter Winker and Kai-Tai Fang Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points . . . . . . . . . . . . . 2028--2042 M. Vanmaele and K. W. Morton and E. Suli and A. Borzi Analysis of the Cell Vertex Finite Volume Method for the Cauchy--Riemann Equations . . . . . . . . . . . . . . . 2043--2062 M. Sofroniou and W. Oevel Symplectic Runge--Kutta schemes. I. Order conditions . . . . . . . . . . . . 2063--2086
Ernst Hairer and Gerhard Wanner Order Conditions for General Two-Step Runge--Kutta Methods . . . . . . . . . . 2087--2089 J. T. Oden and Abani Patra and Yusheng Feng Parallel Domain Decomposition Solver for Adaptive $ h p $ Finite Element Methods 2090--2118 J. C. Butcher and Z. Jackiewicz Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations . . . . 2119--2141 G. N. Milstein and M. V. Tret\cprimeyakov Numerical Methods in the Weak Sense for Stochastic Differential Equations with Small Noise . . . . . . . . . . . . . . 2142--2167 E. Gabetta and L. Pareschi and G. Toscani Relaxation Schemes for Nonlinear Kinetic Equations . . . . . . . . . . . . . . . 2168--2194 Roy A. Nicolaides and Xiaonan Wu Covolume Solutions of Three-Dimensional Div-Curl Equations . . . . . . . . . . . 2195--2203 Ander Murua On Order Conditions for Partitioned Symplectic Methods . . . . . . . . . . . 2204--2211 Tobias von Petersdorff and Christoph Schwab and Reinhold Schneider Multiwavelets for Second Kind Integral Equations . . . . . . . . . . . . . . . 2212--2227 Zhangxin Chen and Richard E. Ewing Fully-Discrete Finite Element Analysis of Multiphase Flow in Groundwater Hydrology . . . . . . . . . . . . . . . 2228--2253 Bjorn Engquist and Erding Luo Convergence of a Multigrid Method for Elliptic Equations with Highly Oscillatory Coefficients . . . . . . . . 2254--2273 Robert D. Russell and Weiwei Sun Spline Collocation Differentiation Matrices . . . . . . . . . . . . . . . . 2274--2287 G. Monegato and I. H. Sloan Numerical Solution of the Generalized Airfoil Equation for an Airfoil with a Flap . . . . . . . . . . . . . . . . . . 2288--2305 Florin \cSabac The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws . . . . . . . . . . . 2306--2318 Eric Boillat On the Locking of the Finite Element Method in Thermoelasticity . . . . . . . 2319--2334 Gabriel N. Gatica and Wolfgang L. Wendland Coupling of Mixed Finite Elements and Boundary Elements for a Hyperelastic Interface Problem . . . . . . . . . . . 2335--2356 Sherman D. Riemenschneider and Zuowei Shen Multidimensional Interpolatory Subdivision Schemes . . . . . . . . . . 2357--2381 I. Perugia A Field-Based Mixed Formulation for the Two-Dimensional Magnetostatic Problem 2382--2391 Ivo M. Babu\vska and Stefan A. Sauter Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers . . . . . 2392--2423 Jianhua Pan Global Superconvergence for the Bilinear-Constant Scheme for the Stokes Problem . . . . . . . . . . . . . . . . 2424--2430 Christoph Pflaum Convergence of the Combination Technique for Second-Order Elliptic Differential Equations . . . . . . . . . . . . . . . 2431--2455 Jan Janssen and Stefan Vandewalle On SOR Waveform Relaxation Methods . . . 2456--2481 Mario A. Casarin Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization . . . . . . . . . . . . . 2482--2502
Patrick Fischer and Mireille Defranceschi Numerical Solution of the Schrödinger Equation in a Wavelet Basis for Hydrogen-like Atoms . . . . . . . . . . 1--12 C. Bourdarias Approximation of the Solution to a System Modeling Heatless Adsorption of Gases . . . . . . . . . . . . . . . . . 13--30 B. Leimkuhler Timestep Acceleration of Waveform Relaxation . . . . . . . . . . . . . . . 31--50 Christian Lécot and Ibrahim Coulibaly A Quasi-Monte Carlo Scheme Using Nets for a Linear Boltzmann Equation . . . . 51--70 Claus B. Schneider Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle . . 71--77 Sven Ehrich On Product Integration with Gauss--Kronrod Nodes . . . . . . . . . . 78--92 Ohannes A. Karakashian and Wadi N. Jureidini A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations . . . . . . . . . . . . . . . 93--120 Chang-Ock Lee Multigrid Methods for the Pure Traction Problem of Linear Elasticity: Mixed Formulation . . . . . . . . . . . . . . 121--145 Guo Ben-Yu and He Li-Ping The Fully Discrete Legendre Spectral Approximation of Two-Dimensional Unsteady Incompressible Fluid Flow in Stream Function Form . . . . . . . . . . 146--176 Andreas Wiegmann and Kenneth P. Bube The Immersed Interface Method for Nonlinear Differential Equations with Discontinuous Coefficients and Singular Sources . . . . . . . . . . . . . . . . 177--200 Thomas Petry On the Stability of the Abramov Transfer for Differential-Algebraic Equations of Index $1$ . . . . . . . . . . . . . . . 201--216 Serguei Maliassov A Two-Level Preconditioner for Schrödinger-Type Singular Elliptic Operator . . . . . . . . . . . . . . . . 217--229 Zhilin Li A Fast Iterative Algorithm for Elliptic Interface Problems . . . . . . . . . . . 230--254 Olivier Cessenat and Bruno Despres Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem . . . 255--299 Eldar Giladi and Gene H. Golub and Joseph B. Keller Inner and Outer Iterations for the Chebyshev Algorithm . . . . . . . . . . 300--319 Zhiqiang Cai and Thomas A. Manteuffel and Stephen F. McCormick and Seymour V. Parter First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem . . . . . . . . . . . . 320--335 Timothy A. Davis and Eugene C. Gartland, Jr. Finite Element Analysis of the Landau-de Gennes Minimization Problem for Liquid Crystals . . . . . . . . . . . . . . . . 336--362 HongSung Jin and Steven Pruess Uniformly Superconvergent Approximations for Linear Two-Point Boundary Value Problems . . . . . . . . . . . . . . . . 363--375 Bo Li and Mitchell Luskin Finite Element Analysis of Microstructure for the Cubic to Tetragonal Transformation . . . . . . . 376--392 Yanzhao Cao and Max D. Gunzburger Least-Squares Finite Element Approximations to Solutions of Interface Problems . . . . . . . . . . . . . . . . 393--405 Zhongying Chen and Yuesheng Xu The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations . . . . . . . . . . . 406--434
Clint N. Dawson and Mary F. Wheeler and Carol S. Woodward A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations . . . . . 435--452 Bingkun Li and Graeme Fairweather and Bernard Bialecki Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables . . . . 453--477 Moshe Goldberg Stable Difference Schemes for Parabolic Systems --- A Numerical Radius Approach 478--493 S. H. Chou and D. Y. Kwak A Covolume Method Based on Rotated Bilinears for the Generalized Stokes Problem . . . . . . . . . . . . . . . . 494--507 C. T. Kelley and David E. Keyes Convergence Analysis of Pseudo-Transient Continuation . . . . . . . . . . . . . . 508--523 Jiri Rohn and Georg Rex Enclosing Solutions of Linear Equations 524--539 Mihai Dorobantu and Björn Engquist Wavelet-Based Numerical Homogenization 540--559 Houde Han and Xiaonan Wu A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations . . . . . . . . . . . . . . . 560--571 W. H. Enright and H. Hayashi Convergence Analysis of the Solution of Retarded and Neutral Delay Differential Equations by Continuous Numerical Methods . . . . . . . . . . . . . . . . 572--585 R. I. McLachlan and G. R. W. Quispel and G. S. Turner Numerical Integrators that Preserve Symmetries and Reversing Symmetries . . 586--599 Jinping Zeng and Shuzi Zhou On Monotone and Geometric Convergence of Schwarz Methods for Two-Sided Obstacle Problems . . . . . . . . . . . . . . . . 600--616 Bernard Bialecki Convergence Analysis of Orthogonal Spline Collocation for Elliptic Boundary Value Problems . . . . . . . . . . . . . 617--631 Benqi Guo and Weiming Cao An Additive Schwarz Method for the $h$-$b$ Version of the Finite Element Method in Three Dimensions . . . . . . . 632--654 J. S. Hesthaven From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex . . . . . . . . . . . . . . 655--676 Cesare Davini and Igino Pitacco Relaxed Notions of Curvature and a Lumped Strain Method for Elastic Plates 677--691 S. Chippada and C. N. Dawson and M. L. Martinez and M. F. Wheeler Finite Element Approximations to the System of Shallow Water Equations I: Continuous-Time \em A Priori Error Estimates . . . . . . . . . . . . . . . 692--711 Amiya K. Pani An $ H^1$-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations . . . . . . . . . 712--727 Jörg Peters and Ulrich Reif Analysis of Algorithms Generalizing B-Spline Subdivision . . . . . . . . . . 728--748 Guang-Shan Jiang and Shih-Hsien Yu Discrete Shocks for Finite Difference Approximations to Scalar Conservation Laws . . . . . . . . . . . . . . . . . . 749--772 Pablo Martín and José M. Farto Increasing the Order of the SMF Method for a Special Type of Problem . . . . . 773--777 M. Ganesh and I. G. Graham and J. Sivaloganathan A New Spectral Boundary Integral Collocation Method for Three-Dimensional Potential Problems . . . . . . . . . . . 778--805 Thomas A. Manteuffel and Klaus J. Ressel Least-Squares Finite-Element Solution of the Neutron Transport Equation in Diffusive Regimes . . . . . . . . . . . 806--835 Patrick Le Tallec and Jan Mandel and Marina Vidrascu A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems . . . . . . . . . . . . . . . . 836--867
Heping Ma Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws 869--892 Heping Ma Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws . . . . . . . . . . . 893--908 Maurizio Falcone and Roberto Ferretti Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes . . . . . . . . . . . . . . . . 909--940 Bosco García-Archilla and Julia Novo and Edriss S. Titi Postprocessing the Galerkin Method: a Novel Approach to Approximate Inertial Manifolds . . . . . . . . . . . . . . . 941--972 C. González and C. Palencia Stability of Time-Stepping Methods for Abstract Time-Dependent Parabolic Problems . . . . . . . . . . . . . . . . 973--989 P. Bochev and Z. Cai and T. A. Manteuffel and S. F. McCormick Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I . . . . 990--1009 G. N. Milstein and E. Platen and H. Schurz Balanced Implicit Methods for Stiff Stochastic Systems . . . . . . . . . . . 1010--1019 Carlos Conca and Axel Osses and Jacques Planchard Asymptotic Analysis Relating Spectral Models in Fluid-Solid Vibrations . . . . 1020--1048 Qiang Du and R. A. Nicolaides and Xiaonan Wu Analysis and Convergence of a Covolume Approximation of the Ginzburg--Landau Model of Superconductivity . . . . . . . 1049--1072 Axel Klar An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit . . . . . . . . . . . . 1073--1094 Carsten Ebmeyer Error Estimates for a Class of Degenerate Parabolic Equations . . . . . 1095--1112 H. Barucq and F. Delaurens and B. Hanouzet Method of Absorbing Boundary Conditions: Phenomena of Error Stabilization . . . . 1113--1129 Xiaojun Chen Global and Superlinear Convergence of Inexact Uzawa Methods for Saddle Point Problems with Nondifferentiable Mappings 1130--1148 Jack Schaeffer Convergence of a Difference Scheme for the Vlasov--Poisson--Fokker--Planck System in One Dimension . . . . . . . . 1149--1175 Xun Jiang and Ricardo H. Nochetto A $ {P}^1$-$ {P}^1$ Finite Element Method for a Phase Relaxation Model I: Quasi-Uniform Mesh . . . . . . . . . . . 1176--1190 Shayne Waldron The Error in Linear Interpolation at the Vertices of a Simplex . . . . . . . . . 1191--1200 Nicolas Neuss $V$-cycle Convergence with Unsymmetric Smoothers and Application to an Anisotropic Model Problem . . . . . . . 1201--1212 O. Axelsson and I. E. Kaporin Minimum Residual Adaptive Multilevel Finite Element Procedure for the Solution of Nonlinear Stationary Problems . . . . . . . . . . . . . . . . 1213--1229 Jouko Tervo An FEM Scheme of a PDE System from Bioreactor Theory with Stability Results 1230--1248 Suzanne L. Weekes The Travelling Wave Scheme for the Navier--Stokes Equations . . . . . . . . 1249--1270 Charles R. Collins Convergence of a Reduced Integration Method for Computing Microstructures . . 1271--1298
Mohammad Asadzadeh A Finite Element Method for the Neutron Transport Equation in an Infinite Cylindrical Domain . . . . . . . . . . . 1299--1314 Kenneth Eriksson and Claes Johnson and Stig Larsson Adaptive Finite Element Methods for Parabolic Problems VI: Analytic Semigroups . . . . . . . . . . . . . . . 1315--1325 Michael Hanke and Ebroul Izquierdo Macana and Roswitha März On Asymptotics in Case of Linear Index-$2$ Differential-Algebraic Equations . . . . . . . . . . . . . . . 1326--1346 A. Aubry and P. Chartier On Improving the Convergence of Radau IIA Methods Applied to Index $2$ DAEs 1347--1367 Paul Hughett Error Bounds for Numerical Inversion of a Probability Characteristic Function 1368--1392 Salim Meddahi An Optimal Iterative Process for the Johnson--Nedelec Method of Coupling Boundary and Finite Elements . . . . . . 1393--1415 Yves Tourigny and Frank Hülsemann A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems . . . . . . . . . . . . . . . . 1416--1438 W. P. Petersen A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations . . . 1439--1451 Pascal Laubin and Marc Baiwir Spline Collocation for a Boundary Integral Equation on Polygons with Cuts 1452--1472 Karl J. Havlak and Harold Dean Victory, Jr. On Deterministic Particle Methods for Solving Vlasov--Poisson--Fokker--Planck Systems . . . . . . . . . . . . . . . . 1473--1519 J. M. Melenk and C. Schwab $ h p $ FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence . . . . . . . . . . . . . . 1520--1557 Xue-Cheng Tai and Magne Espedal Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems . . . . . . . . . . . 1558--1570 J. S. Hesthaven Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators . . . . . . . . . . . . 1571--1593 Matthias Heinkenschloss A Trust Region Method for Norm Constrained Problems . . . . . . . . . . 1594--1620 R. Plato The Method of Conjugate Residuals for Solving the Galerkin Equations Associated with Symmetric Positive Semidefinite Ill-Posed Problems . . . . 1621--1645 Wilhelm Heinrichs Splitting Techniques for the Unsteady Stokes Equations . . . . . . . . . . . . 1646--1662 T. P. Mathew Uniform Convergence of the Schwarz Alternating Method for Solving Singularly Perturbed Advection-Diffusion Equations . . . . . . . . . . . . . . . 1663--1683 Jesus Vigo-Aguiar and José M. Ferrándiz A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems . . 1684--1708
Clint Dawson Analysis of an Upwind-Mixed Finite Element Method for Nonlinear contaminant Transport Equations . . . . . . . . . . 1709--1724 L. Scuderi A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap . . . . . . . . . . . . . . . . . . 1725--1739 Mo Mu and Yunqing Huang An Alternating Crank--Nicolson Method for Decoupling the Ginzburg--Landau Equations . . . . . . . . . . . . . . . 1740--1761 Huang Jianguo and Xi Shitong On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems 1762--1774 Bernardo Cockburn and Pierre-Alain Gremaud and Jimmy Xiangrong Yang \em A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws Part III: Multidimensional Flux-Splitting Monotone Schemes on Non-Cartesian Grids . . . . . 1775--1803 Zlatko Drmac A Tangent Algorithm for Computing the Generalized Singular Value Decomposition 1804--1832 Martin Kruzík Numerical Approach to Double Well Problems . . . . . . . . . . . . . . . . 1833--1849 So-Hsiang Chou and Do Y. Kwak and Panayot S. Vassilevski Mixed Covolume Methods for Elliptic Problems on Triangular Grids . . . . . . 1850--1861 John W. Barrett and Peter Knabner An Improved Error Bound for a Lagrange--Galerkin Method for Contaminant Transport with Non-Lipschitzian Adsorption Kinetics . . 1862--1882 Susanne C. Brenner Overcoming Corner Singularities Using Multigrid Methods . . . . . . . . . . . 1883--1892 C. Bernardi and V. Girault A Local Regularization Operator for Triangular and Quadrilateral Finite Elements . . . . . . . . . . . . . . . . 1893--1916 Christoph Fredebeul A-BDF: A Generalization of the Backward Differentiation Formulae . . . . . . . . 1917--1938 Tao Tang Convergence Analysis for Operator-Splitting Methods Applied to Conservation Laws with Stiff Source Terms . . . . . . . . . . . . . . . . . 1939--1968 Zlatko Drmac Accurate Computation of the Product-Induced Singular Value Decomposition with Applications . . . . 1969--1994 Moshe Goldberg Stable Difference Schemes for Parabolic Systems --- A Numerical Radius Approach II . . . . . . . . . . . . . . . . . . . 1995--2003 Nobito Yamamoto A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem . . . . . . . . . . 2004--2013 Robert Sandboge Quantitative Error Control for Finite Element Methods for One-Dimensional Compressible Flow . . . . . . . . . . . 2014--2034 W. Layton and L. Tobiska A Two-Level Method with Backtracking for the Navier--Stokes Equations . . . . . . 2035--2054 Peter Ashwin and Zhen Mei A Numerical Bifurcation Function for Homoclinic Orbits . . . . . . . . . . . 2055--2069 Leon Greenberg and Marco Marletta Oscillation Theory and Numerical Solution of Sixth Order Sturm--Liouville Problems . . . . . . . . . . . . . . . . 2070--2098 Philippe Destuynder and Brigitte Métivet Explicit Error Bounds for a Nonconforming Finite Element Method . . 2099--2115
Ami Harten and Peter D. Lax and C. David Levermore and newline William J. Morokoff Convex Entropies and Hyperbolicity for General Euler Equations . . . . . . . . 2117--2127 Rémi Abgrall Multiresolution Representation in Unstructured Meshes . . . . . . . . . . 2128--2146 G.-S. Jiang and D. Levy and C.-T. Lin and S. Osher and E. Tadmor High-Resolution Nonoscillatory Central Schemes with Nonstaggered Grids for Hyperbolic Conservation Laws . . . . . . 2147--2168 Brian T. Hayes and Philippe G. LeFloch Nonclassical Shocks and Kinetic Relations: Finite Difference Schemes . . 2169--2194 K. W. Morton On the Analysis of Finite Volume Methods for Evolutionary Problems . . . . . . . 2195--2222 Frédéric Coquel and Beno\^\it Perthame Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics . . . . . . . . . 2223--2249 Richard Liska and Burton Wendroff Composite Schemes for Conservation Laws 2250--2271 Matthieu Bultelle and Magali Grassin and Denis Serre Unstable Godunov Discrete Profiles for Steady Shock Waves . . . . . . . . . . . 2272--2297 Marsha J. Berger and Randall J. LeVeque Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems . . . . . . . . . . . 2298--2316 Yann Brenier and Emmanuel Grenier Sticky Particles and Scalar Conservation Laws . . . . . . . . . . . . . . . . . . 2317--2328 Gunilla Kreiss and Heinz-Otto Kreiss Stability of Steady Solutions of Burgers's Equation . . . . . . . . . . . 2329--2349 Thomas Sonar On Families of Pointwise Optimal Finite Volume ENO Approximations . . . . . . . 2350--2369 Wai Sun Don and David Gottlieb Spectral Simulation of Supersonic Reactive Flows . . . . . . . . . . . . . 2370--2384 Shi Jin and Zhouping Xin Numerical Passage from Systems of Conservation Laws to Hamilton--Jacobi Equations, and Relaxation Schemes . . . 2385--2404 Shi Jin and Lorenzo Pareschi and Giuseppe Toscani Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations . . . . . . . . . . . . . . . 2405--2439 Bernardo Cockburn and Chi-Wang Shu The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems . . . . . . . . . . . . . . . . 2440--2463 Bjorn Engquist and Björn Sjögreen The Convergence Rate of Finite Difference Schemes in the Presence of Shocks . . . . . . . . . . . . . . . . . 2464--2485
Huanan Yang On Wavewise Entropy Inequality for High Resolution Schemes II: Fully Discrete MUSCL Schemes with Exact Evolution in Small Time . . . . . . . . . . . . . . . 1--31 Dominique Chapelle and Rolf Stenberg Stabilized Finite Element Formulations for Shells in a Bending Dominated State 32--73 Christian Schmeiser and Alexander Zwirchmayr Convergence of Moment Methods for Linear Kinetic Equations . . . . . . . . . . . 74--88 Zhendong Luo and Ruxun Liu Mixed Finite Element Analysis and Numerical Solitary Solution for the RLW Equation . . . . . . . . . . . . . . . . 89--104 Bin Han and Rong-Qing Jia Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces . . . 105--124 Thorsten Hohage Convergence Rates of a Regularized Newton Method in Sound-Hard Inverse Scattering . . . . . . . . . . . . . . . 125--142 Ming-Jun Lai and Larry L. Schumaker On the Approximation Power of Splines on Triangulated Quadrangulations . . . . . 143--159 Francesc Ar\`andiga and Rosa Donat and Ami Harten Multiresolution Based on Weighted Averages of the Hat Function I: Linear Reconstruction Techniques . . . . . . . 160--203 R. Hiptmair Multigrid Method for Maxwell's Equations 204--225 S. Chippada and C. N. Dawson and M. L. Martínez-Canales and M. F. Wheeler Finite Element Approximations to the System of Shallow Water Equations, Part II: Discrete-Time \em A Priori Error Estimates . . . . . . . . . . . . . . . 226--250 Peter Monk and Endre Süli The Adaptive Computation of Far-Field Patterns by \em A Posteriori Error Estimation of Linear Functionals . . . . 251--274 A. Friedlander and J. M. Martínez and B. Molina and M. Raydan Gradient Method with Retards and Generalizations . . . . . . . . . . . . 275--289 J. Kacur Solution of Some Free Boundary Problems by Relaxation Schemes . . . . . . . . . 290--316 Georgios Akrivis Finite Difference Methods for the Wide-Angle ``Parabolic'' Equation . . . 317--329
Mark Ainsworth and Ivo Babu\vska Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems . . . . . . 331--353 Tony F. Chan and Pep Mulet On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration . . . . . . 354--367 Bjòrn Fredrik Nielsen Finite Element Discretizations of Elliptic Problems in the Presence of Arbitrarily Small Ellipticity: An Error Analysis . . . . . . . . . . . . . . . . 368--392 C. V. Pao Numerical Analysis of Coupled Systems of Nonlinear Parabolic Equations . . . . . 393--416 V. Drakopoulos and N. Argyropoulos and A. Böhm Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets . . . 417--435 Raymond H. Chan and Shu-fang Xu and Hao-min Zhou On the Convergence Rate of a Quasi-Newton Method for Inverse Eigenvalue Problems . . . . . . . . . . 436--441 Shari Moskow and Vladimir Druskin and Tarek Habashy and Ping Lee and Sofia Davydycheva A Finite Difference Scheme for Elliptic Equations with Rough Coefficients Using a Cartesian Grid Nonconforming to Interfaces . . . . . . . . . . . . . . . 442--464 Alexis Vasseur Kinetic Semidiscretization of Scalar Conservation Laws and Convergence by Using Averaging Lemmas . . . . . . . . . 465--474 Jin Qi-nian Applications of the Modified Discrepancy Principle to Tikhonov Regularization of Nonlinear Ill-Posed Problems . . . . . . 475--490 Michael Dellnitz and Oliver Junge On the Approximation of Complicated Dynamical Behavior . . . . . . . . . . . 491--515 Yunkang Liu Numerical Solution of Implicit Neutral Functional Differential Equations . . . 516--528 Mao De-kang Entropy Satisfaction of a Conservative Shock-Tracking Method . . . . . . . . . 529--550 Yves Achdou and Yvon Maday and Olof Widlund Iterative Substructuring Preconditioners for Mortar Element Methods in Two Dimensions . . . . . . . . . . . . . . . 551--580 Xiao-Chuan Cai and Maksymilian Dryja and Marcus Sarkis Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems 581--606 Paolo Costantini and Carla Manni A Parametric Cubic Element with Tension Properties . . . . . . . . . . . . . . . 607--628 Norman Yarvin and Vladimir Rokhlin An Improved Fast Multipole Algorithm for Potential Fields on the Line . . . . . . 629--666
Michelle Boué and Paul Dupuis Markov Chain Approximations for Deterministic Control Problems with Affine Dynamics and Quadratic Cost in the Control . . . . . . . . . . . . . . 667--695 P. B. Monk and O. Vacus Error Estimates for a Numerical Scheme for Ferromagnetic Problems . . . . . . . 696--718 Jie Shen and Shouhong Wang A Fast and Accurate Numerical Scheme for the Primitive Equations of the Atmosphere . . . . . . . . . . . . . . . 719--737 Paul Arminjon and Marie-Claude Viallon Convergence of a Finite Volume Extension of the Nessyahu--Tadmor Scheme on Unstructured Grids for a Two-Dimensional Linear Hyperbolic Equation . . . . . . . 738--771 Richard E. Ewing and Michael M. Liu and Junping Wang Superconvergence of Mixed Finite Element Approximations over Quadrilaterals . . . 772--787 James M. Hyman and Mikhail Shashkov The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods 788--818 Seymour V. Parter On the Overlapping Grid Method for Elliptic Boundary Value Problems . . . . 819--852 Gunilla Efraimsson and Gunilla Kreiss A Remark on Numerical Errors Downstream of Slightly Viscous Shocks . . . . . . . 853--863 Eric de Sturler Truncation Strategies for Optimal Krylov Subspace Methods . . . . . . . . . . . . 864--889 Hans-Jürgen Reinhardt and Houde Han and Dinh Nho H\`ao Stability and Regularization of a Discrete Approximation to the Cauchy Problem for Laplace's Equation . . . . . 890--905 S. Koc and Jiming Song and W. C. Chew Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem . . . 906--921 Tobin A. Driscoll A Nonoverlapping Domain Decomposition Method for Symm's Equation for Conformal Mapping . . . . . . . . . . . . . . . . 922--934 Richard S. Falk and Gerard R. Richter Explicit Finite Element Methods for Symmetric Hyperbolic Equations . . . . . 935--952 C. Buet and S. Cordier Numerical Analysis of Conservative and Entropy Schemes for the Fokker--Planck--Landau Equation . . . . 953--973 Xun Jiang and Ricardo H. Nochetto and Claudio Verdi A $ P^1 $--$ P^1 $ Finite Element Method for a Phase Relaxation Model II: Adaptively Refined Meshes . . . . . . . 974--999
Patrick Mund and Ernst P. Stephan An Adaptive Two-Level Method for the Coupling of Nonlinear FEM-BEM Equations 1001--1021 J. J. Green Calculating the Maximum Modulus of a Polynomial Using Steckin's Lemma . . . . 1022--1029 Armengol Gasull and Antoni Guillamon and Víctor Mañosa An Analytic-Numerical Method for Computation of the Liapunov and Period Constants Derived from Their Algebraic Structure . . . . . . . . . . . . . . . 1030--1043 Peter K. Moore Finite Difference Methods and Spatial A Posteriori Error Estimates for Solving Parabolic Equations in Three Space Dimensions on Grids with Irregular Nodes 1044--1064 Gerhard Starke Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods . . . . . . . . . . . . . . . . 1065--1077 Stefano Serra How to Choose the Best Iterative Strategy for Symmetric Toeplitz Systems 1078--1103 Yu. A. Kuznetsov Numerical Normalization Techniques for All Codim $2$ Bifurcations of Equilibria in ODE's . . . . . . . . . . . . . . . . 1104--1124 Pavel Bochev and Thomas A. Manteuffel and Stephen F. McCormick Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II . . . . . . . . . . . 1125--1144 A. Zanna Collocation and Relaxed Collocation for the Fer and the Magnus Expansions . . . 1145--1182 Johan Waldén Filter Bank Methods for Hyperbolic PDEs 1183--1233 Faker Ben Belgacem and Yvon Maday Coupling Spectral and Finite Elements for Second Order Elliptic Three-Dimensional Equations . . . . . . 1234--1263 D. Boffi and P. Fernandes and L. Gastaldi and I. Perugia Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation . . . . . . . . . . . . . 1264--1290 Roberto Barrio On the $A$-Stability of Runge--Kutta Collocation Methods Based on Orthogonal Polynomials . . . . . . . . . . . . . . 1291--1303 A. J. Meir and Paul G. Schmidt Analysis and Numerical Approximation of a Stationary MHD Flow Problem with Nonideal Boundary . . . . . . . . . . . 1304--1332
François Golse and Shi Jin and C. David Levermore The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method . . . . . . . . 1333--1369 Jan Mandel and Radek Tezaur and Charbel Farhat A Scalable Substructuring Method by Lagrange Multipliers for Plate Bending Problems . . . . . . . . . . . . . . . . 1370--1391 Jeremy Schiff and S. Shnider A Natural Approach to the Numerical Integration of Riccati Differential Equations . . . . . . . . . . . . . . . 1392--1413 Bernard Bialecki and Ryan I. Fernandes An Orthogonal Spline Collocation Alternating Direction Implicit Crank--Nicolson Method for Linear Parabolic Problems on Rectangles . . . . 1414--1434 C. Bernardi and A. Karageorghis Spectral Element Discretization of the Circular Driven Cavity, Part I: The Laplace Equation . . . . . . . . . . . . 1435--1465 F. Ivanauskas and M. Radziunas On Convergence and Stability of the Explicit Difference Method for Solution of Nonlinear Schrödinger Equations . . . 1466--1481 Qiang Du and Xiaonan Wu Numerical Solution of the Three-Dimensional Ginzburg--Landau Models Using Artificial Boundary . . . . 1482--1506 Axel Klar An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit . . . . . . . . . . . 1507--1527 Miloslav Feistauer and Jirí Felcman and Mária Lukácová-Medvid'ová and Gerald Warnecke Error Estimates for a Combined Finite Volume--Finite Element Method for Nonlinear Convection--Diffusion Problems 1528--1548 Sebastian Reich Backward Error Analysis for Numerical Integrators . . . . . . . . . . . . . . 1549--1570 Carsten Carstensen and Rüdiger Verfürth Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods . . . . . . . . . . . . 1571--1587 Philippe Hoch and Michel Rascle A Numerical Study of a Pathological Example of $p$-System . . . . . . . . . 1588--1603 R. Bruce Kellogg and Martin Stynes $n$-Widths and Singularly Perturbed Boundary Value Problems . . . . . . . . 1604--1620 Georg Dolzmann Numerical Computation of Rank-One Convex Envelopes . . . . . . . . . . . . . . . 1621--1635 Barbara I. Wohlmuth Hierarchical A Posteriori Error Estimators for Mortar Finite Element Methods with Lagrange Multipliers . . . 1636--1658
Alfred S. Carasso Linear and Nonlinear Image Deblurring: A Documented Study . . . . . . . . . . . . 1659--1689 Gary L. Miller and Dafna Talmor and Shang-Hua Teng and Noel Walkington On the Radius-Edge Condition in the Control Volume Method . . . . . . . . . 1690--1708 W. Dörfler Uniform Error Estimates for an Exponentially Fitted Finite Element Method for Singularly Perturbed Elliptic Equations . . . . . . . . . . . . . . . 1709--1738 Eitan Tadmor and Tao Tang Pointwise Error Estimates for Scalar Conservation Laws with Piecewise Smooth Solutions . . . . . . . . . . . . . . . 1739--1758 Joakim Petersson A Finite Element Analysis of Optimal Variable Thickness Sheets . . . . . . . 1759--1778 Ohannes Karakashian and Charalambos Makridakis A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method . . . . . . . 1779--1807 Gerhard Dziuk Discrete Anisotropic Curve Shortening Flow . . . . . . . . . . . . . . . . . . 1808--1830 Stefano Serra Capizzano A Korovkin-Based Approximation of Multilevel Toeplitz Matrices (With Rectangular Unstructured Blocks) via Multilevel Trigonometric Matrix Spaces 1831--1857 B. Le Bailly and J. P. Thiran Computing Complex Polynomial Chebyshev Approximants on the Unit Circle by the Real Remez Algorithm . . . . . . . . . . 1858--1877 W. Dörfler Uniform A Priori Estimates for Singularly Perturbed Elliptic Equations in Multidimensions . . . . . . . . . . . 1878--1900 Mark Ainsworth and William McLean and Thanh Tran The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling . . 1901--1932 F. Brezzi and T. J. R. Hughes and L. D. Marini and A. Russo and E. Süli A Priori Error Analysis of Residual-Free Bubbles for Advection-Diffusion Problems 1933--1948 Stephen Joe An Average $ L_2 $ Discrepancy for Number-Theoretic Rules . . . . . . . . . 1949--1961 Weiwei Sun Spectral Analysis of Hermite Cubic Spline Collocation Systems . . . . . . . 1962--1975