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Jet Wimp Polynomial Expansions of Bessel
Functions and Some Associated Functions 446--458
G. W. Stewart, III On Lehmer's Method for Finding the Zeros
of a Polynomial . . . . . . . . . . . . 829--835, s24--s30
J. Greenstadt Variations on Variable-Metric Methods 1--22
Donald Goldfarb A Family of Variable-Metric Methods
Derived by Variational Means . . . . . . 23--26
L. K. Schubert Modification of a Quasi-Newton Method
for Nonlinear Equations with a Sparse
Jacobian . . . . . . . . . . . . . . . . 27--30
J. M. Varah Maximum Norm Stability of Difference
Approximations to the Mixed Initial
Boundary-Value Problem for the Heat
Equation . . . . . . . . . . . . . . . . 31--44
L. F. Shampine and
R. J. Thompson Difference Methods for Nonlinear
First-Order Hyperbolic Systems of
Equations . . . . . . . . . . . . . . . 45--56
Ephraim L. Rubin and
Stanley Preiser Three-Dimensional Second-Order Accurate
Difference Schemes for Discontinuous
Hydrodynamic Flows . . . . . . . . . . . 57--63
Martin H. Schultz Elliptic Spline Functions and the
Rayleigh--Ritz--Galerkin Method . . . . 65--80
J. D. Lambert Linear Multistep Methods with Mildly
Varying Coefficients . . . . . . . . . . 81--93
P. Silvester Symmetric Quadrature Formulae for
Simplexes . . . . . . . . . . . . . . . 95--100
J. N. Lyness The Calculation of Fourier Coefficients
by the Möbius Inversion of the Poisson
Summation Formula. Part I: Functions
whose Early Derivatives are Continuous 101--135
J. M. Varah Computing Invariant Subspaces of a
General Matrix When the Eigensystem Is
Poorly Conditioned . . . . . . . . . . . 137--149
J. L. Lavoie and
R. Michaud Explicit Expressions for the
Determinants of Certain Matrices . . . . 151--154
D. Kershaw Inequalities on the Elements of the
Inverse of a Certain Tridiagonal Matrix 155--158
Ichizo Ninomiya Generalized Rational Chebyshev
Approximation . . . . . . . . . . . . . 159--169
W. J. Cody and
Kathleen A. Paciorek and
Henry C. Thacher, Jr. Chebyshev Approximations for Dawson's
Integral . . . . . . . . . . . . . . . . 171--178
T. N. E. Greville Table for Third-Degree Spline
Interpolation with Equally Spaced
Arguments . . . . . . . . . . . . . . . 179--183
Fred T. Krogh Efficient Algorithms for Polynomial
Interpolation and Numerical
Differentiation . . . . . . . . . . . . 185--190
Yudell L. Luke Further Approximations for Elliptic
Integrals . . . . . . . . . . . . . . . 191--198
D. G. Zill and
B. C. Carlson Symmetric Elliptic Integrals of the
Third Kind . . . . . . . . . . . . . . . 199--214
Morris Newman A Table of the First Factor for Prime
Cyclotomic Fields . . . . . . . . . . . 215--219
J. H. Jordan and
J. R. Rabung A Conjecture of Paul Erd\Hos Concerning
Gaussian Primes . . . . . . . . . . . . 221--223
Anonymous Corrigenda . . . . . . . . . . . . . . . 243--243
Walter Gautschi On the Construction of Gaussian
Quadrature Rules from Modified Moments 245--260
N. S. Kambo Error of the Newton--Cotes and
Gauss--Legendre Quadrature Formulas . . 261--269
M. Wayne Wilson Discrete Least Squares and Quadrature
Formulas . . . . . . . . . . . . . . . . 271--282
R. F. Goodrich and
F. Stenger Movable Singularities and Quadrature . . 283--300
Robert E. Barnhill and
Gregory M. Nielson An error analysis for numerical multiple
integration. III . . . . . . . . . . . . 301--314
Alfred Carasso and
Seymour V. Parter An Analysis of ``Boundary-Value
Techniques'' for Parabolic Problems . . 315--340
T. W. Sag Chebyshev iteration methods for integral
equations of the second kind . . . . . . 341--355
G. Galimberti and
V. Pereyra Numerical Differentiation and the
Solution of Multidimensional Vandermonde
Systems . . . . . . . . . . . . . . . . 357--364
C. G. Broyden The Convergence of Single-Rank
Quasi-Newton Methods . . . . . . . . . . 365--382
David L. Phillips Generalized Logarithmic Error and
Newton's Method for the $m$ th Root . . 383--389
Ichizo Ninomiya Best Rational Starting Approximations
and Improved Newton Iteration for the
Square Root . . . . . . . . . . . . . . 391--404
E. W. Ng and
C. J. Devine On the Computation of Debye Functions of
Integer Orders . . . . . . . . . . . . . 405--407
Robert L. Pexton Computer Investigation of Coulomb Wave
Functions . . . . . . . . . . . . . . . 409--411
James Alan Cochran and
Judith N. Hoffspiegel Numerical Techniques for Finding $ \nu
$-Zeros of Hankel Functions . . . . . . 413--422
Henri Cohen On Amicable and Sociable Numbers . . . . 423--429
Paul Bratley and
Fred Lunnon and
John McKay Amicable Numbers and Their Distribution 431--432
D. H. Lehmer and
Emma Lehmer and
Daniel Shanks Integer Sequence having Prescribed
Quadratic Character . . . . . . . . . . 433--451
Simcha Brudno On Generating Infinitely Many Solutions
of the Diophantine Equation $ A^6 + B^6
+ C^6 = D^6 + E^6 + F^6 $ . . . . . . . 453--454
W. A. Beyer and
N. Metropolis and
J. R. Neergaard Statistical Study of Digits of Some
Square Roots of Integers in Various
Bases . . . . . . . . . . . . . . . . . 455--473
Martin H. Schultz Error Bounds for Polynomial Spline
Interpolation . . . . . . . . . . . . . 507--515
R. B. Guenther and
E. L. Roetman Some Observations on Interpolation in
Higher Dimensions . . . . . . . . . . . 517--522
Leon Winslow ``Best'' Interpolation, Differentiation,
and Integration Approximations on the
Hardy Space $ {H}^2 $ . . . . . . . . . 523--527
James T. Lewis Computation of Best One-Sided $ {L}_1 $
Approximation . . . . . . . . . . . . . 529--536
S. Berkowitz and
F. J. Garner The Calculation of Multidimensional
Hermite Polynomials and Gram--Charlier
Coefficients . . . . . . . . . . . . . . 537--545
William B. Jones and
G. Hardy Accelerating Convergence of
Trigonometric Approximations . . . . . . 547--560
Philip Rabinowitz and
Nira Richter New Error Coefficients for Estimating
Quadrature Errors for Analytic Functions 561--570
David K. Kahaner Chebyshev Type Quadrature Formulas . . . 571--574
C. J. Knight and
A. C. R. Newbery Trigonometric and Gaussian Quadrature 575--581
Frank G. Lether Cross-Product Cubature Error Bounds . . 583--592
Philip Rabinowitz and
Nira Richter Asymptotic Properties of Minimal
Integration Rules . . . . . . . . . . . 593--609
Alan Solomon and
Faiza Solomon The Initial-Value Problem for the
Equation $ (t u_t)_t = u_{xx} $ . . . . 611--620
Òystein Todenes On the Numerical Solution of the
Diffusion Equation . . . . . . . . . . . 621--627
A. R. Gourlay A Note on Trapezoidal Methods for the
Solution of Initial Value Problems . . . 629--633
H. Brunner Marginal Stability and Stabilization in
the Numerical Integration of Ordinary
Differential Equations . . . . . . . . . 635--646
D. F. Shanno Conditioning of Quasi-Newton Methods for
Function Minimization . . . . . . . . . 647--656
D. F. Shanno and
P. C. Kettler Optimal Conditioning of Quasi-Newton
Methods . . . . . . . . . . . . . . . . 657--664
P. Schlegel The Explicit Inverse of a Tridiagonal
Matrix . . . . . . . . . . . . . . . . . 665--665
Henry E. Fettis A New Method for Computing Toroidal
Harmonics . . . . . . . . . . . . . . . 667--670
W. J. Cody and
K. E. Hillstrom Chebyshev Approximations for the Coulomb
Phase Shift . . . . . . . . . . . . . . 671--677
K. S. Kolbig Complex Zeros of an Incomplete Riemann
Zeta Function and of the Incomplete
Gamma Function . . . . . . . . . . . . . 679--696
David W. Boyd Lower Bounds for the Disk Packing
Constant . . . . . . . . . . . . . . . . 697--704
Andrzej Makowski Remark on a Conjecture of Erd\Hos on
Binomial Coefficients . . . . . . . . . 705--705
John D. Dixon Computing Irreducible Representations of
Groups . . . . . . . . . . . . . . . . . 707--712
E. R. Berlekamp Factoring Polynomials Over Large Finite
Fields . . . . . . . . . . . . . . . . . 713--735
J. R. Rabung and
J. H. Jordan Consecutive Power Residues or
Nonresidues . . . . . . . . . . . . . . 737--740
D. H. Lehmer Note on the Distribution of Ramanujan's
Tau Function . . . . . . . . . . . . . . 741--743
W. A. Beyer and
N. Metropolis and
J. R. Neergaard The Generalized Serial Test Applied to
Expansions of Some Irrational Square
Roots in Various Bases . . . . . . . . . 745--747
Remi Vaillancourt On the Stability of Friedrich's Scheme
and the Modified Lax--Wendroff Scheme 767--770
Victor Pereyra Highly Accurate Numerical Solution of
Casilinear Elliptic Boundary-Value
Problems in $n$ Dimensions . . . . . . . 771--783
Alfred Carasso A Posteriori Bounds in the Numerical
Solution of Mildly Nonlinear Parabolic
Equations . . . . . . . . . . . . . . . 785--792
David M. Young Convergence Properties of the Symmetric
and Unsymmetric Successive
Overrelaxation Methods and Related
Methods . . . . . . . . . . . . . . . . 793--807
James H. Bramble and
Milo\us Zlámal Triangular Elements in the Finite
Element Method . . . . . . . . . . . . . 809--820
J. Burbea A Procedure for Conformal Maps of Simply
Connected Domains by Using the Bergman
Function . . . . . . . . . . . . . . . . 821--829
Philip Rabinowitz and
Nira Richter Chebyshev-Type Integration Rules of
Minimum Norm . . . . . . . . . . . . . . 831--845
Sven-Åke Gustafson Control and Estimation of Computational
Errors in the Evaluation of
Interpolation Formulae and Quadrature
Rules . . . . . . . . . . . . . . . . . 847--854
F. N. Fritsch On the Existence of Regions With Minimal
Third Degree Integration Formulas . . . 855--861
N. K. Basu Error Estimates for a Chebyshev
Quadrature Method . . . . . . . . . . . 863--867
A. C. R. Newbery Trigonometric Interpolation and
Curve-Fitting . . . . . . . . . . . . . 869--876
I. Barrodale and
J. C. Mason Two Simple Algorithms for Discrete
Rational Approximation . . . . . . . . . 877--891
Ake Björck and
Victor Pereyra Solution of Vandermonde Systems of
Equations . . . . . . . . . . . . . . . 893--903
Peter Linz On the Numerical Computation of
Eigenvalues and Eigenvectors of
Symmetric Integral Equations . . . . . . 905--910
F. M. Larkin Optimal Approximation in Hilbert Spaces
with Reproducing Kernel Functions . . . 911--921
J. B. Diaz and
F. T. Metcalf On Iteration Procedures for Equations of
the First Kind, $ A x = y $, and
Picard's Criterion for the Existence of
a Solution . . . . . . . . . . . . . . . 923--935
Robert K. Brayton and
Fred G. Gustavson and
Ralph A. Willoughby Some Results on Sparse Matrices . . . . 937--954
Donald E. Knuth A Note on Solid Partitions . . . . . . . 955--961
Peter Hagis, Jr. Lower Bounds for Relatively Prime
Amicable Numbers of Opposite Parity . . 963--968
Hans Riesel and
Gunnar Gohl Some Calculations Related to Riemann's
Prime Number Formula . . . . . . . . . . 969--983
Anonymous Corrigendum . . . . . . . . . . . . . . 1001--1001
J. H. Bramble and
A. H. Schatz Least Squares Methods for $ 2 m $ th
Order Elliptic Boundary-Value Problems 1--32
Olof B. Widlund On the Effects of Scaling of the
Peaceman--Rachford Method . . . . . . . 33--41
Magnus Bondesson An Interior a Priori Estimate for
Parabolic Difference Operators and an
Application . . . . . . . . . . . . . . 43--58
J. N. Lyness The Calculation of Fourier Coefficients
by the Möbius Inversion of the Poisson
Summation Formula Part II. Piecewise
Continuous Functions and Functions with
Poles near the Interval [0, 1] . . . . . 59--78
D. Nicholson and
P. Rabinowitz and
N. Richter and
D. Zeilberger On the Error in the Numerical
Integration of Chebyshev Polynomials . . 79--86
J. N. Lyness Adjusted Forms of the Fourier
Coefficient Asymptotic Expansion and
Applications in Numerical Quadrature . . 87--104
K. Salkauskas Existence of Quadrature Formulae with
Almost Equal Weights . . . . . . . . . . 105--109
David Galant An Implementation of Christoffel's
Theorem in the Theory of Orthogonal
Polynomials . . . . . . . . . . . . . . 111--113
F. D. Burgoyne Practical Throw-Back Interpolation . . . 115--117
Herbert E. Salzer Formulas for Bivariate Hyperosculatory
Interpolation . . . . . . . . . . . . . 119--133
G. W. Stewart, III Error Analysis of the Algorithm for
Shifting the Zeros of a Polynomial by
Synthetic Division . . . . . . . . . . . 135--139
J. McNamee and
F. Stenger and
E. L. Whitney Whittaker's Cardinal Function in
Retrospect . . . . . . . . . . . . . . . 141--154
Frantisek Fiala Strongly Asymmetric Sequences Generated
by Four Elements . . . . . . . . . . . . 155--162
T. W. Cusick Diophantine Approximation of Ternary
Linear Forms . . . . . . . . . . . . . . 163--180
C. H. Yang On Hadamard Matrices Constructible by
Circulant Submatrices . . . . . . . . . 181--186
G. W. Stewart, III Corrigendum: ``On Lehmer's Method for
Finding the Zeros of a Polynomial'' . . 203--203
Philip Brenner and
Vidar Thomee Contractive Difference Schemes for
Symmetric Hyperbolic Systems . . . . . . 205--217
Melvyn Ciment Stable Difference Schemes with Uneven
Mesh Spacings . . . . . . . . . . . . . 219--227
Gideon Zwas and
Saul Abarbanel Third and Fourth Order Accurate Schemes
for Hyperbolic Equations of Conservation
Law Form . . . . . . . . . . . . . . . . 229--236
J. R. Kuttler A Fourth-Order Finite-Difference
Approximation for the Fixed Membrane
Eigenproblem . . . . . . . . . . . . . . 237--256
Robert S. Stepleman Difference Analogues of Quasi-Linear
Elliptic Dirichlet Problems with Mixed
Derivatives . . . . . . . . . . . . . . 257--269
Fred W. Dorr An Example of Ill-Conditioning in the
Numerical Solution of Singular
Perturbation Problems . . . . . . . . . 271--283
C. G. Broyden The Convergence of an Algorithm for
Solving Sparse Nonlinear Systems . . . . 285--294
C. T. Fike and
P. H. Sterbenz Minimax Approximations Subject to a
Constraint . . . . . . . . . . . . . . . 295--298
Richard F. King Improved Newton Iteration for Integral
Roots . . . . . . . . . . . . . . . . . 299--304
Ll. G. Chambers A Quadratic Formula for Finding the Root
of an Equation . . . . . . . . . . . . . 305--307
David Elliott Uniform Asymptotic Expansions of the
Jacobi Polynomials and an Associated
Function . . . . . . . . . . . . . . . . 309--315
Robert Spira Calculation of the Gamma Function by
Stirling's Formula . . . . . . . . . . . 317--322
Yudell L. Luke Miniaturized Tables of Bessel Functions 323--330
Chih-Bing Ling and
Jung Lin A New Method of Evaluation of Howland
Integrals . . . . . . . . . . . . . . . 331--337
F. Matta and
A. Reichel Uniform Computation of the Error
Function and Other Related Functions . . 339--344
W. A. Beyer and
R. B. Roof and
Dorothy Williamson The Lattice Structure of Multiplicative
Congruential Pseudo-Random Vectors . . . 345--363
J. M. Pollard The Fast Fourier Transform in a Finite
Field . . . . . . . . . . . . . . . . . 365--374
Michael A. Malcolm A Note on a Conjecture of L. J. Mordell 375--377
Hansraj Gupta Chains of Quadratic Residues . . . . . . 379--382
Wayne L. McDaniel On the Divisibility of an Odd Perfect
Number by the Sixth Power of a Prime . . 383--385
K. Y. Choong and
D. E. Daykin and
C. R. Rathbone Rational Approximations to $ \pi $ . . . 387--392
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 393--404
Anonymous Table Errata . . . . . . . . . . . . . . 405--408
Anthony J. Strecok Table errata: \booktitleHandbook of
mathematical functions with formulas,
graphs, and mathematical tables (Nat.
Bur. Standards, Washington, D. C.,
1964), edited by Milton Abramowitz and
Irene A. Stegun . . . . . . . . . . . . 405--405
Henry E. Fettis Table errata: \booktitleTables of
toroidal harmonics. I: Orders 0 5, all
significant degrees (Aerospace Res.
Lab., Office of Aerospace Res., United
States Air Force, Wright-Patterson Air
Force Base, Ohio, 1969) by Fettis and
James C. Caslin . . . . . . . . . . . . 405--407
Henry E. Fettis Table errata: \booktitleTables of
toroidal harmonics, II: Orders 5 10, all
significant degrees (Aerospace Res.
Lab., Office of Aerospace Res. United
States Air Force, Wright-Patterson Air
Force Base, Ohio, 1969) by Fettis and
James C. Caslin . . . . . . . . . . . . 407--408
Daniel Shanks Corrigendum to: On generating infinitely
many solutions of the Diophantine
equation $ A^6 + B^6 + C^6 = D^6 + E^6 +
F^6 $, (Math. Comp. 24 (1970), 453--454)
by Simcha Brudno . . . . . . . . . . . . 409--409
Daniel Shanks Corrigendum to: ``Statistical study of
digits of some square roots of integers
in various bases'' (Math. Comp. \bf 24
(1970), 455--473) by W. A. Beyer, N.
Metropolis and J. R. Neergaard . . . . . 409--409
Anonymous Corrigenda . . . . . . . . . . . . . . . 409--409
Anonymous Notice . . . . . . . . . . . . . . . . . 411
Joel N. Franklin Stability of Bounded Solutions of Linear
Functional Equations . . . . . . . . . . 413--424
Gary G. Sackett Numerical Solution of a Parabolic Free
Boundary Problem Arising in Statistical
Decision Theory . . . . . . . . . . . . 425--434
Colin W. Cryer The Method of Christopherson for Solving
Free Boundary Problems for Infinite
Journal Bearings by Means of Finite
Differences . . . . . . . . . . . . . . 435--443
L. F. Shampine and
H. A. Watts Comparing Error Estimators for
Runge--Kutta Methods . . . . . . . . . . 445--455
R. W. Klopfenstein and
C. B. Davis PECE Algorithms for the Solution of
Stiff Systems of Ordinary Differential
Equations . . . . . . . . . . . . . . . 457--473
T. N. Robertson The Linear Two-Point Boundary-Value
Problem on an Infinite Interval . . . . 475--481
J. N. Lyness The Calculation of Fourier Coefficients
by the Möbius Inversion of the Poisson
Summation Formula. Part III: Functions
Having Algebraic Singularities . . . . . 483--493
C. S. Duris Optimal Quadrature Formulas Using
Generalized Inverses. Part I: General
Theory and Minimum Variance Formulas . . 495--504
Alan Feldstein and
Richard K. Miller Error Bounds for Compound Quadrature of
Weakly Singular Integrals . . . . . . . 505--520
R. K. Miller On Ignoring the Singularity in Numerical
Quadrature . . . . . . . . . . . . . . . 521--532
M. L. Glasser An Elliptic Integral Identity . . . . . 533--534
M. L. Glasser and
V. E. Wood A Closed Form Evaluation of the Elliptic
Integral . . . . . . . . . . . . . . . . 535--536
W. J. Cody and
K. E. Hillstrom and
Henry C. Thacher, Jr. Chebyshev Approximations for the Riemann
Zeta Function . . . . . . . . . . . . . 537--547
A. C. R. Newbery A Generalized Interpolation Algorithm 549--552
Robert E. Huddleston Some Relations Between the Values of a
Function and its First Derivative at $n$
Abscissa Points . . . . . . . . . . . . 553--558
J. E. Dennis, Jr. On the convergence of Broyden's method
for nonlinear systems of equations . . . 559--567
A. A. Goldstein and
J. F. Price On Descent from Local Minima . . . . . . 569--574
Bernard H. Rosman Exponential Chebyshev Approximation on
Finite Subsets of $ \lbrack 0, 1 \rbrack
$ . . . . . . . . . . . . . . . . . . . 575--577
Ahmed H. Sameh On Jacobi and Jacobi-like Algorithms for
a Parallel Computer . . . . . . . . . . 579--590
Christian H. Reinsch A Stable, Rational $ {QR} $ Algorithm
for the Computation of the Eigenvalues
of an Hermitian, Tridiagonal Matrix . . 591--597
James L. Phillips The Triangular Decomposition of Hankel
Matrices . . . . . . . . . . . . . . . . 599--602
Robert Riley Homomorphisms of Knot Groups on Finite
Groups . . . . . . . . . . . . . . . . . 603--619
Ronald Alter On a Diophantine Equation Related to
Perfect Codes . . . . . . . . . . . . . 621--624
N. M. Stephens On the Feit--Thompson Conjecture . . . . 625--625
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 627--633
B. N. P. Book Review: A. S. Householder,
\booktitleKWIC Index for Matrices in
Numerical Analysis, Volume I: Primary
Authors A--J, viii + 124 pp.,
\booktitleVolume II: Primary Authors
K--Z, vii + 151 pp., 1969, Oak Ridge
National Laboratory, Oak Ridge,
Tennessee, 28 cm. Available from
National Technical Information Service,
U. S. Department of Commerce,
Springfield, Virginia 22151. Price:
Printed copy \$3.00, Microfiche \$0.65,
each volume . . . . . . . . . . . . . . 628--628
J. C. Eilbeck Table errata: \booktitleHigher
transcendental functions. Vol. I, II
(McGraw-Hill, New York, 1953) by A.
Erdélyi, W. Magnus, F. Oberhettinger and
F. G. Tricomi . . . . . . . . . . . . . 635
Anonymous Table Errata . . . . . . . . . . . . . . 635
Anonymous Corrigendum . . . . . . . . . . . . . . 637--637
John R. Rice Matrix Representations of Nonlinear
Equation Iterations--Application to
Parallel Computation . . . . . . . . . . 639--647
O. L. Mangasarian Convergent Generalized Monotone
Splitting of Matrices . . . . . . . . . 649--653
G. T. McAllister The Dirichlet Problem for a Class of
Elliptic Difference Equations . . . . . 655--673
Jan Krzysztof Kowalski A Finite-Difference Method for Parabolic
Differential Equations with Mixed
Derivatives . . . . . . . . . . . . . . 675--698
L. M. Delves and
K. O. Mead On the Convergence Rates of Variational
Methods. I: Asymptotically Diagonal
Systems . . . . . . . . . . . . . . . . 699--716
W. L. Miranker Matricial Difference Schemes for
Integrating Stiff Systems of Ordinary
Differential Equations . . . . . . . . . 717--728
Bruce Chartres and
Robert Stepleman Convergence of Difference Methods for
Initial and Boundary Value Problems with
Discontinuous Data . . . . . . . . . . . 729--732
George G. Ross On the Computation of Some Grunsky
Coefficients Relevant to the Bieberbach
Conjecture . . . . . . . . . . . . . . . 733--741
J. Burbea A Numerical Determination of the Modulus
of Doubly Connected Domains by Using the
Bergman Curvature . . . . . . . . . . . 743--756
George U. Ramos Roundoff Error Analysis of the Fast
Fourier Transform . . . . . . . . . . . 757--768
N. Liron Infinite Sums of Roots for a Class of
Transcendental Equations and Bessel
Functions of Order One-Half . . . . . . 769--781
R. Wong and
E. Rosenbloom Series Expansions of $ {W}_{k, m}(z) $
Involving Parabolic Cylinder Functions 783--787
Yudell L. Luke Miniaturized Tables of Bessel Functions,
II . . . . . . . . . . . . . . . . . . . 789--795
W. D. Hoskins Table for Third-Degree Spline
Interpolation Using Equi-Spaced Knots 797--801
Richard Franke Obtaining Cubatures for Rectangles and
Other Planar Regions by Using Orthogonal
Polynomials . . . . . . . . . . . . . . 803--817
P. D. Tuan On the Remainder in Quadrature Rules . . 819--826
David K. Kahaner Some Polynomials for Complex Quadrature 827--830
L. W. Johnson and
R. D. Riess Minimal Quadratures for Functions of
Low-Order Continuity . . . . . . . . . . 831--835
Daniel Shanks Gauss's Ternary Form Reduction and the
$2$-Sylow Subgroup . . . . . . . . . . . 837--853
U. Dieter Pseudo-Random Numbers: The Exact
Distribution of Pairs . . . . . . . . . 855--883
S. L. G. Choi Covering the Set of Integers by
Congruence Classes of Distinct Moduli 885--895
Gordon H. Bradley Algorithms for Hermite and Smith Normal
Matrices and Linear Diophantine
Equations . . . . . . . . . . . . . . . 897--907
J. H. Cadwell Large Intervals Between Consecutive
Primes . . . . . . . . . . . . . . . . . 909--913
Peter Hagis, Jr. Unitary Amicable Numbers . . . . . . . . 915--918
D. Rosen and
G. S. Patterson, Jr. Some Numerical Evidence Concerning the
Uniqueness of the Markov Numbers . . . . 919--921
M. Lal and
A. Forbes A Note on Chowla's Function . . . . . . 923--925
Jacques Dutka The Square Root of $2$ to $ 1, 000, 000$
Decimals . . . . . . . . . . . . . . . . 927--930
Anonymous Corrigendum . . . . . . . . . . . . . . 947--947
Ivo Babu\vska The Finite Element Method for Infinite
Domains. I . . . . . . . . . . . . . . . 1--11
Stanley Osher Stability of parabolic difference
approximations to certain mixed initial
boundary value problems . . . . . . . . 13--39
B. Eilon A note concerning the two-step
Lax--Wendroff method in three dimensions 41--43
N. K. Madsen Convergence of singular difference
approximations for the discrete ordinate
equations in $x$-$y$ geometry . . . . . 45--50
Karl G. Guderley and
Chen-Chi Hsu A Predictor-Corrector Method for a
Certain Class of Stiff Differential
Equations . . . . . . . . . . . . . . . 51--69
R. K. Jain Some $A$-stable methods for stiff
ordinary differential equations . . . . 71--77
J. C. Butcher An Algebraic Theory of Integration
Methods . . . . . . . . . . . . . . . . 79--106
J. C. Butcher A convergence criterion for a class of
integration methods . . . . . . . . . . 107--117
Alston S. Householder On a Condition for the Nonsingularity of
a Matrix . . . . . . . . . . . . . . . . 119--120
J. W. Rainey and
G. J. Habetler Tridiagonalization of completely
nonnegative matrices . . . . . . . . . . 121--128
Ronald Bass A Rank Two Algorithm for Unconstrained
Minimization . . . . . . . . . . . . . . 129--143
John Greenstadt A Quasi-Newton Method with No
Derivatives . . . . . . . . . . . . . . 145--166
A. K. Cline Rate of Convergence of Lawson's
Algorithm . . . . . . . . . . . . . . . 167--176
Richard Weiss Product integration for the generalized
Abel equation . . . . . . . . . . . . . 177--190
D. Kershaw The orders of approximation of the first
derivative of cubic splines at the knots 191--198
Jack Williams Numerical Chebyshev approximation by
interpolating rationals . . . . . . . . 199--206
A. R. Curtis and
P. Rabinowitz On the Gaussian integration of Chebyshev
polynomials . . . . . . . . . . . . . . 207--211
P. D. Tuan and
David Elliott Coefficients in series expansions for
certain classes of functions . . . . . . 213--232
Richard Bellman and
B. G. Kashef and
R. Vasudevan A Useful Approximation to $ e^{-t^2} $ 233--235
Yudell L. Luke Miniaturized Tables of Bessel Functions.
III . . . . . . . . . . . . . . . . . . 237--240
D. M. Chipman The numerical computation of two
transcendental functions related to the
exponential integral . . . . . . . . . . 241--249
Jet Wimp Some Transformations of Monotone
Sequences . . . . . . . . . . . . . . . 251--254
D. E. Amos and
W. G. Bulgren Computation of a Multivariate $ {F} $
Distribution . . . . . . . . . . . . . . 255--264
Daniel Shanks and
Mohan Lal Bateman's Constants Reconsidered and the
Distribution of Cubic Residues . . . . . 265--285
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 287--303
W. Rheinboldt Book Review: A. S. Householder,
\booktitleKWIC Index for the Numerical
Treatment of Nonlinear Equations, Oak
Ridge National Laboratory, Oak Ridge,
Tennessee, 1970, vii + 129 pp., 28 cm.
Available from U. S. Department of
Commerce, Springfield, Va. 22151. Price:
printed copy \$3.00; microfiche \$0.65. 287--303
Anonymous Table Errata . . . . . . . . . . . . . . 305--307
Robert F. MacKinnon Table errata: \booktitleTable of
integrals, series, and products (English
translation of the fourth Russian
edition, Academic Press, New York, 1965)
by I. S. Gradshteyn and I. M. Ryzhik . . 305
Jet Wimp Corrigendum: \booktitlePolynomial
expansions of Bessel functions and some
associated functions (Math. Comp. \bf 16
(1962), 446--458) . . . . . . . . . . . 309--309
W. F. Lunnon Corrigendum: \booktitleExplicit
expressions for the determinants of
certain matrices (Math. Comp. \bf 24
(1970), 151--154) by J. L. Lavoie and R.
Michaud . . . . . . . . . . . . . . . . 309
Anonymous Corrigenda . . . . . . . . . . . . . . . 309--309
Louis Bauer and
Edward L. Reiss Block five diagonal matrices and the
fast numerical solution of the
biharmonic equation . . . . . . . . . . 311--326
John K. Hayes and
David K. Kahaner and
Richard G. Kellner An Improved Method for Numerical
Conformal Mapping . . . . . . . . . . . 327--334
L. W. Ehrlich Coupled harmonic equations, SOR, and
Chebyshev acceleration . . . . . . . . . 335--343
David R. Kincaid Norms of the Successive Overrelaxation
Method . . . . . . . . . . . . . . . . . 345--357
R. B. Simpson Existence and error estimates for
solutions of a discrete analog of
nonlinear eigenvalue problems . . . . . 359--375
R. L. Johnston and
S. K. Pal The numerical solution of hyperbolic
systems using bicharacteristics . . . . 377--392
W. D. Hoskins and
P. J. Ponzo Some Properties of a Class of Band
Matrices . . . . . . . . . . . . . . . . 393--400
P. Lancaster and
H. K. Farahat Norms on Direct Sums and Tensor Products 401--414
Bernie L. Hulme One-Step Piecewise Polynomial Galerkin
Methods for Initial Value Problems . . . 415--426
E. Gekeler On the solution of systems of equations
by the epsilon algorithm of Wynn . . . . 427--436
A. K. Paul Anharmonic Frequency Analysis . . . . . 437--447
Thomas J. Osler An Integral Analogue of Taylor's Series
and its Use in Computing Fourier
Transforms . . . . . . . . . . . . . . . 449--460
Torsten Strom Monotonicity in Romberg Quadrature . . . 461--465
A. Pelios and
R. W. Klopfenstein Minimal error constant numerical
differentiation (N.D.) formulas . . . . 467--475
David K. Kahaner Minimum norm differentiation formulas
with improved roundoff error bounds . . 477--485
Geneva G. Belford Uniform approximation of vector-valued
functions with a constraint . . . . . . 487--492
S. E. Weinstein Uniform Approximation Through
Partitioning . . . . . . . . . . . . . . 493--503
S. W. Kahng Best $ {L}_p $ Approximation . . . . . . 505--508
Peter Linz A Method for Computing Bessel Function
Integrals . . . . . . . . . . . . . . . 509--513
Robert F. MacKinnon The asymptotic expansions of Hankel
transforms and related integrals . . . . 515--527
Chih-Bing Ling and
Jung Lin On Evaluation of Moments of $ {K}_\nu
(t) / {I}_\nu (t) $ . . . . . . . . . . 529--537
D. B. Hunter and
T. Regan A note on the evaluation of the
complementary error function . . . . . . 539--541
B. C. Carlson An algorithm for computing logarithms
and arctangents . . . . . . . . . . . . 543--549
K. S. Kolbig Complex zeros of two incomplete Riemann
zeta functions . . . . . . . . . . . . . 551--565
Alan Borning Some Results for $ k ! \pm 1 $ and $ 2
\cdot 3 \cdot 5 \cdots p \pm 1 $ . . . . 567--570
Walter Borho On Thabit ibn Kurrah's formula for
amicable numbers . . . . . . . . . . . . 571--578
M. Lal and
P. Gillard On the Equation $ \phi (n) = \phi (n +
k) $ . . . . . . . . . . . . . . . . . . 579--583
E. I. Book Review: \booktitleConstructive
Aspects of the Fundamental Theorem of
Algebra, by B. Dejon and P. Henrici . . 588--589
Anonymous Corrigendum . . . . . . . . . . . . . . 601--601
Heinz-Otto O. Kreiss Difference approximations for boundary
and eigenvalue problems for ordinary
differential equations . . . . . . . . . 605--624
H. Brunner A Note on Modified Optimal Linear
Multistep Methods . . . . . . . . . . . 625--631
James H. Bramble and
Vidar Thomee Semidiscrete-Least Squares Methods for a
Parabolic Boundary Value Problem . . . . 633--648
Bertil Gustafsson and
Heinz-Otto Kreiss and
Arne Sundström Stability theory of difference
approximations for mixed initial
boundary value problems. II . . . . . . 649--686
P. J. Davis and
P. Rabinowitz On the nonexistence of simplex
integration rules for infinite integrals 687--688
David K. Kahaner Numerical Quadrature by the $ \epsilon
$-Algorithm . . . . . . . . . . . . . . 689--693
J. H. Hetherington An Error Bound for Quadratures . . . . . 695--698
J. H. Rowland and
Y. L. Varol Exit criteria for Simpson's compound
rule . . . . . . . . . . . . . . . . . . 699--703
David R. Kincaid and
David M. Young The modified successive overrelaxation
method with fixed parameters . . . . . . 705--717
Leroy J. Derr Inversion of Isoclinal Matrices . . . . 719--721
Earl H. McKinney Generalized Recursive Multivariate
Interpolation . . . . . . . . . . . . . 723--735
James T. Lewis Computation of Best Monotone
Approximations . . . . . . . . . . . . . 737--747
M. G. Cox A note on Chambers' method for finding a
zero of a function . . . . . . . . . . . 749--750
K. S. Kolbig On the Zeros of the Incomplete Gamma
Function . . . . . . . . . . . . . . . . 751--755
Jerry L. Fields The asymptotic expansion of the Meijer
$G$-function . . . . . . . . . . . . . . 757--765
Samuel S. Wagstaff, Jr. On $k$-Free Sequences of Integers . . . 767--771
Charles R. Wall and
Phillip L. Crews and
Donald B. Johnson Density Bounds for the Sum of Divisors
Function . . . . . . . . . . . . . . . . 773--777
Charles R. Wall Density Bounds for Euler's Function . . 779--783
David G. Cantor and
Paul H. Galyean and
Horst G. Zimmer A continued fraction algorithm for real
algebraic numbers . . . . . . . . . . . 785--791
Harald Niederreiter On the Distribution of Pseudo-Random
Numbers Generated by the Linear
Congruential Method . . . . . . . . . . 793--795
Anonymous Corrigendum . . . . . . . . . . . . . . 815--815
George E. Forsythe Von Neumann's comparison method for
random sampling from the normal and
other distributions . . . . . . . . . . 817--826
D. Goldfarb Modification Methods for Inverting
Matrices and Solving Systems of Linear
Algebraic Equations . . . . . . . . . . 829--852
Robert J. Plemmons Monotonicity and Iterative
Approximations Involving Rectangular
Matrices . . . . . . . . . . . . . . . . 853--858
J. M. Varah On the Solution of Block-Tridiagonal
Systems Arising from Certain
Finite-Difference Equations . . . . . . 859--868
James H. Bramble and
Todd Dupont and
Vidar Thomee Projection methods for Dirichlet's
problem in approximating polygonal
domains with boundary-value corrections 869--879
Bernie L. Hulme Discrete Galerkin and related one-step
methods for ordinary differential
equations . . . . . . . . . . . . . . . 881--891
Richard F. Sincovec On the solution of the equations arising
from collocation with cubic B-splines 893--895
Thomas I. Seidman and
Robert J. Korsan Endpoint Formulas for Interpolatory
Cubic Splines . . . . . . . . . . . . . 897--900
Gerhard Merz Remark on a Paper by Huddleston . . . . 901--902
Thomas J. Osler The Integral Analog of the Leibniz Rule 903--915
Peter R. Lipow and
Frank Stenger How Slowly Can Quadrature Formulas
Converge? . . . . . . . . . . . . . . . 917--922
Walter Gautschi The Condition of Orthogonal Polynomials 923--924
R. Kress On the General Hermite Cardinal
Interpolation . . . . . . . . . . . . . 925--933
W. Morven Gentleman Optimal multiplication chains for
computing a power of a symbolic
polynomial . . . . . . . . . . . . . . . 935--939
F. W. J. Olver and
D. J. Sookne Note on Backward Recurrence Algorithms 941--947
R. Parnes Complex zeros of the modified Bessel
function $ K_n(Z) $ . . . . . . . . . . 949--953
A. J. Strecok and
J. A. Gregory High Precision Evaluation of the
Irregular Coulomb Wave Functions . . . . 955--961
Shoon K. Kim The Asymptotic Expansion of a
Hypergeometric Function $_2 {F}_2 (1,
\alpha; \rho_1, \rho_2; z)$ . . . . . . 963--963
Henry E. Fettis An Explicit Addition Formula for the
Inverse Jacobian Elliptic Functions . . 965--967
H. M. Srivastava and
J. P. Singhal A unified presentation of certain
classical polynomials . . . . . . . . . 969--975
T. W. Cusick Diophantine approximation of ternary
linear forms. II . . . . . . . . . . . . 977--993
H. C. Williams and
C. R. Zarnke Some Prime Numbers of the Forms $ 2
{A3}^n + 1 $ and $ 2 {A3}^n - 1 $ . . . 995--998
M. S. Cheema and
W. E. Conway Numerical investigation of certain
asymptotic results in the theory of
partitions . . . . . . . . . . . . . . . 999--1005
Svein Mossige Table of Irreducible Polynomials Over $
\mathrm {GF} \lbrack 2 \rbrack $ of
Degrees 10 Through 20 . . . . . . . . . 1007--1009
John Brillhart Note on Representing a Prime as a Sum of
Two Squares . . . . . . . . . . . . . . 1011--1013
Anonymous Corrigendum . . . . . . . . . . . . . . 1031--1031
Alexandre Joel Chorin Accurate Evaluation of Wiener Integrals 1--15
Jim Douglas, Jr. and
Todd Dupont A finite element collocation method for
quasilinear parabolic equations . . . . 17--28
Gerald Browning and
Heinz-Otto Kreiss and
Joseph Oliger Mesh Refinement . . . . . . . . . . . . 29--39
Moshe Goldberg A note on the stability of an iterative
finite-difference method for hyperbolic
systems . . . . . . . . . . . . . . . . 41--44
B. Fornberg On the Instability of Leap-Frog and
Crank--Nicolson Approximations of a
Nonlinear Partial Differential Equation 45--57
G. T. McAllister and
E. F. Sabotka Discrete Green's Functions . . . . . . . 59--80
Stephen Hilbert A Mollifier Useful for Approximations in
Sobolev Spaces and Some Applications to
Approximating Solutions of Differential
Equations . . . . . . . . . . . . . . . 81--89
L. F. Shampine Local extrapolation in the solution of
ordinary differential equations . . . . 91--97
Arun N. Netravali Spline approximation to the solution of
the Volterra integral equation of the
second kind . . . . . . . . . . . . . . 99--106
Malcolm A. MacLeod Improved computation of cubic natural
splines with equi-spaced knots . . . . . 107--109
C. M. Lee and
F. D. K. Roberts A Comparison of Algorithms for Rational
$ l_\infty $ Approximation . . . . . . . 111--121
W. J. Cody and
Anthony J. Strecok and
Henry C. Thacher, Jr. Chebyshev Approximations for the Psi
Function . . . . . . . . . . . . . . . . 123--127
Bernard J. Laurenzi Derivatives of Whittaker Functions $
{W}_{k, 1 / 2} $ and $ {M}_{k, 1 / 2} $
with Respect to Order $ {K} $ . . . . . 129--132
P. J. Erdelsky Computing the Brouwer Degree in $ {R}^2
$ . . . . . . . . . . . . . . . . . . . 133--137
Werner C. Rheinboldt and
James S. Vandergraft A Simple Approach to the
Perron--Frobenius Theory for Positive
Operators on General Partially-Ordered
Finite-Dimensional Linear Spaces . . . . 139--145
J. Rissanen Algorithms for Triangular Decomposition
of Block Hankel and Toeplitz Matrices
with Application to Factoring Positive
Matrix Polynomials . . . . . . . . . . . 147--154
John E. Blackburn and
Henry H. Crapo and
Denis A. Higgs A Catalogue of Combinatorial Geometries 155--166
H. Brown and
J. Neubuser and
H. Zassenhaus On Integral Groups. III: Normalizer . . 167--182
Daniel Shanks and
Richard Serafin Quadratic Fields with Four Invariants
Divisible by $3$ . . . . . . . . . . . . 183--187
H. J. J. te Riele A Note on the Catalan--Dickson
Conjecture . . . . . . . . . . . . . . . 189--192
William A. Webb Numerical Results for Waring's Problem
in $ \mathrm {GF} \lbrack q, x \rbrack $ 193--196
Jean-Marie-François Chamayou A Probabilistic Approach to a
Differential-Difference Equation Arising
in Analytic Number Theory . . . . . . . 197--203
Ivo Babu\vska The Finite Element Method with Penalty 221--228
Garth A. Baker Simplified proofs of error estimates for
the least squares method for Dirichlet's
problem . . . . . . . . . . . . . . . . 229--235
B. L. Buzbee and
Alfred Carasso On the numerical computation of
parabolic problems for preceding times 237--266
H. Nosrati A modified Butcher formula for
integration of stiff systems of ordinary
differential equations . . . . . . . . . 267--272
J. N. Lyness and
K. K. Puri The Euler--Maclaurin Expansion for the
Simplex . . . . . . . . . . . . . . . . 273--293
Frank de Hoog and
Richard Weiss Asymptotic Expansions for Product
Integration . . . . . . . . . . . . . . 295--306
J. H. Hetherington Note on Error Bounds for Numerical
Integration . . . . . . . . . . . . . . 307--316
M. J. Munteanu and
L. L. Schumaker On a method of Carasso and Laurent for
constructing interpolating splines . . . 317--325
Dietrich Braess Chebyshev approximation by exponentials
on finite subsets . . . . . . . . . . . 327--331
J. V. Petty A winding number algorithm for closed
polygonal paths . . . . . . . . . . . . 333--337
Oliver Aberth Iteration methods for finding all zeros
of a polynomial simultaneously . . . . . 339--344
R. L. Page On computing some extremal periodic
positive-definite functions . . . . . . 345--353
C. C. Paige An Error Analysis of a Method for
Solving Matrix Equations . . . . . . . . 355--359
T. W. Sag and
J. W. Wamsley On Computing the Minimal Number of
Defining Relations for Finite Groups . . 361--368
David W. Boyd An Algorithm for Generating the Sphere
Coordinates in a Three-Dimensional
Osculatory Packing . . . . . . . . . . . 369--377
Robert Spira Calculation of the Ramanujan $ \tau
$-Dirichlet Series . . . . . . . . . . . 379--385
Wells Johnson On the vanishing of the Iwasawa
invariant $ \mu p $ for $ p < 8000 $ . . 387--396
L. J. Lander Three Thirteens . . . . . . . . . . . . 397--397
M. C. Wunderlich On the Gaussian Primes on the Line $
\mathrm {IM}({X}) = 1 $ . . . . . . . . 399--400
Henry E. Fettis and
James C. Caslin and
Kenneth R. Cramer Complex zeros of the error function and
of the complementary error function . . 401--407
Henry E. Fettis and
James C. Caslin and
Kenneth R. Cramer Saddle Points of the Complementary Error
Function . . . . . . . . . . . . . . . . 409--412
D. E. Amos Bounds on Iterated Coerror Functions and
Their Ratios . . . . . . . . . . . . . . 413--427
R. Wong An Asymptotic Expansion of $ {W}_{k,
m}(z) $ with Large Variable and
Parameters . . . . . . . . . . . . . . . 429--436
Anonymous Corrigendum . . . . . . . . . . . . . . 453--453
Harold N. Shapiro Integer Vectors with Interprimed
Components . . . . . . . . . . . . . . . 455--462
John J. Cannon and
Lucien A. Dimino and
George Havas and
Jane M. Watson Implementation and Analysis of the
Todd--Coxeter Algorithm . . . . . . . . 463--490
Kermit Rose and
Simcha Brudno More About Four Biquadrates Equal One
Biquadrate . . . . . . . . . . . . . . . 491--494
Frank McNolty Some probability density functions and
their characteristic functions . . . . . 495--504
S. Abarbanel and
D. Gottlieb Higher order accuracy finite difference
algorithms for quasi-linear,
conservation law hyperbolic systems . . 505--523
J. H. Bramble and
J. E. Osborn Rate of convergence estimates for
nonselfadjoint eigenvalue approximations 525--549
Steven A. Pruess Solving linear boundary value problems
by approximating the coefficients . . . 551--561
Joseph A. Guzek and
Gene A. Kemper A new error analysis for a cubic spline
approximate solution of a class of
Volterra integro-differential equations 563--570
R. N. Castleton and
L. J. Grimm A first order method for differential
equations of neutral type . . . . . . . 571--577
Åke Björck and
Gene H. Golub Numerical Methods for Computing Angles
between Linear Subspaces . . . . . . . . 579--594
V. Pereyra and
G. Scherer Efficient computer manipulation of
tensor products with applications to
multidimensional approximation . . . . . 595--605
G. A. Watson The calculation of best linear one-sided
$ L^p $ approximations . . . . . . . . . 607--620
Richard O. Hays Multi-Dimensional Extensions of the
Chebyshev Polynomials . . . . . . . . . 621--624
Laurance C. Eisenhart and
George E. Trapp, Jr. Computation of Hermite Polynomials . . . 625--632
David W. Kammler Chebyshev polynomials corresponding to a
semi-infinite interval and an
exponential weight factor . . . . . . . 633--637
A. C. R. Newbery Error Analysis for Fourier Series
Evaluation . . . . . . . . . . . . . . . 639--644
K. Salkauskas Almost-Interpolatory Chebyshev
Quadrature . . . . . . . . . . . . . . . 645--654
F. G. Lether Cubature Error Bounds for Analytic
Functions . . . . . . . . . . . . . . . 655--668
John W. Wrench Erratum: Concerning Two Series for the
Gamma Function . . . . . . . . . . . . . 681--682
Anonymous Corrigenda . . . . . . . . . . . . . . . 683--683
Achi Brandt Generalized local maximum principles for
finite-difference operators . . . . . . 685--718
Theodore E. Dushane Convergence for a Vortex Method for
Solving Euler's Equation . . . . . . . . 719--728
Eli Turkel Symmetrization of the Fluid Dynamic
Matrices with Applications . . . . . . . 729--736
William H. Ford and
T. W. Ting Stability and convergence of difference
approximations to pseudo-parabolic
partial differential equations . . . . . 737--743
Stewart Venit Mesh refinements for parabolic equations
of second order . . . . . . . . . . . . 745--754
B. A. Troesch and
H. R. Troesch Eigenfrequencies of an Elliptic Membrane 755--765
B. Andreas Troesch Elliptical Membranes with Smallest
Second Eigenvalue . . . . . . . . . . . 767--772
Niel K. Madsen A Posteriori Error Bounds for Numerical
Solutions of the Neutron Transport
Equation . . . . . . . . . . . . . . . . 773--780
F. M. Carrano A modified Bairstow method for multiple
zeros of a polynomial . . . . . . . . . 781--792
J. C. Butcher The order of numerical methods for
ordinary differential equations . . . . 793--806
G. Micula Approximate Solution of the Differential
Equation $ y'' = f(x, y) $ with Spline
Functions . . . . . . . . . . . . . . . 807--816
Edgar A. Cohen, Jr. Polynomial approximation of a function
and its first derivative in near minimax
norms . . . . . . . . . . . . . . . . . 817--827
W. D. Hoskins Boundary Expansions for Spline
Interpolation . . . . . . . . . . . . . 829--830
George D. Andria and
George D. Byrne and
David R. Hill Integration Formulas and Schemes Based
on $g$-Splines . . . . . . . . . . . . . 831--838
H. S. Wrigge An Elliptic Integral Identity . . . . . 839--840
J. S. R. Chisholm Rational Approximants Defined from
Double Power Series . . . . . . . . . . 841--848
James L. Phillips Error analysis for direct linear
integral equation methods . . . . . . . 849--859
Bernard Danloy Numerical Construction of Gaussian
Quadrature Formulas for $ \int^1_0 ( -
\Log x) \cdot x^\alpha \cdot f(x) \cdot
\, d x $ and $ \int^\infty_0 {E}_m(x)
\cdot f(x) \cdot \, d x $ . . . . . . . 861--869
Peter Linz and
T. E. Kropp A note on the computation of integrals
involving products of trigonometric and
Bessel functions . . . . . . . . . . . . 871--872
Shmuel S. Oren Self-Scaling Variable Metric Algorithms
without Line Search for Unconstrained
Minimization . . . . . . . . . . . . . . 873--885
Jo Ann Howell An algorithm for the exact reduction of
a matrix to Frobenius form using modular
arithmetic. I . . . . . . . . . . . . . 887--904
Jo Ann Howell An algorithm for the exact reduction of
a matrix to Frobenius form using modular
arithmetic. II . . . . . . . . . . . . . 905--920
L. J. Lardy An Extrapolated Gauss--Seidel Iteration
for Hessenberg Matrices . . . . . . . . 921--926
J. H. Ahrens and
U. Dieter Extensions of Forsythe's method for
random sampling from the normal
distribution . . . . . . . . . . . . . . 927--937
J. E. Dutt and
T. K. Lin and
L. C. Tao New Approximations to Familiar Functions 939--942
Bryant Tuckerman A search procedure and lower bound for
odd perfect numbers . . . . . . . . . . 943--949
Peter Hagis, Jr. A Lower Bound for the Set of Odd Perfect
Numbers . . . . . . . . . . . . . . . . 951--953
Peter Hagis, Jr. and
Wayne L. McDaniel On the largest prime divisor of an odd
perfect number . . . . . . . . . . . . . 955--957
Richard P. Brent The first occurrence of large gaps
between successive primes . . . . . . . 959--963
P. A. Morris Computational Problems in $
{S}$-Function Theory . . . . . . . . . . 965--971
Richard H. Hudson A Note on Dirichlet Characters . . . . . 973--975
Wayne Stahnke Primitive Binary Polynomials . . . . . . 977--980
Richard P. Stauduhar The Determination of Galois Groups . . . 981--996
Alexandre J. Chorin and
Daniel Shanks Corrigenda: \em Accurate Evaluation of
Wiener Integrals and \em A Note on the
Catalan--Dickson Conjecture . . . . . . 1011--1012
Vidar Thomee and
Lars Wahlbin Convergence rates of parabolic
difference schemes for non-smooth data 1--13
Joseph Oliger Fourth order difference methods for the
initial boundary-value problem for
hyperbolic equations . . . . . . . . . . 15--25
Daniel S. Watanabe and
J. Richard Flood An implicit fourth order difference
method for viscous flows . . . . . . . . 27--32
R. L. Johnston and
S. K. Pal Numerical solution of Lundquist
equations of magnetohydrodynamics . . . 33--44
Masahiro Hinata and
Masaaki Shimasaki and
Takeshi Kiyono Numerical solution of Plateau's problem
by a finite element method . . . . . . . 45--60
H. Brunner Global solution of the generalized Abel
integral equation by implicit
interpolation . . . . . . . . . . . . . 61--67
M. Z. Nashed and
Grace Wahba Convergence rates of approximate least
squares solutions of linear integral and
operator equations of the first kind . . 69--80
J. N. Lyness Computational techniques based on the
Lanczos representation . . . . . . . . . 81--123
Walter Gautschi and
Hiroki Yanagiwara On Chebyshev-Type Quadratures . . . . . 125--134
Robert Piessens and
Maria Branders A note on the optimal addition of
abscissas to quadrature formulas of
Gauss and Lobatto type . . . . . . . . . 135--139
L. F. Shampine Limiting Precision in Differential
Equation Solvers . . . . . . . . . . . . 141--144
A. Prothero and
A. Robinson On the stability and accuracy of
one-step methods for solving stiff
systems of ordinary differential
equations . . . . . . . . . . . . . . . 145--162
Jack Williams and
Frank de Hoog A Class of $A$-Stable Advanced Multistep
Methods . . . . . . . . . . . . . . . . 163--177
Geneva G. Belford Vector-Valued Approximation and its
Application to Fitting Exponential Decay
Curves . . . . . . . . . . . . . . . . . 179--184
J. B. Diaz and
T. J. Osler Differences of Fractional Order . . . . 185--202
Paul T. Boggs A new algorithm for the Chebyshev
solution of overdetermined linear
systems . . . . . . . . . . . . . . . . 203--217
I. S. Duff On the number of nonzeros added when
Gaussian elimination is performed on
sparse random matrices . . . . . . . . . 219--230
James R. Bunch and
John E. Hopcroft Triangular factorization and inversion
by fast matrix multiplication . . . . . 231--236
Marvin J. Goldstein Reduction of the eigenproblem for
Hermitian persymmetric matrices . . . . 237--238
D. E. Amos Computation of modified Bessel functions
and their ratios . . . . . . . . . . . . 239--251
Ingemar Nasell Inequalities for Modified Bessel
Functions . . . . . . . . . . . . . . . 253--256
S. N. Samaddar Some Integrals Involving Associated
Legendre Functions . . . . . . . . . . . 257--263
M. L. Glasser Reduction Formulas for Multiple Series 265--266
M. D. Hendy Applications of a Continued Fraction
Algorithm to Some Class Number Problems 267--277
Carol Neild and
Daniel Shanks On the $3$-Rank of Quadratic Fields and
the Euler Product . . . . . . . . . . . 279--291
Daniel Shanks and
John W. Wrench, Jr. Brun's Constant . . . . . . . . . . . . 293--299
Mohan Lal Iterates of the Unitary Totient Function 301--302
Ronald Alter and
Thaddeus B. Curtz A Note on Congruent Numbers . . . . . . 303--305
I. O. Angell and
H. J. Godwin Some Factorizations of $ 10^n \pm 1 $ 307--308
H. J. J. te Riele Four Large Amicable Pairs . . . . . . . 309--312
Robert E. Dressler and
Thomas Parker $ 12, 758 $ . . . . . . . . . . . . . . 313--314
Richard P. Brent The Distribution of Small Gaps Between
Successive Primes . . . . . . . . . . . 315--324
Anonymous Corrigendum . . . . . . . . . . . . . . 343--343
Robert Piessens and
Maria Branders Supplement to A Note on the Optimal
Addition of Abscissas to Quadrature
Formulas of Gauss and Lobatto Type . . . 344--347
D. Fischer and
G. Golub and
O. Hald and
C. Leiva and
O. Widlund On Fourier--Toeplitz Methods for
Separable Elliptic Problems . . . . . . 349--368
H. J. van Linde High-Order Finite-Difference Methods for
Poisson's Equation . . . . . . . . . . . 369--391
Milos Zlamal Finite Element Methods for Parabolic
Equations . . . . . . . . . . . . . . . 393--404
J. Thomas King Semidiscrete Least-Squares Methods for
Second Order Parabolic Problems With
Nonhomogeneous Data . . . . . . . . . . 405--411
M. Goldberg and
S. Abarbanel Stable approximations for hyperbolic
systems with moving internal boundary
conditions . . . . . . . . . . . . . . . 413--447
Richard Weiss The application of implicit Runge--Kutta
and collocation methods to
boundary-value problems . . . . . . . . 449--464
Arthur David Snider and
Gary Charles Fleming Approximation by Aliasing with
Application to ``Certaine'' Stiff
Differential Equations . . . . . . . . . 465--473
H. Brunner Recursive collocation for the numerical
solution of stiff ordinary differential
equations . . . . . . . . . . . . . . . 475--481
I. J. Schoenberg and
S. D. Silliman On Semicardinal Quadrature Formulae . . 483--497
Ravindra Kumar and
M. K. Jain Quadrature Formulas for Semi-Infinite
Integrals . . . . . . . . . . . . . . . 499--503
P. E. Gill and
G. H. Golub and
W. Murray and
M. A. Saunders Methods for Modifying Matrix
Factorizations . . . . . . . . . . . . . 505--535
G. W. Stewart Modifying Pivot Elements in Gaussian
Elimination . . . . . . . . . . . . . . 537--542
W. M. Gentleman and
S. C. Johnson The evaluation of determinants by
expansion by minors and the general
problem of substitution . . . . . . . . 543--548
J. E. Dennis, Jr. and
Jorge J. More A characterization of superlinear
convergence and its application to
quasi-Newton methods . . . . . . . . . . 549--560
M. Lal and
P. Gillard Evaluation of a constant associated with
a parking problem . . . . . . . . . . . 561--564
C. de Boor and
James W. Daniel Splines with Nonnegative $ {B}$-Spline
Coefficients . . . . . . . . . . . . . . 565--568
R. E. Huddleston On the conditional equivalence of two
starting methods for the second
algorithm of Remez . . . . . . . . . . . 569--572
J. A. Blackburn and
Y. Beaudoin A note on Chambers' method . . . . . . . 573--574
W. F. Breig and
A. L. Crosbie Numerical computation of a generalized
exponential integral function . . . . . 575--579
J. M. Blair Rational Chebyshev approximations for
the modified Bessel functions $ I_0 (x)
$ and $ I_1 (x) $ . . . . . . . . . . . 581--583
Henry E. Fettis A stable algorithm for computing the
inverse error function in the `tail-end'
region . . . . . . . . . . . . . . . . . 585--587
George E. Collins and
Ellis Horowitz The Minimum Root Separation of a
Polynomial . . . . . . . . . . . . . . . 589--597
W. A. Beyer and
M. S. Waterman Error analysis of a computation of
Euler's constant . . . . . . . . . . . . 599--604
V. L. Deshpande Confluent Expansions for Functions of
Two Variables . . . . . . . . . . . . . 605--611
M. L. Glasser Some definite integrals of the product
of two Bessel functions of the second
kind: (order zero) . . . . . . . . . . . 613--615
S. J. Benkoski and
P. Erd\Hos On Weird and Pseudoperfect Numbers . . . 617--623
D. H. Lehmer and
Emma Lehmer A New Factorization Technique Using
Quadratic Forms . . . . . . . . . . . . 625--635
R. Sherman Lehman Factoring Large Integers . . . . . . . . 637--646
E. F. Ecklund, Jr. and
P. Erd\Hos and
J. L. Selfridge A New Function Associated with the Prime
Factors of $ \binom {n}{k} $ . . . . . . 647--649
Robert E. Dressler and
Andrzej Makowski and
Thomas Parker Sums of distinct primes from congruence
classes modulo 12 . . . . . . . . . . . 651--652
Wells Johnson Irregular Prime Divisors of the
Bernoulli Numbers . . . . . . . . . . . 653--657
David C. Hunt The character table of an
eight-dimensional orthogonal group . . . 659--660
David C. Hunt The Character Table of Fischer's Simple
Group, $ {M}(23) $ . . . . . . . . . . . 660--661
B. N. Parlett The Rayleigh Quotient Iteration and Some
Generalizations for Nonnormal Matrices 679--693
Axel Ruhe $ \mathrm {SOR}$-Methods for the
Eigenvalue Problem with Large Sparse
Matrices . . . . . . . . . . . . . . . . 695--710
Geneva G. Belford and
E. H. Kaufman, Jr. An application of approximation theory
to an error estimate in linear algebra 711--712
Gurudas Chatterjee Negative Integral Powers of a Bidiagonal
Matrix . . . . . . . . . . . . . . . . . 713--714
Marvin J. Goldstein Reduction of the pseudoinverse of a
Hermitian persymmetric matrix . . . . . 715--717
R. S. Anderssen and
B. J. Omodei On the stability of uniformly
asymptotically diagonal systems . . . . 719--730
Claude Brezinski and
Alain C. Rieu The solution of systems of equations
using the epsilon --- algorithm, and an
application to boundary-value problems 731--741
James M. Varah A comparison of some numerical methods
for two-point boundary value problems 743--755
Alfred Carasso A Least Squares Procedure for the Wave
Equation . . . . . . . . . . . . . . . . 757--767
Ravindra Kumar A Class of Quadrature Formulas . . . . . 769--778
David C. Shreve $ {L}^p $ Approximation of Fourier
Transforms and Certain Interpolating
Splines . . . . . . . . . . . . . . . . 779--787
A. C. R. Newbery Error Analysis for Polynomial Evaluation 789--793
William B. Jones and
W. J. Thron Numerical stability in evaluating
continued fractions . . . . . . . . . . 795--810
J. H. McCabe A continued fraction expansion, with a
truncation error estimate, for Dawson's
integral . . . . . . . . . . . . . . . . 811--816
R. G. Buschman Finite sum representations for partial
derivatives of special functions with
respect to parameters . . . . . . . . . 817--824
Carl H. FitzGerald Optimal Indexing of the Vertices of
Graphs . . . . . . . . . . . . . . . . . 825--831
H. H. Baker and
A. K. Dewdney and
A. L. Szilard Generating the Nine-Point Graphs . . . . 833--838
Richard B. Lakein Computation of the ideal class group of
certain complex quartic fields . . . . . 839--846
Wayne L. McDaniel On Multiple Prime Divisors of Cyclotomic
Polynomials . . . . . . . . . . . . . . 847--850
David E. Penney and
Carl Pomerance A Search for Elliptic Curves With Large
Rank . . . . . . . . . . . . . . . . . . 851--853
Sol Weintraub A Compact Prime Listing . . . . . . . . 855--857
Paul Abrahams Book Review: Niklaus Wirth,
\booktitleSystematic Programming: An
Introduction, Prentice-Hall, Inc.,
Englewood Cliffs, N.J., 1973, 167 pp.,
24 cm. . . . . . . . . . . . . . . . . . 881--883
Anonymous Corrigenda . . . . . . . . . . . . . . . 887--887
Joel N. Franklin On Tikhonov's Method for Ill-Posed
Problems . . . . . . . . . . . . . . . . 889--907
C. G. L. Johnson Estimates near plane portions of the
boundary for discrete elliptic boundary
problems . . . . . . . . . . . . . . . . 909--935
Joachim A. Nitsche and
Alfred H. Schatz Interior Estimates for Ritz--Galerkin
Methods . . . . . . . . . . . . . . . . 937--958
Alfred H. Schatz An observation concerning Ritz--Galerkin
methods with indefinite bilinear forms 959--962
Richard S. Falk Error estimates for the approximation of
a class of variational inequalities . . 963--971
Eckart Gekeler On the Eigenvectors of a
Finite-Difference Approximation to the
Sturm--Liouville Eigenvalue Problem . . 973--979
M. Lentini and
V. Pereyra A variable order finite difference
method for nonlinear multipoint boundary
value problems . . . . . . . . . . . . . 981--1003
Dale W. Alspaugh The application of invariant imbedding
to the solution of linear two-point
boundary value problems on an infinite
interval . . . . . . . . . . . . . . . . 1005--1015
W. L. Miranker and
J. P. Morreeuw Semianalytic numerical studies of
turning points arising in stiff boundary
value problems . . . . . . . . . . . . . 1017--1034
E. F. Sarkany and
W. Liniger Exponential fitting of matricial
multistep methods for ordinary
differential equations . . . . . . . . . 1035--1052
Olavi Nevanlinna and
Aarne H. Sipila A nonexistence theorem for explicit
$A$-stable methods . . . . . . . . . . . 1053--1055
A. Nadeau and
J. Guyard and
M. R. Feix Algebraic-Numerical Method for the
Slightly Perturbed Harmonic Oscillator 1057--1066
R. Fletcher and
M. J. D. Powell On the Modification of $ {LDL}^T $
Factorizations . . . . . . . . . . . . . 1067--1087
William F. Trench Inversion of Toeplitz Band Matrices . . 1089--1095
G. D. Taylor and
J. Williams Existence questions for the problem of
Chebyshev approximation by interpolating
rationals . . . . . . . . . . . . . . . 1097--1103
Herbert E. Salzer Some problems in optimally stable
Lagrangian differentiation . . . . . . . 1105--1115
Harald Niederreiter On the distribution of pseudo-random
numbers generated by the linear
congruential method. II . . . . . . . . 1117--1132
Kenneth S. Williams A Quadratic Partition of Primes $ \equiv
1 (\operatorname {mod} 7) $ . . . . . . 1133--1136
Daniel Shanks The Simplest Cubic Fields . . . . . . . 1137--1152
M. Mignotte An Inequality About Factors of
Polynomials . . . . . . . . . . . . . . 1153--1157
Jacob T. B. Beard, Jr. Computing in $ \mathrm {GF}(q) $ . . . . 1159--1166
Jacob T. B. Beard, Jr. and
Karen I. West Some Primitive Polynomials of the Third
Kind . . . . . . . . . . . . . . . . . . 1166--1167
Jacob T. B. Beard, Jr. and
Karen I. West Factorization Tables for $ x^n - 1 $
Over $ \mathrm {GF}(q) $ . . . . . . . . 1167--1168
Anonymous Corrigenda . . . . . . . . . . . . . . . 1183--1184
Tom M. Apostol The resultant of the cyclotomic
polynomials $ F^m(a x) $ and $ F^n(b x)
$ . . . . . . . . . . . . . . . . . . . 1--6
Paul T. Bateman and
George B. Purdy and
Samuel S. Wagstaff, Jr. Some Numerical Results on Fekete
Polynomials . . . . . . . . . . . . . . 7--23
Elwyn R. Berlekamp The Design of Slowly Shrinking Labelled
Squares . . . . . . . . . . . . . . . . 25--27
M. N. Bleicher and
P. Erd\Hos The Number of Distinct Subsums of $
{\sum }^N_1 l / i $ . . . . . . . . . . 29--42
Richard P. Brent Irregularities in the distribution of
primes and twin primes . . . . . . . . . 43--56
Stefan A. Burr On detecting a periodic event by means
of periodic observations. I . . . . . . 57--65
L. Carlitz and
Richard Scoville A Generating Function for Triangular
Partitions . . . . . . . . . . . . . . . 67--77
Fred Cohen and
J. L. Selfridge Not every number is the sum or
difference of two prime powers . . . . . 79--81
P. Erd\Hos and
R. L. Graham and
I. Z. Ruzsa and
E. G. Straus On the Prime Factors of $ \binom {2n}{n}
$ . . . . . . . . . . . . . . . . . . . 83--92
Walter Gautschi Nonexistence of Chebyshev-Type
Quadratures on Infinite Intervals . . . 93--99
Richard K. Guy and
J. L. Selfridge What Drives an Aliquot Sequence? . . . . 101--107
John C. Hallyburton, Jr. and
John Brillhart Two New Factors of Fermat Numbers . . . 109--112
Wells Johnson Irregular Primes and Cyclotomic
Invariants . . . . . . . . . . . . . . . 113--120
Donald E. Knuth Estimating the Efficiency of Backtrack
Programs . . . . . . . . . . . . . . . . 121--136
Richard B. Lakein Computation of the ideal class group of
certain complex quartic fields. II . . . 137--144
K. Mahler A necessary and sufficient condition for
transcendency . . . . . . . . . . . . . 145--153
J. C. P. Miller On Factorisation, with a Suggested New
Approach . . . . . . . . . . . . . . . . 155--172
W. H. Mills Continued Fractions and Linear
Recurrences . . . . . . . . . . . . . . 173--180
Michael A. Morrison A Note on Primality Testing Using Lucas
Sequences . . . . . . . . . . . . . . . 181--182
Michael A. Morrison and
John Brillhart A method of factoring and the
factorization of $ F^7 $ . . . . . . . . 183--205
Morris Newman Congruence Subgroups of the Modular
Group . . . . . . . . . . . . . . . . . 207--213
John Riordan The distribution of crossings of chords
joining pairs of 2n points on a circle 215--222
Raphael M. Robinson The Structure of Certain Triple Systems 223--241
J. Barkley Rosser and
Lowell Schoenfeld Sharper Bounds for the Chebyshev
Functions $ {\Theta }(x) $ and $ {\Psi
}(x) $ . . . . . . . . . . . . . . . . . 243--269
Daniel Shanks Calculation and Applications of Epstein
Zeta Functions . . . . . . . . . . . . . 271--287
H. M. Stark On Complex Quadratic Fields with
Class-Number Two . . . . . . . . . . . . 289--302
E. G. Straus A Combinatorial Theorem in Group Theory 303--309
Paul Turan Power Sum Method and the Approximative
Solution of Algebraic Equations . . . . 311--318
Peter J. Weinberger On Small Zeros of Dirichlet $
{L}$-Functions . . . . . . . . . . . . . 319--328
Claes Johnson and
Vidar Thomee Error estimates for a finite element
approximation of a minimal surface . . . 343--349
Milos Zlamal Finite element multistep discretizations
of parabolic boundary value problems . . 350--359
Jim Douglas, Jr. and
Todd Dupont The effect of interpolating the
coefficients in nonlinear parabolic
Galerkin procedures . . . . . . . . . . 360--389
Ivo G. Rosenberg and
Frank Stenger A lower Bound on the Angles of Triangles
Constructed by Bisecting the Longest
Side . . . . . . . . . . . . . . . . . . 390--395
Bertil Gustafsson The convergence rate for difference
approximations to mixed initial boundary
value problems . . . . . . . . . . . . . 396--406
G. R. McGuire and
J. Ll. Morris Explicit-Implicit Schemes for the
Numerical Solution of Nonlinear
Hyperbolic Systems . . . . . . . . . . . 407--424
Avishai Livne Seven-Point Difference Schemes for
Hyperbolic Equations . . . . . . . . . . 425--433
B. M. Marder GAP --- a PIC-type fluid code . . . . . 434--446
Alfred Carasso Coupled sound and heat flow and the
method of least squares . . . . . . . . 447--463
H. B. Keller Approximation methods for nonlinear
problems with application to two point
boundary value problems . . . . . . . . 464--474
Jim Douglas, Jr. and
Todd Dupont and
Lars Wahlbin Optimal $ {L}_\infty $ Error Estimates
for Galerkin Approximations to Solutions
of Two-Point Boundary Value Problems . . 475--483
Jorg Hertling and
Alexandru I. Schiop On the Stability of the Ritz--Galerkin
Method for Hammerstein Equations . . . . 484--488
G. K. Gupta and
C. S. Wallace Some new multistep methods for solving
ordinary differential equations . . . . 489--500
Byron L. Ehle and
Zdenek Picel Two-Parameter, Arbitrary Order,
Exponential Approximations for Stiff
Equations . . . . . . . . . . . . . . . 501--511
John K. Hayes and
David K. Kahaner and
Richard G. Kellner A numerical comparison of integral
equations of the first and second kind
for conformal mapping . . . . . . . . . 512--521
James T. Lewis Restricted range approximation and its
application to digital filter design . . 522--539
Jerry M. Wolfe Discrete Rational $ {L}_p $
Approximation . . . . . . . . . . . . . 540--548
Charles B. Dunham Chebyshev Approximation by Interpolating
Rationals on $ \lbrack \alpha, \infty) $ 549--551
Charles B. Dunham A difficulty in Williams' algorithm for
interpolating rationals . . . . . . . . 552--553
Kenneth O. Leland An algorithm for winding numbers for
closed polygonal paths . . . . . . . . . 554--558
D. B. Hunter Some Properties of Orthogonal
Polynomials . . . . . . . . . . . . . . 559--565
A. J. Zajta and
W. Pandikow Conversion of Continued Fractions into
Power Series . . . . . . . . . . . . . . 566--572
R. Wong On Laplace Transforms Near the Origin 573--576
Jet Wimp Differential-Difference Properties of
Hypergeometric Polynomials . . . . . . . 577--581
B. Fornberg and
K. S. Kolbig Complex zeros of the Jonquiere or
polylogarithm function . . . . . . . . . 582--599
G. W. Stewart Gershgorin theory for the generalized
eigenvalue problem $ A x = \lambda B x $ 600--606
Ned Anderson A generalization of the method of
averages for overdetermined linear
systems . . . . . . . . . . . . . . . . 607--614
Inderjit Singh and
George Poole and
Thomas Boullion A class of Hessenberg matrices with
known pseudoinverse and Drazin inverse 615--619
John Brillhart and
D. H. Lehmer and
J. L. Selfridge New primality criteria and
factorizations of $ 2^m \pm 1 $ . . . . 620--647
J. S. Book Review: R. W. Hamming,
\booktitleNumerical Methods for
Scientists and Engineers, 2nd ed.,
McGraw-Hill Book Co., New York, 1973, ix
+ 721 pp., 24 cm. . . . . . . . . . . . 648--649
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 648--669
Anonymous Table Errata . . . . . . . . . . . . . . 670--670
Anonymous Corrigenda . . . . . . . . . . . . . . . 673--674
Anonymous An Addendum to 12,758 . . . . . . . . . 675--675
James H. Bramble and
Joachim A. Nitsche and
Alfred H. Schatz Maximum-Norm Interior Estimates for
Ritz--Galerkin Methods . . . . . . . . . 677--688
Jim Douglas, Jr. and
Todd Dupont A Galerkin method for a nonlinear
Dirichlet problem . . . . . . . . . . . 689--696
Gunilla Skollermo A Fourier method for the numerical
solution of Poisson's equation . . . . . 697--711
John E. Osborn Spectral Approximation for Compact
Operators . . . . . . . . . . . . . . . 712--725
R. E. Barnhill and
J. A. Gregory Polynomial interpolation to boundary
data on triangles . . . . . . . . . . . 726--735
John Morgan and
Ridgway Scott A Nodal Basis for $ {C}^1 $ Piecewise
Polynomials of Degree $ n \geq 5 $ . . . 736--740
David R. Hill On comparing Adams and natural spline
multistep formulas . . . . . . . . . . . 741--745
Richard Weiss Bifurcation in difference approximations
to two-point boundary value problems . . 746--760
J. H. Ahlberg and
T. Ito A collocation method for two-point
boundary value problems . . . . . . . . 761--776
Steven M. Serbin Computational investigations of
least-squares type methods for the
approximate solution of boundary value
problems . . . . . . . . . . . . . . . . 777--793
E. Rakotch Numerical solution for eigenvalues and
eigenfunctions of a Hermitian kernel and
an error estimate . . . . . . . . . . . 794--805
Seymour Haber Adaptive Integration and Improper
Integrals . . . . . . . . . . . . . . . 806--809
Robert Piessens and
Ann Haegemans Cubature formulas of degree nine for
symmetric planar regions . . . . . . . . 810--815
Kenneth W. Brodlie On Bairstow's method for the solution of
polynomial equations . . . . . . . . . . 816--826
U. Dieter How to Calculate Shortest Vectors in a
Lattice . . . . . . . . . . . . . . . . 827--833
S. H. Tung On lower and upper bounds of the
difference between the arithmetic and
the geometric mean . . . . . . . . . . . 834--836
Luc Wuytack On the Osculatory Rational Interpolation
Problem . . . . . . . . . . . . . . . . 837--843
Nabih N. Abdelmalek An efficient method for the discrete
linear $ {L^1} $ approximation problem 844--850
Helaman Rolfe Pratt Ferguson and
Dale E. Nielsen and
Grant Cook A partition formula for the integer
coefficients of the theta function nome 851--855
David G. Carta Low-Order Approximations for the Normal
Probability Integral and the Error
Function . . . . . . . . . . . . . . . . 856--862
V. B. Headley and
V. K. Barwell On the distribution of the zeros of
generalized Airy functions . . . . . . . 863--877
Yasuhiko Ikebe The Zeros of Regular Coulomb Wave
Functions and of Their Derivatives . . . 878--887
Thomas J. Osler An Identity for Simplifying Certain
Generalized Hypergeometric Functions . . 888--893
Jerry L. Fields and
Mourad E. H. Ismail Polynomial Expansions . . . . . . . . . 894--902
George D. Poole Generalized $ {M}$-Matrices and
Applications . . . . . . . . . . . . . . 903--910
M. D. Atkinson An Algorithm for Finding the Blocks of a
Permutation Group . . . . . . . . . . . 911--913
Carl Pomerance The second largest prime factor of an
odd perfect number . . . . . . . . . . . 914--921
Peter Hagis, Jr. and
Wayne L. McDaniel On the largest prime divisor of an odd
perfect number. II . . . . . . . . . . . 922--924
Andrew Bremner An equation of Mordell . . . . . . . . . 925--928
M. Rosenblatt Multiply Schemes and Shuffling . . . . . 929--934
Paul S. Wang and
Linda Preiss Rothschild Factoring Multivariate Polynomials Over
the Integers . . . . . . . . . . . . . . 935--950
I. Borosh and
C. J. Moreno and
H. Porta Elliptic Curves Over Finite Fields. II 951--964
David E. Penney and
Carl Pomerance Three Elliptic Curves with Rank at Least
Seven . . . . . . . . . . . . . . . . . 965--967
G. W. Hedstrom Models of difference schemes for $ u^t +
u^x = 0 $ by partial differential
equations . . . . . . . . . . . . . . . 969--977
Lars Wahlbin A modified Galerkin procedure with
Hermite cubics for hyperbolic problems 978--984
Melvyn Ciment and
Stephen H. Leventhal Higher order compact implicit schemes
for the wave equation . . . . . . . . . 985--994
Garth A. Baker A finite element method for first order
hyperbolic equations . . . . . . . . . . 995--1006
R. D. Russell and
J. M. Varah A comparison of global methods for
linear two-point boundary value problems 1007--1019
William W. Hager and
Gilbert Strang Free Boundaries and Finite Elements in
One Dimension . . . . . . . . . . . . . 1020--1031
J. Oliver A Curiosity of Low-Order Explicit
Runge--Kutta Methods . . . . . . . . . . 1032--1036
R. F. Warming and
Richard M. Beam and
B. J. Hyett Diagonalization and simultaneous
symmetrization of the gas-dynamic
matrices . . . . . . . . . . . . . . . . 1037--1045
A. C. R. Newbery Polynomial Evaluation Schemes . . . . . 1046--1050
Philip E. Gill and
Walter. Murray and
Michael A. Saunders Methods for Computing and Modifying the
$ L D V $ Factors of a Matrix . . . . . 1051--1077
Charles B. Dunham Convergence of the Fraser--Hart
Algorithm for Rational Chebyshev
Approximation . . . . . . . . . . . . . 1078--1082
Yudell L. Luke and
Bing Yuan Ting and
Marilyn J. Kemp On Generalized Gaussian Quadrature . . . 1083--1093
Ralph Shapiro Linear Filtering . . . . . . . . . . . . 1094--1097
Dalton R. Hunkins Cubatures of precision 2k and 2k+1 for
hyperrectangles . . . . . . . . . . . . 1098--1104
C. W. Groetsch On existence criteria and approximation
procedures for integral equations of the
first kind . . . . . . . . . . . . . . . 1105--1108
N. M. Temme Uniform asymptotic expansions of the
incomplete gamma functions and the
incomplete beta function . . . . . . . . 1109--1114
H. M. Srivastava and
Rekha Panda Some analytic or asymptotic confluent
expansions for functions of several
variables . . . . . . . . . . . . . . . 1115--1128
M. D. Hendy The distribution of ideal class numbers
of real quadratic fields . . . . . . . . 1129--1134
Frank Gerth, III A Note on $l$-Class Groups of Number
Fields . . . . . . . . . . . . . . . . . 1135--1137
Samuel S. Wagstaff, Jr. Zeros of $p$-Adic $ {L}$-Functions . . . 1138--1143
Torleiv Klove Sums of Distinct Elements from a Fixed
Set . . . . . . . . . . . . . . . . . . 1144--1149
N. Esper Tables of reductions of symmetrized
inner products (`inner plethysms') of
ordinary irreducible representations of
symmetric groups . . . . . . . . . . . . 1150--1151
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 1152--1165
E. I. Book Review: Alston S. Householder.
\booktitlePrinciples of Numerical
Analysis, Dover, New York, 1974, x + 274
pp., 21 cm. Price \$4.00 (paperbound)} 1152--1165
Anonymous Table Errata . . . . . . . . . . . . . . 1166
Richard P. Brent Table errata: \booktitleAlgorithms for
minimization without derivatives
(Prentice-Hall, Englewood Cliffs, N.J.,
1973) . . . . . . . . . . . . . . . . . 1166
Daniel Shanks Corrigenda: \booktitleCalculation and
applications of Epstein zeta functions
(Math. Comp. \bf 29 (1975), 271--287) 1167
Anonymous Corrigenda . . . . . . . . . . . . . . . 1167--1167
J. N. Lyness An error functional expansion for
$N$-dimensional quadrature with an
integrand function singular at a point 1--23
David L. Barrow Existence of Gauss interpolation
formulas for the one-dimensional heat
equation . . . . . . . . . . . . . . . . 24--34
S. Ellacott and
Jack Williams Linear Chebyshev approximation in the
complex plane using Lawson's algorithm 35--44
Charles B. Dunham Rational approximation with a vanishing
weight function and with a fixed value
at zero . . . . . . . . . . . . . . . . 45--47
Don R. Wilhelmsen A nearest point algorithm for convex
polyhedral cones and applications to
positive linear approximation . . . . . 48--57
D. H. Thomas Pseudospline Interpolation for Space
Curves . . . . . . . . . . . . . . . . . 58--67
V. Girault Nonelliptic approximation of a class of
partial differential equations with
Neumann boundary condition . . . . . . . 68--91
Robert S. Stepleman Tridiagonal fourth order approximations
to general two-point nonlinear boundary
value problems with mixed boundary
conditions . . . . . . . . . . . . . . . 92--103
Werner C. Rheinboldt On Measures of Ill-Conditioning for
Nonlinear Equations . . . . . . . . . . 104--111
L. B. Rall A quadratically convergent iteration
method for computing zeros of operators
satisfying autonomous differential
equations . . . . . . . . . . . . . . . 112--114
Larry Nazareth Generation of conjugate directions for
unconstrained minimization without
derivatives . . . . . . . . . . . . . . 115--131
Robert C. Ward The $ \mathrm {QR} $ Algorithm and
Hyman's Method on Vector Computers . . . 132--142
Alois Schett Properties of the Taylor series
expansion coefficients of the Jacobian
elliptic functions . . . . . . . . . . . 143--147
C. H. Yang Maximal Binary Matrices and Sum of Two
Squares . . . . . . . . . . . . . . . . 148--153
Michael Anshel Decision Problems for $ {HNN} $ Groups
and Vector Addition Systems . . . . . . 154--156
H. C. Williams and
J. S. Judd Determination of the primality of $N$ by
using factors of $ N^2 \pm 1$ . . . . . 157--172
Daniel Shanks Class groups of the quadratic fields
found by F. Diaz y Diaz . . . . . . . . 173--178
Jacob T. B. Beard, Jr. and
Karen I. West Factorization Tables for Trinomials Over
$ \mathrm {GF}(q) $ . . . . . . . . . . 179--183
I. O. Angell A Table of Totally Real Cubic Fields . . 184--187
Anonymous Corrigenda . . . . . . . . . . . . . . . 198--198
Paul T. Boggs and
J. E. Dennis, Jr. A stability analysis for perturbed
nonlinear iterative methods . . . . . . 199--215
Arthur David Snider Error Analysis for a Stiff System
Procedure . . . . . . . . . . . . . . . 216--219
Arthur David Snider Numerical applications of reflection to
partial differential equations . . . . . 220--240
Richard S. Falk An analysis of the finite element method
using Lagrange multipliers for the
stationary Stokes equations . . . . . . 241--249
J. J. Blair Higher order approximations to the
boundary conditions for the finite
element method . . . . . . . . . . . . . 250--262
J. Kadlec On the evaluation of some integrals
occurring in scattering problems . . . . 263--277
G. W. Reddien Finite-Difference Approximations to
Singular Sturm--Liouville Eigenvalue
Problems . . . . . . . . . . . . . . . . 278--282
Lawrence F. Wiederholt Stability of multistep methods for delay
differential equations . . . . . . . . . 283--290
A. H. Stroud Some fourth degree integration formulas
for simplexes . . . . . . . . . . . . . 291--294
Herbert E. Salzer Converting interpolation series into
Chebyshev series by recurrence formulas 295--302
R. G. Buschman Inequalities for Hypergeometric
Functions . . . . . . . . . . . . . . . 303--305
Michael Willett Characteristic $m$-Sequences . . . . . . 306--311
Pierre Barrucand and
H. C. Williams and
L. Baniuk A computational technique for
determining the class number of a pure
cubic field . . . . . . . . . . . . . . 312--323
Paul S. Wang Factoring multivariate polynomials over
algebraic number fields . . . . . . . . 324--336
Lowell Schoenfeld Sharper bounds for the Chebyshev
functions $ \theta (x) $ and $ \psi (x)
$. II . . . . . . . . . . . . . . . . . 337--360
Gerhard Rosenberger The Uniqueness of the Markoff Numbers 361--365
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 371--380
Harald Niederreiter and
Charles F. Osgood A uniform distribution question related
to numerical analysis . . . . . . . . . 366--370
David R. Hill Table errata: ``On comparing Adams and
natural spline multistep formulas''
(Math. Comp. \bf 29 (1975), 741--745) 381--381
D. Shanks Table errata: ``Regular continued
fractions for $ \pi $ and $ \gamma $'',
(Math. Comp. 25 (1971), 403); ``Rational
approximations to $ \pi $'' (ibid. 25
(1971), 387--392) by K. Y. Choong, D. E.
Daykin and C. R. Rathbone . . . . . . . 381--381
Anonymous Table Errata . . . . . . . . . . . . . . 381--381
W. L. Miranker and
G. Wahba An averaging method for the stiff highly
oscillatory problem . . . . . . . . . . 383--399
M. S. Mock Projection methods with different trial
and test spaces . . . . . . . . . . . . 400--416
G. K. Gupta Some new high-order multistep formulae
for solving stiff equations . . . . . . 417--432
W\lodzimierz Proskurowski and
Olof Widlund On the numerical solution of Helmholtz's
equation by the capacitance matrix
method . . . . . . . . . . . . . . . . . 433--468
J. K. Shaw and
L. W. Johnson and
R. D. Riess Accelerating Convergence of
Eigenfunction Expansions . . . . . . . . 469--477
Michael J. Best and
Klaus Ritter A Class of Accelerated Conjugate
Direction Methods for Linearly
Constrained Minimization Problems . . . 478--504
R. F. Streit The $ T^{+m} $ transformation . . . . . 503--511
Roland F. Streit The $ {T}_{+m} $ Transformation . . . . 505--511
Paul T. Boggs The convergence of the Ben-Israel
iteration for nonlinear least squares
problems . . . . . . . . . . . . . . . . 512--522
J. J. More and
J. A. Trangenstein On the global convergence of Broyden's
method . . . . . . . . . . . . . . . . . 523--540
Henry E. Fettis Complex Roots of $ \sin z = a z, \cos z
= a z $, and $ \cosh z = a z $ . . . . . 541--545
S. K. Zaremba On Cartesian Products of Good Lattices 546--552
M. E. Cohen Extensions of the Mehler--Weisner and
Other Results for the Hermite Function 553--564
Eugene Salamin Computation of $ \pi $ Using
Arithmetic-Geometric Mean . . . . . . . 565--570
Harald Niederreiter On the distribution of pseudo-random
numbers generated by the linear
congruential method. III . . . . . . . . 571--597
Ray Steiner and
Ronald Rudman On an algorithm of Billevich for finding
units in algebraic number fields . . . . 598--609
Duncan A. Buell Class Groups of Quadratic Fields . . . . 610--623
John McKay The largest degrees of irreducible
characters of the symmetric group . . . 624--631
J. Alonso Groups of Square-Free Order, An
Algorithm . . . . . . . . . . . . . . . 632--637
Josef Blass A Note on Diophantine Equation $ {Y}^2 +
k = {X}^5 $ . . . . . . . . . . . . . . 638--640
P. Erd\Hos On Asymptotic Properties of Aliquot
Sequences . . . . . . . . . . . . . . . 641--645
Simcha Brudno Triples of Sixth Powers with Equal Sums 646--648
Richard H. Hudson Generalizations of a classical theorem
in number theory . . . . . . . . . . . . 649--656
Solomon W. Golomb Properties of the Sequence $ 3 \cdot 2^n
+ 1 $ . . . . . . . . . . . . . . . . . 657--663
Anonymous Corrigendum . . . . . . . . . . . . . . 679--679
Ridgway Scott Optimal $ {L}^\infty $ Estimates for the
Finite Element Method on Irregular
Meshes . . . . . . . . . . . . . . . . . 681--697
Richard S. Falk A Finite Element Method for the
Stationary Stokes Equations Using Trial
Functions which do not have to Satisfy $
\operatorname {div} \upsilon = 0 $ . . . 698--702
David Gottlieb and
Eli Turkel Dissipative Two-Four Methods for
Time-Dependent Problems . . . . . . . . 703--723
Joseph Oliger Hybrid difference methods for the
initial boundary-value problem for
hyperbolic equations . . . . . . . . . . 724--738
Rolf Jeltsch A Necessary Condition for $A$-Stability
of Multistep Multiderivative Methods . . 739--746
John M. Bownds On solving weakly singular Volterra
equations of the first kind with
Galerkin approximations . . . . . . . . 747--757
Ian H. Sloan Improvement by iteration for compact
operator equations . . . . . . . . . . . 758--764
Carl de Boor A bound on the $ L^\infty $-norm of $
L^2 $ --- approximation by splines in
terms of a global mesh ratio . . . . . . 765--771
J. W. Daniel and
W. B. Gragg and
L. Kaufman and
G. W. Stewart Reorthogonalization and Stable
Algorithms for Updating the
Gram--Schmidt QR Factorization . . . . . 772--795
Donald Goldfarb Factorized variable metric methods for
unconstrained optimization . . . . . . . 796--811
Giovanni Monegato A Note on Extended Gaussian Quadrature
Rules . . . . . . . . . . . . . . . . . 812--817
Ulrich Eckhardt A Rational Approximation to Weierstrass'
$ \wp $-Function . . . . . . . . . . . . 818--826
J. M. Blair and
C. A. Edwards and
J. H. Johnson Rational Chebyshev approximations for
the inverse of the error function . . . 827--830
Masashi Okamoto Asymptotic Normality in Monte Carlo
Integration . . . . . . . . . . . . . . 831--837
Morris Newman Asymptotic formulas related to free
products of cyclic groups . . . . . . . 838--846
Kenneth S. Williams Explicit Criteria for Quintic
Residuacity . . . . . . . . . . . . . . 847--853
Harvey Cohn Dyadotropic Polynomials . . . . . . . . 854--862
Robert Spira Zeros of Hurwitz Zeta Functions . . . . 863--866
H. C. Williams and
J. S. Judd Some Algorithms for Prime Testing Using
Generalized Lehmer Functions . . . . . . 867--886
H. C. Williams and
J. Broere A computational technique for evaluating
L(1, chi ) and the class number of a
real quadratic field . . . . . . . . . . 887--893
Anonymous Corrigenda . . . . . . . . . . . . . . . 900--900
Victor Pereyra and
Wlodzimierz Proskurowski and
Olof Widlund High order fast Laplace solvers for the
Dirichlet problem on general regions . . 1--16
Charles K. Chui and
Philip W. Smith and
Joseph D. Ward On the Smoothness of Best $ {L}_2 $
Approximants from Nonlinear Spline
Manifolds . . . . . . . . . . . . . . . 17--23
J. P. Hennart One-Step Piecewise Polynomial Multiple
Collocation Methods for Initial Value
Problems . . . . . . . . . . . . . . . . 24--36
J. M. Varah On the condition number of local bases
for piecewise cubic polynomials . . . . 37--44
Garth A. Baker Finite element methods for elliptic
equations using nonconforming elements 45--59
Peter H. Sammon A Discrete Least Squares Method . . . . 60--65
Joseph E. Flaherty and
R. E. O'Malley, Jr. The numerical solution of boundary value
problems for stiff differential
equations . . . . . . . . . . . . . . . 66--93
J. H. Bramble and
A. H. Schatz Higher order local accuracy by averaging
in the finite element method . . . . . . 94--111
Arieh Iserles Functional Fitting --- New Family of
Schemes for Integration of Stiff O.D.E. 112--123
Rolf Jeltsch Multistep methods using higher
derivatives and damping at infinity . . 124--138
Jack W. Mosevich Identifying differential equations by
Galerkin's method . . . . . . . . . . . 139--147
J. A. Meijerink and
H. A. van der Vorst An Iterative Solution Method for Linear
Systems of Which the Coefficient Matrix
is a Symmetric $M$-Matrix . . . . . . . 148--162
James R. Bunch and
Linda Kaufman Some Stable Methods for Calculating
Inertia and Solving Symmetric Linear
Systems . . . . . . . . . . . . . . . . 163--179
Alan Feldstein and
J. F. Traub Asymptotic behavior of vector
recurrences with applications . . . . . 180--192
J. A. Ford A Generalization of the Jenkins--Traub
Method . . . . . . . . . . . . . . . . . 193--203
George Miel On a Posteriori Error Estimates . . . . 204--213
Stephen E. Derenzo Approximations for Hand Calculators
Using Small Integer Coefficients . . . . 214--222
F. G. Lether Subtracting out complex singularities in
numerical integration . . . . . . . . . 223--229
Herbert E. Salzer Osculatory and Hyperosculatory Cubature
Formulas . . . . . . . . . . . . . . . . 230--234
Robert T. Moenck On the efficiency of algorithms for
polynomial factoring . . . . . . . . . . 235--250
D. P. McCarthy The optimal algorithm to evaluate $ x^n
$ using elementary multiplication
methods . . . . . . . . . . . . . . . . 251--256
R. P. Boas, Jr. Growth of Partial Sums of Divergent
Series . . . . . . . . . . . . . . . . . 257--264
I. O. Angell and
H. J. Godwin On Truncatable Primes . . . . . . . . . 265--267
T. Ojala Euclid's algorithm in the cyclotomic
field $ Q(\zeta^{16}) $ . . . . . . . . 268--273
Masao Kishore Odd perfect numbers not divisible by 3
are divisible by at least ten distinct
primes . . . . . . . . . . . . . . . . . 274--279
T. W. Cusick The Szekeres Multidimensional Continued
Fraction . . . . . . . . . . . . . . . . 280--317
F. L. Bauer Angstl's mechanism for checking
well-formedness of parenthesis-free
formulae . . . . . . . . . . . . . . . . 318--320
Henry C. Thacher Book Review: \booktitleApplied and
Computational Complex Analysis, by Peter
Henrici . . . . . . . . . . . . . . . . 325--326
Anonymous Corrigendum . . . . . . . . . . . . . . 330--330
Anonymous Acknowledgement . . . . . . . . . . . . 331--331
Achi Brandt Multi-Level Adaptive Solutions to
Boundary-Value Problems . . . . . . . . 333--390
P. A. Raviart and
J. M. Thomas Primal hybrid finite element methods for
2nd order elliptic equations . . . . . . 391--413
A. H. Schatz and
L. B. Wahlbin Interior maximum norm estimates for
finite element methods . . . . . . . . . 414--442
E. N. Houstis Application of method of collocation on
lines for solving nonlinear hyperbolic
problems . . . . . . . . . . . . . . . . 443--456
Frank Natterer Uniform convergence of Galerkin's method
for splines on highly nonuniform meshes 457--468
Moshe Goldberg On a boundary extrapolation theorem by
Kreiss . . . . . . . . . . . . . . . . . 469--477
Martin H. Gutknecht Existence of a solution to the discrete
Theodorsen equation for conformal
mappings . . . . . . . . . . . . . . . . 478--480
A. J. Jerri Computations of the Hill Functions of
Higher Order . . . . . . . . . . . . . . 481--484
Jackson N. Henry Comparison of algorithms for
multivariate rational approximation . . 485--494
David A. Field Estimates of the speed of convergence of
continued fraction expansions of
functions . . . . . . . . . . . . . . . 495--502
D. Dijkstra A continued fraction expansion for a
generalization of Dawson's integral . . 503--510
M. E. Cohen Some classes of generating functions for
the Laguerre and Hermite polynomials . . 511--518
Wells Johnson On congruences related to the first case
of Fermat's last theorem . . . . . . . . 519--526
John R. Durbin and
K. Bolling Farmer On projective representations of finite
wreath products . . . . . . . . . . . . 527--535
Wilhelm Plesken and
Michael Pohst On Maximal Finite Irreducible Subgroups
of $ {GL}(n, \mathbf {Z}) $: I. The Five
and Seven Dimensional Cases . . . . . . 536--551
Wilhelm Plesken and
Michael Pohst On Maximal Finite Irreducible Subgroups
of $ {GL}(n, \mathbf {Z}) $: II. The Six
Dimensional Case . . . . . . . . . . . . 552--573
Craig Cato The orders of the known simple groups as
far as one trillion . . . . . . . . . . 574--577
H. C. Williams Certain Pure Cubic Fields With
Class-Number One . . . . . . . . . . . . 578--580
F. T. Howard Numbers Generated by the Reciprocal of $
e^x - x - 1 $ . . . . . . . . . . . . . 581--598
D. H. Lehmer Prime Factors of Cyclotomic Class
Numbers . . . . . . . . . . . . . . . . 599--607
Peter Hagis, Jr. and
Graham Lord Quasi-Amicable Numbers . . . . . . . . . 608--611
Anonymous Corrigendum . . . . . . . . . . . . . . 617--617
Alan E. Berger and
Richard S. Falk An error estimate for the truncation
method for the solution of parabolic
obstacle variational inequalities . . . 619--628
Björn Engquist and
Andrew Majda Absorbing boundary conditions for the
numerical simulation of waves . . . . . 629--651
Vidar Thomee High order local approximations to
derivatives in the finite element method 652--660
Max D. Gunzburger On the stability of Galerkin methods for
initial-boundary value problems for
hyperbolic systems . . . . . . . . . . . 661--675
Frank R. de Hoog and
Richard Weiss The application of linear multistep
methods to singular initial value
problems . . . . . . . . . . . . . . . . 676--690
Alan Goldfine Taylor series methods for the solution
of Volterra integral and
integro-differential equations . . . . . 691--707
Hermann Brunner Discretization of Volterra integral
equations of the first kind . . . . . . 708--716
David F. McAllister and
Eli Passow and
John A. Roulier Algorithms for Computing Shape
Preserving Spline Interpolations to Data 717--725
Nai-fu Chen Inverse Iteration on Defective Matrices 726--732
W. D. Hoskins and
D. S. Meek The infinity norm of a certain type of
symmetric circulant matrix . . . . . . . 733--737
Avram Sidi Uniqueness of Padé approximants from
series of orthogonal polynomials . . . . 738--739
F. P. Preparata and
D. V. Sarwate Computational complexity of Fourier
transforms over finite fields . . . . . 740--751
Robert L. Pexton and
Arno D. Steiger Roots of two transcendental equations
involving spherical Bessel functions . . 752--753
Michael Pohst and
Hans Zassenhaus An effective number geometric method of
computing the fundamental units of an
algebraic number field . . . . . . . . . 754--770
Richard P. Brent Computation of the regular continued
fraction for Euler's constant . . . . . 771--777
H. C. Williams and
R. Holte Computation of the Solution of $ x^3 + D
y^3 = 1 $ . . . . . . . . . . . . . . . 778--785
Duncan A. Buell Small class numbers and extreme values
of $L$-functions of quadratic fields . . 786--796
G. Matthew and
H. C. Williams Some New Primes of the Form $ k \cdot
2^n + 1 $ . . . . . . . . . . . . . . . 797--798
Anonymous Corrigendum . . . . . . . . . . . . . . 808--808
F. Brezzi and
C. Johnson and
B. Mercier Analysis of a mixed finite element
method for elasto-plastic plates . . . . 809--817
Garth A. Baker and
James H. Bramble and
Vidar Thomee Single step Galerkin approximations for
parabolic problems . . . . . . . . . . . 818--847
A. Y. Le Roux A Numerical Conception of Entropy for
Quasi-Linear Equations . . . . . . . . . 848--872
Dennis C. Jespersen A least squares decomposition method for
solving elliptic equations . . . . . . . 873--880
A. G. Morris and
T. S. Horner Chebyshev polynomials in the numerical
solution of differential equations . . . 881--891
R. A. Nicolaides On the $ l^2 $ Convergence of an
Algorithm for Solving Finite Element
Equations . . . . . . . . . . . . . . . 892--906
Reinhard Frank and
Joerg Hertling and
Christoph W. Ueberhuber An extension of the applicability of
iterated deferred corrections . . . . . 907--915
Carl de Boor and
Blair Swartz Comments on the Comparison of Global
Methods for Linear Two-Point Boundary
Value Problems . . . . . . . . . . . . . 916--921
P. Alfeld and
J. D. Lambert Correction in the dominant space: a
numerical technique for a certain class
of stiff initial value problems . . . . 922--938
R. Sacks-Davis Error estimates for a stiff differential
equation procedure . . . . . . . . . . . 939--953
Ph. L. Toint On sparse and symmetric matrix updating
subject to a linear equation . . . . . . 954--961
David Gay Modifying singular values: existence of
solutions to systems of nonlinear
equations having a possibly singular
Jacobian matrix . . . . . . . . . . . . 962--973
Nabih N. Abdelmalek Computing the strict Chebyshev solution
of overdetermined linear equations . . . 974--983
David L. Barrow Gauss interpolation formulas and totally
positive kernels . . . . . . . . . . . . 984--993
Walter Gautschi Anomalous convergence of a continued
fraction for ratios of Kummer functions 994--999
Robert L. Pexton and
Arno D. Steiger Roots of two transcendental equations
determining the frequency spectra of
standing spherical electromagnetic waves 1000--1002
Alois Schett Recurrence formula of the Taylor series
expansion coefficients of the Jacobian
elliptic functions . . . . . . . . . . . 1003--1005
Joel Berman and
Kit Hanes Optimizing the arrangement of points on
the unit sphere . . . . . . . . . . . . 1006--1008
A. J. Kinderman and
J. F. Monahan and
J. G. Ramage Computer methods for sampling from
Student's $t$ distribution . . . . . . . 1009--1018
Charles J. Parry Real quadratic fields with class numbers
divisible by five . . . . . . . . . . . 1019--1029
Sol Weintraub Seventeen Primes in Arithmetic
Progression . . . . . . . . . . . . . . 1030--1030
F. W. Long Corrections to Dickson's table of three
dimensional division algebras over $ F_5
$ . . . . . . . . . . . . . . . . . . . 1031--1033
D. A. Buell and
H. C. Williams and
K. S. Williams On the Imaginary Bicyclic Biquadratic
Fields With Class-Number $2$ . . . . . . 1034--1042
Bryant Tuckerman Corrigendum . . . . . . . . . . . . . . 1051--1051
Simeon Ola. Fatunla An Implicit Two-Point Numerical
Integration Formula for Linear and
Nonlinear Stiff Systems of Ordinary
Differential Equations . . . . . . . . . 1--11
G. K. Gupta Implementing Second-Derivative Multistep
Methods Using the Nordsieck Polynomial
Representation . . . . . . . . . . . . . 13--18
Arieh Iserles $A$-Stability and Dominating Pairs . . . 19--33
Luis Kramarz Global Approximations to Solutions of
Initial Value Problems . . . . . . . . . 35--59
Alvin Bayliss A double shooting scheme for certain
unstable and singular boundary value
problems . . . . . . . . . . . . . . . . 61--71
A. H. Schatz and
L. B. Wahlbin Maximum Norm Estimates in the Finite
Element Method on Plane Polygonal
Domains. Part 1 . . . . . . . . . . . . 73--109
J. Thomas King and
Steven M. Serbin Computational experiments and techniques
for the penalty method with
extrapolation . . . . . . . . . . . . . 111--126
R. A. Nicolaides On the observed rate of convergence of
an iterative method applied to a model
elliptic difference equation . . . . . . 127--133
Lois Mansfield A Clough--Tocher type element useful for
fourth order problems over nonpolygonal
domains . . . . . . . . . . . . . . . . 135--142
Melvyn Ciment and
Stephen H. Leventhal A note on the operator compact implicit
method for the wave equation . . . . . . 143--147
Apostolos Hadjidimos Accelerated Overrelaxation Method . . . 149--157
E. N. Houstis and
T. S. Papatheodorou A collocation method for Fredholm
integral equations of the second kind 159--173
S. Winograd On Computing the Discrete Fourier
Transform . . . . . . . . . . . . . . . 175--199
John Greenstadt Revision of a Derivative-Free
Quasi-Newton Method . . . . . . . . . . 201--221
W. G. Dotson, Jr. An iterative process for nonlinear
monotonic nonexpansive operators in
Hilbert space . . . . . . . . . . . . . 223--225
Harold G. Diamond Stability of Rounded Off Inverses Under
Iteration . . . . . . . . . . . . . . . 227--232
Edwin H. Kaufman, Jr. and
David J. Leeming and
G. D. Taylor A Combined Remes-Differential Correction
Algorithm for Rational Approximation . . 233--242
Giovanni Monegato Positivity of the weights of extended
Gauss--Legendre quadrature rules . . . . 243--245
Giovanni Monegato Some remarks on the construction of
extended Gaussian quadrature rules . . . 247--252
William J. Gordon and
James A. Wixom Shepard's Method of ``Metric
Interpolation'' to Bivariate and
Multivariate Interpolation . . . . . . . 253--264
Paul W. Schmidt Evaluation of the Integral $
\int^\infty_0 \frac {t^{2 \alpha - 1}
J_\nu (x \sqrt {1 + t^2})}{(1 +
t^2)^{\alpha + \beta - 1}} d t $ . . . . 265--269
A. R. DiDonato An Approximation for $ \int^\infty_x
e^{-t^2 / 2} t^p d t, x > 0, p $ Real . . 271--275
Z. Drezner Computation of the Bivariate Normal
Integral . . . . . . . . . . . . . . . . 277--279
Carter Bays and
Richard H. Hudson On the Fluctuations of Littlewood for
Primes of the Form $ 4 n \pm 1 $ . . . . 281--286
Hans Zassenhaus A Remark on the Hensel Factorization
Method . . . . . . . . . . . . . . . . . 287--292
H. J. Godwin A Note on Congruent Numbers . . . . . . 293--295
Wells Johnson On the $p$-Divisibility of the Fermat
Quotients . . . . . . . . . . . . . . . 297--301
Masao Kishore Odd integers $N$ with five distinct
prime factors for which $ 2 - 10^{-12} <
\sigma (N) / N < 2 + 10^{-12}$ . . . . . 303--309
Olavi Nevanlinna On the convergence of difference
approximations to nonlinear contraction
semigroups in Hilbert spaces . . . . . . 321--334
Philippe G. Ciarlet Interpolation error estimates for the
reduced Hsieh--Clough--Tocher triangle 335--344
Jim Douglas, Jr. and
Todd Dupont and
Mary F. Wheeler A Quasi-Projection Analysis of Galerkin
Methods for Parabolic and Hyperbolic
Equations . . . . . . . . . . . . . . . 345--362
Amiram Harten The artificial compression method for
computation of shocks and contact
discontinuities. III. Self-adjusting
hybrid schemes . . . . . . . . . . . . . 363--389
Aurel Galantai The comparison of numerical methods for
solving polynomial equations . . . . . . 391--397
E. Rakotch Improved error estimates for numerical
solutions of symmetric integral
equations . . . . . . . . . . . . . . . 399--404
Daniel S. Watanabe Block Implicit One-Step Methods . . . . 405--414
J. Christiansen and
R. D. Russell Error analysis for spline collocation
methods with application to knot
selection . . . . . . . . . . . . . . . 415--419
W. Fraser and
J. M. Bennett A Method of Virtual Displacements for
the Degenerate Discrete $ l_1 $
Approximation Problem . . . . . . . . . 421--430
David L. Barrow On Multiple Node Gaussian Quadrature
Formulae . . . . . . . . . . . . . . . . 431--439
Alexandra Banegas Fast Poisson Solvers for Problems with
Sparsity . . . . . . . . . . . . . . . . 441--446
Binh Lam On the Convergence of a Quasi-Newton
Method for Sparse Nonlinear Systems . . 447--451
W. L. Miranker and
M. van Veldhuizen The Method of Envelopes . . . . . . . . 453--496
J. R. Cash An extension of Olver's method for the
numerical solution of linear recurrence
relations . . . . . . . . . . . . . . . 497--510
Robert L. Pexton and
Arno D. Steiger Roots of two transcendental equations as
functions of a continuous real parameter 511--518
V. Zakian and
M. J. Edwards Tabulation of constants for full grade $
I_{MN} $ approximants . . . . . . . . . 519--531
T. C. Benton and
H. D. Knoble Common Zeros of Two Bessel Functions . . 533--535
Theresa P. Vaughan A generalization of the simple continued
fraction algorithm . . . . . . . . . . . 537--558
H. Eisenbeis and
G. Frey and
B. Ommerborn Computation of the 2-Rank of Pure Cubic
Fields . . . . . . . . . . . . . . . . . 559--569
Carter Bays and
Richard H. Hudson Details of the first region of integers
$x$ with $ \pi_{3, 2}(x) < \pi_{3, 1}(x)$ 571--576
D. H. Lehmer and
J. M. Masley Table of the Cyclotomic Class Numbers $
h^\ast (p) $ and Their Factors for $ 200
< p < 521 $ . . . . . . . . . . . . . . . 577--582
Samuel S. Wagstaff, Jr. The Irregular Primes to $ 125000 $ . . . 583--591
Paul W. Bunting and
Jan van Leeuwen and
Dov Tamari Deciding associativity for partial
multiplication tables of order 3 . . . . 593--605
Louis Halle Rowen and
Uri Schild A scalar expression for matrices with
symplectic involution . . . . . . . . . 607--613
Michael Anshel Vector groups and the equality problem
for vector addition systems . . . . . . 614--616
R. Ernvall and
T. Metsänkylä Cyclotomic Invariants and $
{E}$-Irregular Primes . . . . . . . . . 617--629
J. Riddell and
C. Chan Some Extremal $2$-Bases . . . . . . . . 630--634
R. S. Stevens and
R. Shantaram Computer-Generated van der Waerden
Partitions . . . . . . . . . . . . . . . 635--636
F. Diaz y Diaz On Some Families of Imaginary Quadratic
Fields . . . . . . . . . . . . . . . . . 637--650
H. J. S. Book Review: Martin Gutknecht, Peter
Henrici, Peter Lauchli, and Hans-Rudolf
Schwarz, \booktitleHeinz Rutishauser:
Vorlesungen Uber Numerische Mathematik
Vols. 1 and 2 . . . . . . . . . . . . . 651--652
J. M. Blair and
C. A. Edwards and
J. H. Johnson Addendum: ``Rational Chebyshev
approximations for the Bickley functions
$ K i_n(x) $'' (Math. Comp. 32 (1978),
no. 143, 876--886) . . . . . . . . . . . Microfiche supplement
Milos Zlamal Superconvergence and reduced integration
in the finite element method . . . . . . 663--685
Ole H. Hald The Inverse Sturm--Liouville Problem and
the Rayleigh--Ritz Method . . . . . . . 687--705
Anne M. Burns A necessary condition for the stability
of a difference approximation to a
hyperbolic system of partial
differential equations . . . . . . . . . 707--724
A. E. Frey and
C. A. Hall and
T. A. Porsching Some results on the global inversion of
bilinear and quadratic isoparametric
finite element transformations . . . . . 725--749
John P. Coleman and
Julie Mohamed On de Vogelaere's Method for $ y'' =
f(x, y) $ . . . . . . . . . . . . . . . 751--762
P. W. Gaffney To Compute the Optimal Interpolation
Formula . . . . . . . . . . . . . . . . 763--777
James Lucien Howland The resultant iteration for determining
the stability of a polynomial . . . . . 779--789
Ole Hald and
Vincenza Mauceri del Prete Convergence of vortex methods for
Euler's equations . . . . . . . . . . . 791--809
W. F. Smyth The Construction of Rational Iterating
Functions . . . . . . . . . . . . . . . 811--827
Robert B. Schnabel Minimum norm symmetric quasi-Newton
updates restricted to subspaces . . . . 829--837
Ph. L. Toint Some Numerical Results Using a Sparse
Matrix Updating Formula in Unconstrained
Optimization . . . . . . . . . . . . . . 839--851
I. Barrodale and
L. M. Delves and
J. C. Mason Linear Chebyshev approximation of
complex-valued functions . . . . . . . . 853--863
Walter Gautschi and
Josef Slavik On the computation of modified Bessel
function ratios . . . . . . . . . . . . 865--875
J. M. Blair and
C. A. Edwards and
J. H. Johnson Rational Chebyshev approximations for
the Bickley functions $ K i_n(x) $ . . . 876--886
Shui Nee Chow and
John Mallet-Paret and
James A. Yorke Finding zeroes of maps: homotopy methods
that are constructive with probability
one . . . . . . . . . . . . . . . . . . 887--899
Chih Bing Ling Further Evaluation of Howland Integrals 900--904
H. C. Williams and
R. Holte Some Observations on Primality Testing 905--917
J. M. Pollard Monte Carlo Methods for Index
Computation $ (\bmod p) $ . . . . . . . 918--924
N. S. Jeans and
M. D. Hendy Determining the fundamental unit of a
pure cubic field given any unit . . . . 925--935
Charles M. Grinstead On a method of solving a class of
Diophantine equations . . . . . . . . . 936--940
D. E. Shippee Four New Factors of Fermat Numbers . . . 941--941
James H. Bramble and
Ridgway Scott Simultaneous approximation in scales of
Banach spaces . . . . . . . . . . . . . 947--954
H. B. Keller and
V. Pereyra Symbolic Generation of Finite Difference
Formulas . . . . . . . . . . . . . . . . 955--971
J. Giroire and
J. C. Nedelec Numerical Solution of an Exterior
Neumann Problem Using a Double Layer
Potential . . . . . . . . . . . . . . . 973--990
I. Babu\vska and
J. E. Osborn Numerical treatment of eigenvalue
problems for differential equations with
discontinuous coefficients . . . . . . . 991--1023
R. Bruce Kellogg and
Alice Tsan Analysis of some difference
approximations for a singular
perturbation problem without turning
points . . . . . . . . . . . . . . . . . 1025--1039
Andrew Majda and
James McDonough and
Stanley Osher The Fourier Method for Nonsmooth Initial
Data . . . . . . . . . . . . . . . . . . 1041--1081
R. A. Nicolaides On Multigrid Convergence in the
Indefinite Case . . . . . . . . . . . . 1082--1086
Riaz A. Usmani Discrete variable methods for a boundary
value problem with engineering
applications . . . . . . . . . . . . . . 1087--1096
Moshe Goldberg and
Eitan Tadmor Scheme-independent stability criteria
for difference approximations of
hyperbolic initial-boundary value
problems. I . . . . . . . . . . . . . . 1097--1107
Rolf Jeltsch Complete Characterization of Multistep
Methods with an Interval of Periodicity
for Solving $ y'' = f(x, y) $ . . . . . 1108--1114
L. F. Shampine Limiting precision in differential
equation solvers. II. Sources of trouble
and starting a code . . . . . . . . . . 1115--1122
D. L. Hicks Stability analysis of WONDY (a hydrocode
based on the artificial viscosity method
of von Neumann and Richtmyer) for a
special case of Maxwell's law . . . . . 1123--1130
D. L. Barrow and
C. K. Chui and
P. W. Smith and
J. D. Ward Unicity of best mean approximation by
second order splines with variable knots 1131--1143
C. J. O'Neill and
T. Downs A numerical accuracy consideration in
polynomial deflation . . . . . . . . . . 1144--1146
Baker Kearfott A Proof of Convergence and an Error
Bound for the Method of Bisection in $
{\bf R}^n $ . . . . . . . . . . . . . . 1147--1153
David F. McAllister and
John A. Roulier Interpolation by Convex Quadratic
Splines . . . . . . . . . . . . . . . . 1154--1162
R. C. Y. Chin and
G. W. Hedstrom A dispersion analysis for difference
schemes: tables of generalized Airy
functions . . . . . . . . . . . . . . . 1163--1170
Paul W. Schmidt An asymptotic approximation for a type
of Fourier integral . . . . . . . . . . 1171--1182
H. Wolkowicz and
S. Zlobec Calculating the best approximate
solution of an operator equation . . . . 1183--1213
Paul S. Wang An improved multivariate polynomial
factoring algorithm . . . . . . . . . . 1215--1231
J. L. Schonfelder Chebyshev expansions for the error and
related functions . . . . . . . . . . . 1232--1240
Hansraj Gupta Finite Differences of the Partition
Function . . . . . . . . . . . . . . . . 1241--1243
David W. Boyd Pisot and Salem numbers in intervals of
the real line . . . . . . . . . . . . . 1244--1260
Charles J. Parry On the Class Number of Relative
Quadratic Fields . . . . . . . . . . . . 1261--1270
Lajos Takács A Sum of Binomial Coefficients . . . . . 1271--1273
W. W. Stothers Free Subgroups of the Free Product of
Cyclic Groups . . . . . . . . . . . . . 1274--1280
R. E. Crandall On the ``$ 3 x + 1 $'' Problem . . . . . 1281--1292
J. Fischer and
J. McKay The Nonabelian Simple Groups $ {G},
|{G}| < 10^6 $ --- Maximal Subgroups . . 1293--1302
J. H. McCabe A Further Correspondence Property of $
{M} $ Fractions . . . . . . . . . . . . 1303--1305
H. C. Williams Some Primes with Interesting Digit
Patterns . . . . . . . . . . . . . . . . 1306--1310
P. L. Walker On an Integral Summable to $ 2 \xi (s) /
s(s - 1) $ . . . . . . . . . . . . . . . 1311--1316
Rolf Jeltsch and
Daniel Shanks Corrigenda: Microfiche (January 1977)
and \em Gauss's Ternary Form Reduction
and the $2$-Sylow Subgroup . . . . . . . 1328--1329
Max D. Gunzburger and
Robert J. Plemmons Energy-conserving norms for the solution
of hyperbolic systems of partial
differential equations . . . . . . . . . 1--10
Gunilla Sköllermo Error analysis of finite difference
schemes applied to hyperbolic
initial-boundary value problems . . . . 11--35
Vidar Thomée Some interior estimates for semidiscrete
Galerkin approximations for parabolic
equations . . . . . . . . . . . . . . . 37--62
William G. Kolata Eigenvalue approximation by the finite
element method: the method of Lagrange
multipliers . . . . . . . . . . . . . . 63--76
Julio César Díaz A collocation-Galerkin method for
Poisson's equation on rectangular
regions . . . . . . . . . . . . . . . . 77--84
Frank Stenger A ``sinc-Galerkin'' method of solution
of boundary value problems . . . . . . . 85--109
Peter Alfeld Inverse linear multistep methods for the
numerical solution of initial value
problems of ordinary differential
equations . . . . . . . . . . . . . . . 111--124
G. K. Gupta and
C. S. Wallace A new step-size changing technique for
multistep methods . . . . . . . . . . . 125--138
Darrell Schmidt and
Kenneth L. Wiggins Minimax approximate solutions of linear
boundary value problems . . . . . . . . 139--148
Jane Cullum The effective choice of the smoothing
norm in regularization . . . . . . . . . 149--170
C. C. Paige Computer Solution and Perturbation
Analysis of Generalized Linear Least
Squares Problems . . . . . . . . . . . . 171--183
Paul N. Swarztrauber A Parallel Algorithm for Solving General
Tridiagonal Equations . . . . . . . . . 185--199
John L. Donaldson Minkowski reduction of integral matrices 201--216
B. N. Parlett and
D. S. Scott The Lánczos Algorithm with Selective
Orthogonalization . . . . . . . . . . . 217--238
D. S. Scott How to Make the Lánczos Algorithm
Converge Slowly . . . . . . . . . . . . 239--247
J. N. Lyness A Bench Mark Experiment for Minimization
Algorithms . . . . . . . . . . . . . . . 249--264
J. N. Lyness The affine scale invariance of
minimization algorithms . . . . . . . . 265--287
Ronald D. Armstrong and
James P. Godfrey Two Linear Programming Algorithms for
the Linear Discrete $ L_+1 $ Norm
Problem . . . . . . . . . . . . . . . . 289--300
David Elliott and
D. F. Paget Gauss type quadrature rules for Cauchy
principal value integrals . . . . . . . 301--309
Stuart R. Keller On the Surface Area of the Ellipsoid . . 310--314
Avram Sidi Convergence properties of some nonlinear
sequence transformations . . . . . . . . 315--326
Siegfried M. Rump Polynomial Minimum Root Separation . . . 327--336
J. R. Philip Note on the Kelvin Phase Functions . . . 337--341
Walter Gautschi The Condition of Polynomials in Power
Form . . . . . . . . . . . . . . . . . . 343--352
N. L. Balazs and
H. C. Pauli and
O. B. Dabbousi Tables of Weyl fractional integrals for
the Airy function . . . . . . . . . . . 353--358
Harvey Cohn Dyadotropic Polynomials. II . . . . . . 359--367
H. C. Williams and
P. A. Buhr Calculation of the Regulator of $
{Q}(\sqrt {D}) $ by use of the Nearest
Integer Continued Fraction Algorithm . . 369--381
R. E. Crandall and
M. A. Penk A Search for Large Twin Prime Pairs . . 383--388
Vincent G. Cioffari The Euclidean condition in pure cubic
and complex quartic fields . . . . . . . 389--398
Carl Pomerance The Prime Number Graph . . . . . . . . . 399--408
Shoji Kyuno An Inductive Algorithm to Construct
Finite Lattices . . . . . . . . . . . . 409--421
S. Conde and
S. L. Kalla The $ \nu $-zeros of $ {J}_{- \nu }(x)$ 423--426
David M. Gay Corrigenda: ``Modifying singular values:
existence of solutions to systems of
nonlinear equations having a possibly
singular Jacobian matrix'' (Math. Comp.
\bf 31 (1977), no. 140, 962--973) . . . 432--433
Reijo Ernvall Corrigenda: ``Cyclotomic invariants and
$E$-irregular primes'' (Math. Comp. 32
(1978), no. 142, 617--629) by Ernvall
and T. Metsänkylä . . . . . . . . . . . . 433--433
I. Babu\vska and
W. C. Rheinboldt Analysis of Optimal Finite-Element
Meshes in $ {R}^1 $ . . . . . . . . . . 435--463
A. H. Schatz and
L. B. Wahlbin Maximum Norm Estimates in the Finite
Element Method on Plane Polygonal
Domains. Part 2, Refinements . . . . . . 465--492
Mitchell Luskin Convergence of a finite element method
for the approximation of normal modes of
the oceans . . . . . . . . . . . . . . . 493--519
Trond Steihaug and
Arne Wolfbrandt An attempt to avoid exact Jacobian and
nonlinear equations in the numerical
solution of stiff differential equations 521--534
Peter Alfeld An improved version of the reduction to
scalar CDS method for the numerical
solution of separably stiff initial
value problems . . . . . . . . . . . . . 535--539
G. J. Cooper and
A. Sayfy Semiexplicit $A$-Stable Runge--Kutta
Methods . . . . . . . . . . . . . . . . 541--556
J. M. Varah On the efficient implementation of
implicit Runge--Kutta methods . . . . . 557--561
Vassilios A. Dougalis Multistep-Galerkin methods for
hyperbolic equations . . . . . . . . . . 563--584
Michael Ghil and
Ramesh Balgovind A Fast Cauchy--Riemann Solver . . . . . 585--635
R. Leonard Brown Stability of sequences generated by
nonlinear differential systems . . . . . 637--645
R. C. Y. Chin and
G. W. Hedstrom and
K. E. Karlsson A simplified Galerkin method for
hyperbolic equations . . . . . . . . . . 647--658
U. Ascher and
J. Christiansen and
R. D. Russell A collocation solver for mixed order
systems of boundary value problems . . . 659--679
Axel Ruhe Implementation Aspects of Band Lánczos
Algorithms for Computation of
Eigenvalues of Large Sparse Symmetric
Matrices . . . . . . . . . . . . . . . . 680--687
C. H. Yang Hadamard matrices, finite sequences, and
polynomials defined on the unit circle 688--693
Sven-Åke Gustafson On Stable Calculation of Linear
Functionals . . . . . . . . . . . . . . 694--704
Charles J. Gladwin Quadrature rule methods for Volterra
integral equations of the first kind . . 705--716
Martin Stynes On faster convergence of the bisection
method for certain triangles . . . . . . 717--721
Krzysztof Sikorski A three-dimensional analogue to the
method of bisections for solving
nonlinear equations . . . . . . . . . . 722--738
James L. Blue A Legendre Polynomial Integral . . . . . 739--741
Walter Gautschi On the preceding paper ``A Legendre
polynomial integral'' by James L. Blue 742--743
Henry C. Thacher, Jr. New Backward Recurrences for Bessel
Functions . . . . . . . . . . . . . . . 744--764
A. G. Petschek and
R. E. Williamson and
W. J. Krauser and
P. C. White Monte Carlo functional expansion
calculation of free molecular flows . . 765--777
Robert Morris The Dilogarithm Function of a Real
Argument . . . . . . . . . . . . . . . . 778--787
John Detrich and
Robert W. Conn Finite sum evaluation of the Gauss
hypergeometric function in an important
special case . . . . . . . . . . . . . . 788--791
M. L. Glasser A Note on the Integral $ \int^\infty_0
t^{2 \alpha - 1}(1 + t^2)^{1 - \alpha -
\beta } {J}_\nu (x \sqrt {1 + t^2}) d t
$ . . . . . . . . . . . . . . . . . . . 792--793
Ch. A. Charalambides Bernoulli related polynomials and
numbers . . . . . . . . . . . . . . . . 794--804
P. Lambin and
J. P. Vigneron Tables for the Gaussian Computation of $
\int^\infty_0 x^\alpha e^{-x}f(x) d x $
for Values of $ \alpha $ Varying
Continuously Between $ - 1 $ and $ + 1 $ 805--811
John McKay and
Kiang Chuen Young The Nonabelian Simple Groups $ {G} $, $
{|G|} < 10^6$---Minimal Generating Pairs 812--814
J. S. Frame The Hankel power sum matrix inverse and
the Bernoulli continued fraction . . . . 815--826
Ronald J. Evans and
Jay Roderick Hill The Cyclotomic Numbers of Order Sixteen 827--835
F. Diaz y Diaz and
Daniel Shanks and
H. C. Williams Quadratic Fields With $3$-Rank Equal to
$4$ . . . . . . . . . . . . . . . . . . 836--840
H. G. Kopetzky and
W. Schwarz Two conjectures of B. R. Santos
concerning totitives . . . . . . . . . . 841--844
H. J. Godwin Corrigenda: ``A note on congruent
numbers'' (Math. Comp. \bf 32 (1978),
no. 141, 293--295) . . . . . . . . . . . 847--847
C. M. Lee and
F. D. K. Roberts Corrigenda: ``A comparison of algorithms
for rational $ l_{\infty } $
approximation'' (Math. Comp. 27 (1973),
111--121) . . . . . . . . . . . . . . . 847--847
H. C. Williams Errata: ``Certain pure cubic fields with
class-number one'' [Math. Comp. \bf 31
(1977), no. 138, 578--580, MR \bf 55
#5578] . . . . . . . . . . . . . . . . . 847--848
Dianne P. O'Leary and
Olof Widlund Capacitance matrix methods for the
Helmholtz equation on general
three-dimensional regions . . . . . . . 849--879
Louis W. Ehrlich A Marching Technique for Nonseparable
Equations . . . . . . . . . . . . . . . 881--890
P. Lesaint and
P. A. Raviart Finite element collocation methods for
first-order systems . . . . . . . . . . 891--918
Marie-Noëlle Le Roux Semidiscretization in Time for Parabolic
Problems . . . . . . . . . . . . . . . . 919--931
R. A. Nicolaides On some theoretical and practical
aspects of multigrid methods . . . . . . 933--952
Sukumar Chakravarthy and
Dale Anderson Numerical Conformal Mapping . . . . . . 953--969
T. D. Bui A Note on the Rosenbrock Procedure . . . 971--975
David G. Korn and
Jules J. Lambiotte, Jr. Computing the Fast Fourier Transform on
a vector computer . . . . . . . . . . . 977--992
G. Monegato and
J. N. Lyness On the numerical evaluation of a
particular singular two-dimensional
integral . . . . . . . . . . . . . . . . 993--1002
Elise de Doncker New Euler--Maclaurin expansions and
their application to quadrature over the
$s$-dimensional simplex . . . . . . . . 1003--1018
Roland Kusterer and
Manfred Reimer Stable Evaluation of Polynomials in Time
$ \log n $ . . . . . . . . . . . . . . . 1019--1031
Stanley E. Babb, Jr. and
James W. Cafky Operational evaluation of certain
infinite Bessel function integrals . . . 1033--1039
Robert L. Pexton and
Arno D. Steiger Degenerate roots of three transcendental
equations involving spherical Bessel
functions . . . . . . . . . . . . . . . 1041--1048
Bruno Gabutti On high precision methods for computing
integrals involving Bessel functions . . 1049--1057
Henry E. Fettis An asymptotic expansion for the upper
percentage points of the $
\chi^2$-distribution . . . . . . . . . . 1059--1064
John F. Monahan Extensions of von Neumann's method for
generating random variables . . . . . . 1065--1069
Dan Zwillinger A Goldbach Conjecture Using Twin Primes 1071--1071
Samuel S. Wagstaff, Jr. Greatest of the least primes in
arithmetic progressions having a given
modulus . . . . . . . . . . . . . . . . 1073--1080
J. C. Lagarias and
A. M. Odlyzko On computing Artin $ {L}$-functions in
the critical strip . . . . . . . . . . . 1081--1095
Samuel S. Wagstaff, Jr. Solution of Nathanson's exponential
congruence . . . . . . . . . . . . . . . 1097--1100
Brendan D. McKay Transitive Graphs With Fewer Than Twenty
Vertices . . . . . . . . . . . . . . . . 1101--1121
Richard E. Ewing and
Richard S. Falk Numerical approximation of a Cauchy
problem for a parabolic partial
differential equation . . . . . . . . . 1125--1144
Saul Abarbanel and
David Gottlieb Stability of two-dimensional initial
boundary value problems using leap-frog
type schemes . . . . . . . . . . . . . . 1145--1155
Tsutomu Ikeda and
Tomoyasu Nakagawa On the SHASTA FCT Algorithm for the
Equation $ \frac {\partial \rho }
{\partial t} + \frac {\partial
}{\partial x}(\upsilon (\rho) \rho) = 0
$ . . . . . . . . . . . . . . . . . . . 1157--1169
David Hoff A finite difference scheme for a system
of two conservation laws with artificial
viscosity . . . . . . . . . . . . . . . 1171--1193
Peter Alfeld A special class of explicit linear
multistep methods as basic methods for
the correction in the dominant space
technique . . . . . . . . . . . . . . . 1195--1212
Wolf-Jürgen Beyn The exact order of convergence for
finite difference approximations to
ordinary boundary value problems . . . . 1213--1228
Robert D. Skeel Equivalent Forms of Multistep Formulas 1229--1250
G. K. Gupta A polynomial representation of hybrid
methods for solving ordinary
differential equations . . . . . . . . . 1251--1256
R. S. Stepleman and
N. D. Winarsky Adaptive Numerical Differentiation . . . 1257--1264
Fred T. Krogh Recurrence relations for computing with
modified divided differences . . . . . . 1265--1271
Steven Pruess Alternatives to the Exponential Spline
in Tension . . . . . . . . . . . . . . . 1273--1281
Stephen Demko On Bounding $ \| A^{-1} \|_\infty $ for
Banded $A$ . . . . . . . . . . . . . . . 1283--1288
Dianne P. O'Leary and
G. W. Stewart and
James S. Vandergraft Estimating the Largest Eigenvalue of a
Positive Definite Matrix . . . . . . . . 1289--1292
Dominique Dumont A combinatorial interpretation for the
Schett recurrence on the Jacobian
elliptic functions . . . . . . . . . . . 1293--1297
K. V. Leung and
S. S. Ghaderpanah An application of the finite element
approximation method to find the complex
zeros of the modified Bessel function $
{K}_n(z) $ . . . . . . . . . . . . . . . 1299--1306
Harvey Cohn Cyclic-Sixteen Class Fields for $ {Q}( -
p)^{1 / 2} $ by Modular Arithmetic . . . 1307--1316
H. C. Williams and
Daniel Shanks A Note on Class-Number One in Pure Cubic
Fields . . . . . . . . . . . . . . . . . 1317--1320
William W. Adams On a relationship between the
convergents of the nearest integer and
regular continued fractions . . . . . . 1321--1331
Robert Baillie New Primes of the Form $ k \cdot 2^n + 1
$ . . . . . . . . . . . . . . . . . . . 1333--1336
H. C. Williams and
E. Seah Some Primes of the Form $ (a^n - 1) / (a
- 1) $ . . . . . . . . . . . . . . . . . 1337--1342
Emil Grosswald and
Peter Hagis, Jr. Arithmetic Progressions Consisting Only
of Primes . . . . . . . . . . . . . . . 1343--1352
Joseph L. Gerver and
L. Thomas Ramsey Sets of Integers With No Long Arithmetic
Progressions Generated by the Greedy
Algorithm . . . . . . . . . . . . . . . 1353--1359
Richard P. Brent On the zeros of the Riemann zeta
function in the critical strip . . . . . 1361--1372
W. A. Beyer and
W. W. Wood Corrigenda: ``The lattice structure of
multiplicative congruential
pseudo-random vectors'' [Math. Comp. \bf
25 (1971), 345--363, MR \bf 46 #8373] by
W. A. Beyer, R. B. Roof, and Dorothy
Williamson . . . . . . . . . . . . . . . 445--446