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Cornelius 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