Last update:
Tue Jan 2 07:16:42 MST 2024
Michael G. Crandall and
Andrew Majda Monotone difference approximations for
scalar conservation laws . . . . . . . . 1--21
Ragnar Winther A conservative finite element method for
the Korteweg--de Vries equation . . . . 23--43
Björn Engquist and
Stanley Osher Stable and entropy satisfying
approximations for transonic flow
calculations . . . . . . . . . . . . . . 45--75
Alfred H. Schatz A weak discrete maximum principle and
stability of the finite element method
in $ {L}_{\infty } $ on plane polygonal
domains. I . . . . . . . . . . . . . . . 77--91
Vidar Thomée Negative norm estimates and
superconvergence in Galerkin methods for
parabolic problems . . . . . . . . . . . 93--113
Ragnar Winther Initial Value Methods for Parabolic
Control Problems . . . . . . . . . . . . 115--125
Seymour V. Parter On the roles of ``stability'' and
``convergence'' in semidiscrete
projection methods for initial-value
problems . . . . . . . . . . . . . . . . 127--154
Arthur G. Werschulz Computational complexity of one-step
methods for systems of differential
equations . . . . . . . . . . . . . . . 155--174
B. A. Troesch The Shooting Method Applied to a Cyclic
Inequality . . . . . . . . . . . . . . . 175--184
George J. Miel Majorizing sequences and error bounds
for iterative methods . . . . . . . . . 185--202
John W. Evans and
William B. Gragg and
Randall J. LeVeque On least squares exponential sum
approximation with positive coefficients 203--211
J. N. Lyness and
G. Monegato Quadrature error functional expansions
for the simplex when the integrand
function has singularities at vertices 213--225
Bradley W. Dickinson Solution of linear equations with
rational Toeplitz matrices . . . . . . . 227--233
George Marsaglia Generating Random Variables With a
$t$-Distribution . . . . . . . . . . . . 235--236
J. L. Schonfelder Very high accuracy Chebyshev expansions
for the basic trigonometric functions 237--244
Wilhelm Plesken and
Michael Pohst On Maximal Finite Irreducible Subgroups
of $ {GL}(n, \mathbf {Z}) $: III. The
Nine Dimensional Case . . . . . . . . . 245--258
Wilhelm Plesken and
Michael Pohst On Maximal Finite Irreducible Subgroups
of $ {GL}(n, \mathbf {Z}) $: IV. Remarks
on Even Dimensions with Applications to
$ n = 8 $ . . . . . . . . . . . . . . . 259--275
Wilhelm Plesken and
Michael Pohst On Maximal Finite Irreducible Subgroups
of $ {GL}(n, \mathbf {Z}) $: V. The
Eight Dimensional Case and a Complete
Description of Dimensions Less Than Ten 277--301
Mark Templer On the Primality of $ k! + 1 $ and $ 2
\ast 3 \ast 5 \ast \cdots \ast p + 1 $ 303--304
Richard P. Brent and
Edwin M. McMillan Some new algorithms for high-precision
computation of Euler's constant . . . . 305--312
D. W. MacLean Residue Classes of the Partition
Function . . . . . . . . . . . . . . . . 313--317
Richard K. Guy and
J. L. Selfridge Corrigendum to: ``What drives an aliquot
sequence?'' [Math. Comp. \bf 29 (1975),
101--107, MR \bf 52 #5542] . . . . . . . 319--321
Herbert E. Salzer Misstatements in Milne-Thomson, Calculus
of Finite Differences, Macmillan,
London, 1933 . . . . . . . . . . . . . . 323--324
J. W. Corrigendum . . . . . . . . . . . . . . 332--332
Robert E. Lynch and
John R. Rice A high-order difference method for
differential equations . . . . . . . . . 333--372
Simeon Ola Fatunla Numerical integrators for stiff and
highly oscillatory differential
equations . . . . . . . . . . . . . . . 373--390
Lasse K. Karlsen Computation of steady shocks by
second-order finite-difference schemes 391--400
Garth A. Baker and
Vassilios A. Dougalis On the $ {L}^{\infty }$-convergence of
Galerkin approximations for second-order
hyperbolic equations . . . . . . . . . . 401--424
Wolfgang Hackbusch Convergence of multi-grid iterations
applied to difference equations . . . . 425--440
Todd Dupont and
Ridgway Scott Polynomial approximation of functions in
Sobolev spaces . . . . . . . . . . . . . 441--463
C. C. Paige Error Analysis of Some Techniques for
Updating Orthogonal Decompositions . . . 465--471
T. A. Manteuffel An Incomplete Factorization Technique
for Positive Definite Linear Systems . . 473--497
D. F. Shanno On variable-metric methods for sparse
Hessians . . . . . . . . . . . . . . . . 499--514
A. N. Stokes A Stable Quotient-Difference Algorithm 515--519
J. T. Marti On the convergence of an algorithm
computing minimum-norm solutions of
ill-posed problems . . . . . . . . . . . 521--527
Richard I. Shrager and
Edward Hill, Jr. Nonlinear curve-fitting in the $ {L}_1 $
and $ {L}_{\infty } $ norms . . . . . . 529--541
Daniel Minoli Inductive Formulae for General Sum
Operations . . . . . . . . . . . . . . . 543--545
Bruce W. Char On Stieltjes' continued fraction for the
gamma function . . . . . . . . . . . . . 547--551
Arne Fransén and
Staffan Wrigge High-precision values of the gamma
function and of some related
coefficients . . . . . . . . . . . . . . 553--566
H. C. Williams and
G. Cormack and
E. Seah Calculation of the Regulator of a Pure
Cubic Field . . . . . . . . . . . . . . 567--611
Rodney James The Groups of Order $ p^6 $ ($p$ an Odd
Prime) . . . . . . . . . . . . . . . . . 613--637
Daniel Minoli Issues in Nonlinear Hyperperfect Numbers 639--645
Samuel S. Wagstaff, Jr. $p$-divisibility of certain sets of
Bernoulli numbers . . . . . . . . . . . 647--649
Anonymous Corrigenda . . . . . . . . . . . . . . . 652--652
James H. Bramble and
Peter H. Sammon Efficient Higher Order Single Step
Methods for Parabolic Problems: Part I 655--677
Carl de Boor and
Blair Swartz Collocation approximation to eigenvalues
of an ordinary differential equation:
the principle of the thing . . . . . . . 679--694
Alan E. Berger and
Jay M. Solomon and
Melvyn Ciment and
Stephen H. Leventhal and
Bernard C. Weinberg Generalized OCI schemes for boundary
layer problems . . . . . . . . . . . . . 695--731
Blair Swartz Compact, implicit difference schemes for
a differential equation's side
conditions . . . . . . . . . . . . . . . 733--746
L. R. Lundin A cardinal function method of solution
of the equation $ {\Delta } u = u - u^3
$ . . . . . . . . . . . . . . . . . . . 747--756
David P. Maher Existence theorems for transforms over
finite rings with applications to 2-D
convolution . . . . . . . . . . . . . . 757--765
J. R. Cash A note on Olver's algorithm for the
solution of second-order linear
difference equations . . . . . . . . . . 767--772
Jorge Nocedal Updating Quasi-Newton Matrices with
Limited Storage . . . . . . . . . . . . 773--782
Athena Makroglou Convergence of a block-by-block method
for nonlinear Volterra
integro-differential equations . . . . . 783--796
D. Meek A Mean Value Theorem for Linear
Functionals . . . . . . . . . . . . . . 797--802
F. M. Larkin Root-Finding by Fitting Rational
Functions . . . . . . . . . . . . . . . 803--816
Robert D. Skeel Iterative Refinement Implies Numerical
Stability for Gaussian Elimination . . . 817--832
Avram Sidi Analysis of convergence of the $
{T}$-transformation for power series . . 833--850
Avram Sidi Numerical quadrature and nonlinear
sequence transformations; unified rules
for efficient computation of integrals
with algebraic and logarithmic endpoint
singularities . . . . . . . . . . . . . 851--874
Adhemar Bultheel Recursive algorithms for the matrix Padé
problem . . . . . . . . . . . . . . . . 875--892
T. S. Horner Recurrence relations for the
coefficients in Chebyshev series
solutions of ordinary differential
equations . . . . . . . . . . . . . . . 893--905
J. R. Philip The convergence and partial convergence
of alternating series . . . . . . . . . 907--916
G. Allasia and
F. Bonardo On the Numerical Evaluation of Two
Infinite Products . . . . . . . . . . . 917--931
Godfrey L. Isaacs Exponential Laws for Fractional
Differences . . . . . . . . . . . . . . 933--936
Marietta J. Tretter and
G. W. Walster Further comments on the computation of
modified Bessel function ratios . . . . 937--939
Jeffrey S. Leon On an algorithm for finding a base and a
strong generating set for a group given
by generating permutations . . . . . . . 941--974
Gary B. Gostin A Factor of $ {F}_{17} $ . . . . . . . . 975--976
F. T. Howard A Special Class of Bell Polynomials . . 977--989
M. K. Agrawal and
J. H. Coates and
D. C. Hunt and
A. J. van der Poorten Elliptic curves of conductor $ 11 $ . . 991--1002
Carl Pomerance and
J. L. Selfridge and
Samuel S. Wagstaff, Jr. The Pseudoprimes to $ 25 \cdot 10^9 $ 1003--1026
Peter Hagis, Jr. Outline of a proof that every odd
perfect number has at least eight prime
factors . . . . . . . . . . . . . . . . 1027--1032
I. Babu\vska and
J. Osborn and
J. Pitkäranta Analysis of Mixed Methods Using Mesh
Dependent Norms . . . . . . . . . . . . 1039--1062
Claes Johnson and
J.-Claude Nédélec On the coupling of boundary integral and
finite element methods . . . . . . . . . 1063--1079
Joseph E. Pasciak Spectral and Pseudo Spectral Methods for
Advection Equations . . . . . . . . . . 1081--1092
Mitchell Luskin A finite element method for first-order
hyperbolic systems . . . . . . . . . . . 1093--1112
Juhani Pitkäranta Local Stability Conditions for the
Babu\vska Method of Lagrange Multipliers 1113--1129
Charles I. Goldstein Variational crimes and $ {L}^{\infty } $
error estimates in the finite element
method . . . . . . . . . . . . . . . . . 1131--1157
G. J. Cooper and
A. Sayfy Additive methods for the numerical
solution of ordinary differential
equations . . . . . . . . . . . . . . . 1159--1172
Peter Alfeld A method of skipping the transient phase
in the solution of separably stiff
ordinary initial value problems . . . . 1173--1176
C. P. Katti Five-diagonal sixth order methods for
two-point boundary value problems
involving fourth order differential
equations . . . . . . . . . . . . . . . 1177--1179
George F. Corliss Integrating ODEs in the complex
plane---pole vaulting . . . . . . . . . 1181--1189
Beny Neta On determination of best-possible
constants in integral inequalities
involving derivatives . . . . . . . . . 1191--1193
Martin Stynes On faster convergence of the bisection
method for all triangles . . . . . . . . 1195--1201
Warren E. Ferguson, Jr. The construction of Jacobi and periodic
Jacobi matrices with prescribed spectra 1203--1220
Günter Meinardus and
G. D. Taylor Optimal Partitioning of Newton's Method
for Calculating Roots . . . . . . . . . 1221--1230
Steven M. Serbin On Factoring a Class of Complex
Symmetric Matrices Without Pivoting . . 1231--1234
Indu Mati Anand Numerical Stability of Nested Dissection
Orderings . . . . . . . . . . . . . . . 1235--1249
Thomas Ericsson and
Axel Ruhe The spectral transformation Lánczos
method for the numerical solution of
large sparse generalized symmetric
eigenvalue problems . . . . . . . . . . 1251--1268
M. Madalena Martins On an accelerated overrelaxation
iterative method for linear systems with
strictly diagonally dominant matrix . . 1269--1273
Philip Rabinowitz The exact degree of precision of
generalized Gauss--Kronrod integration
rules . . . . . . . . . . . . . . . . . 1275--1283
Richard F. King An efficient one-point extrapolation
method for linear convergence . . . . . 1285--1290
Luigi Gatteschi On Some Orthogonal Polynomial Integrals 1291--1298
J. P. Vigneron and
Ph. Lambin Gaussian quadrature of integrands
involving the error function . . . . . . 1299--1307
John P. Boyd The Rate of Convergence of Hermite
Function Series . . . . . . . . . . . . 1309--1316
Andrés Cruz and
Javier Sesma Modulus and phase of the reduced
logarithmic derivative of the
cylindrical Bessel function . . . . . . 1317--1324
Henry E. Fettis On Some Trigonometric Integrals . . . . 1325--1329
David Levin On accelerating the convergence of
infinite double series and integrals . . 1331--1345
Peter Wilker An Efficient Algorithmic Solution of the
Diophantine Equation $ u^2 + 5 v^2 = m $ 1347--1352
Michael Willett Arithmetic in a Finite Field . . . . . . 1353--1359
David W. Boyd Reciprocal Polynomials Having Small
Measure . . . . . . . . . . . . . . . . 1361--1377
John Brillhart Note on Irreducibility Testing . . . . . 1379--1381
Bennett Setzer The determination of all imaginary,
quartic, Abelian number fields with
class number $1$ . . . . . . . . . . . . 1383--1386
Curt Noll and
Laura Nickel The $ 25 $ th and $ 26 $ th Mersenne
Primes . . . . . . . . . . . . . . . . . 1387--1390
Robert Baillie and
Samuel S. Wagstaff, Jr. Lucas Pseudoprimes . . . . . . . . . . . 1391--1417
G. V. Cormack and
H. C. Williams Some Very Large Primes of the Form $ k
\cdot 2^m + 1 $ . . . . . . . . . . . . 1419--1421
H. C. Williams Improving the speed of calculating the
regulator of certain pure cubic fields 1423--1434
Richard P. Brent The First Occurrence of Certain Large
Prime Gaps . . . . . . . . . . . . . . . 1435--1436
Robert P. Backstrom Table errata: ``A method of factoring
and the factorization of $ F_7 $''
[Math. Comp. \bf 29 (1975), 183--205, MR
\bf 51 #8017] by M. A. Morrison and J.
Brillhart . . . . . . . . . . . . . . . 1444--1444
Jason A. Carlson Gallas Table errata: \em Table of integrals,
series Gallas and products [English
translation of the fourth Russian
edition, Academic Press, New York, 1965
and MR \bf 33 #5952] by I. S.
Grad\vste\uìn and I. M. Ry\vzik . . . . . 1444--1444
Fred T. Krogh Corrigendum: ``Recurrence relations for
computing with modified divided
differences'' [Math. Comp. \bf 33
(1979), no. 148, 1265--1271, MR
80f:65094] . . . . . . . . . . . . . . . 1445--1445
Carl de Boor and
Blair Swartz Collocation approximation to eigenvalues
of an ordinary differential equation:
numerical illustrations . . . . . . . . 1--19
Carl de Boor and
Blair Swartz Local piecewise polynomial projection
methods for an O.D.E. which give
high-order convergence at knots . . . . 21--33
Randolph E. Bank and
Todd Dupont An optimal order process for solving
finite element equations . . . . . . . . 35--51
Douglas N. Arnold and
Jim Douglas, Jr. and
Vidar Thomée Superconvergence of a finite element
approximation to the solution of a
Sobolev equation in a single space
variable . . . . . . . . . . . . . . . . 53--63
Ragnar Winther A stable finite element method for
initial-boundary value problems for
first-order hyperbolic systems . . . . . 65--86
William J. Layton Estimates away from a discontinuity for
dissipative Galerkin methods for
hyperbolic equations . . . . . . . . . . 87--92
A. Y. Le Roux Stability of Numerical Schemes Solving
Quasi-Linear Wave Equations . . . . . . 93--105
David Gottlieb The Stability of
Pseudospectral-Chebyshev Methods . . . . 107--118
Claude Bardos and
Michel Bercovier and
Olivier Pironneau The Vortex Method with Finite Elements 119--136
Jean Descloux and
Mitchell Luskin and
Jacques Rappaz Approximation of the spectrum of closed
operators: the determination of normal
modes of a rotating basin . . . . . . . 137--154
Harry Munz Uniform expansions for a class of finite
difference schemes for elliptic boundary
value problems . . . . . . . . . . . . . 155--170
A. Iserles Quadrature methods for stiff ordinary
differential systems . . . . . . . . . . 171--182
G. Avdelas and
A. Hadjidimos Optimum accelerated overrelaxation
method in a special case . . . . . . . . 183--187
Bengt Fornberg A vector implementation of the fast
Fourier transform algorithm . . . . . . 189--191
K. S. Thomas Galerkin Methods for Singular Integral
Equations . . . . . . . . . . . . . . . 193--205
Claus Schneider Product integration for weakly singular
integral equations . . . . . . . . . . . 207--213
P. W. Hemker and
H. Schippers Multiple grid methods for the solution
of Fredholm integral equations of the
second kind . . . . . . . . . . . . . . 215--232
K. Glashoff and
K. Roleff A new method for Chebyshev approximation
of complex-valued functions . . . . . . 233--239
J. F. Mahoney Partial fraction evaluation by an
escalation technique . . . . . . . . . . 241--246
Peter McCullagh A rapidly convergent series for
computing $ \psi (z) $ and its
derivatives . . . . . . . . . . . . . . 247--248
M. M. Shepherd and
J. G. Laframboise Chebyshev Approximation of $ (1 + 2 x)
\exp (x^2) \operatorname {erfc} x $ in $
0 \leq x < \infty $ . . . . . . . . . . . 249--253
John D. Dixon Asymptotically Fast Factorization of
Integers . . . . . . . . . . . . . . . . 255--260
Leonard Adleman and
Frank Thomson Leighton An $ {O}(n^{1 / 10.89}) $ Primality
Testing Algorithm . . . . . . . . . . . 261--266
Rudolf Land Computation of Pólya Polynomials of
Primitive Permutation Group . . . . . . 267--278
Sol Weintraub A Large Prime Gap . . . . . . . . . . . 279--279
Hiroshi Gunji and
Dennis Arnon On Polynomial Factorization Over Finite
Fields . . . . . . . . . . . . . . . . . 281--287
D. H. Lehmer On Fermat's Quotient, Base Two . . . . . 289--290
Daniel Shanks and
H. C. Williams Gunderson's Function in Fermat's Last
Theorem . . . . . . . . . . . . . . . . 291--295
Herman J. J. te Riele Hyperperfect Numbers With Three
Different Prime Factors . . . . . . . . 297--298
Peter Hagis, Jr. Unitary Hyperperfect Numbers . . . . . . 299--301
W. Borho Some Large Primes and Amicable Numbers 303--304
Henry E. Fettis Table errata: \em Higher transcendental
functions, Vol. II [McGraw-Hill, New
York, 1953, F. Oberhettinger MR \bf 15,
419] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 315--315
N. M. Temme Table errata: \em Formulas and theorems
for the special functions of
mathematical physics [third edition,
Springer, New York, 1966 and F.
Oberhettinger MR \bf 38 #1291] by W.
Magnus and R. P. Soni . . . . . . . . . 315--316
Robert L. Pexton Table errata: \em Formulas and theorems
for the special functions of
mathematical physics [third edition,
Springer, New York, 1966 and F.
Oberhettinger MR \bf 38 #1291] by W.
Magnus and R. P. Soni . . . . . . . . . 316--317
Henry E. Fettis Table errata: \em Handbook of elliptic
integrals for engineers and physicists
[second edition, Springer, New York,
1971 and MR \bf 43 #3506] by P. F. Byrd
and M. D. Friedman . . . . . . . . . . . 317--317
Henry E. Fettis Table errata: \em Table of integrals,
series, and products [English
translation of the fourth Russian
edition, Academic Press, New York, 1965;
MR \bf 33 #5952] by I. S. Gradshteyn [I.
S. Grad\vste\uìn] and I. M. Ryzhik [I. M.
Ry\vzik] . . . . . . . . . . . . . . . . 317--318, 320
Henry E. Fettis Table errata: \em A table of the
complete elliptic integral of the first
kind for complex values of the modulus,
Part I [Rep. No. ARL 69-0172, Aerospace
Res. Lab., Wright--Patterson Air Force
Base, Ohio, 1969; MR \bf 40 #6725] by
Fettis and J. C. Caslin . . . . . . . . 318
S. N. Stuart Table errata: \em A course of modern
analysis [fourth edition, Cambridge
Univ. Press, Cambridge 1927 and 180] by
E. T. Whittaker Jbuch \bf 53 and G. N.
Watson . . . . . . . . . . . . . . . . . 319--319
Herbert E. Salzer Errata: \em A history of numerical
analysis from the 16th through the 19th
century [Springer, New York, 1977]. MR
\bf 58 #4774 by H. H. Goldstine . . . . 319--320
Björn Engquist and
Stanley Osher One-sided difference approximations for
nonlinear conservation laws . . . . . . 321--351
Amiram Harten and
Hillel Tal-Ezer On a fourth order accurate implicit
finite difference scheme for hyperbolic
conservation laws. I. Nonstiff strongly
dynamic problems . . . . . . . . . . . . 353--373
Gerard R. Richter Numerical identification of a spatially
varying diffusion coefficient . . . . . 375--386
C. I. Goldstein The finite element method with
nonuniform mesh sizes for unbounded
domains . . . . . . . . . . . . . . . . 387--404
M. Djaoua A method of calculation of lifting flows
around two-dimensional corner-shaped
bodies . . . . . . . . . . . . . . . . . 405--425
B. Mercier and
J. Osborn and
J. Rappaz and
P.-A. Raviart Eigenvalue Approximation by Mixed and
Hybrid Methods . . . . . . . . . . . . . 427--453
M. Delfour and
W. Hager and
F. Trochu Discontinuous Galerkin methods for
ordinary differential equations . . . . 455--473
John R. Rice and
Elias N. Houstis and
Wayne R. Dyksen A population of linear, second order,
elliptic partial differential equations
on rectangular domains. Part I . . . . . 475--484
Stephen F. McCormick A Mesh Refinement Method for $ A x =
\lambda B x $ . . . . . . . . . . . . . 485--498
L. F. Shampine Type-Insensitive ODE Codes Based on
Implicit $ {A}$-Stable Formulas . . . . 499--510
Ian H. Sloan Quadrature methods for integral
equations of the second kind over
infinite intervals . . . . . . . . . . . 511--523
Borislav D. Bojanov Uniqueness of the optimal nodes of
quadrature formulae . . . . . . . . . . 525--546
Walter Gautschi Minimal solutions of three-term
recurrence relations and orthogonal
polynomials . . . . . . . . . . . . . . 547--554
Staffan Wrigge Calculation of the Taylor Series
Expansion Coefficients of the Jacobian
Elliptic Function $ \mathrm {sn}(x, k) $ 555--564
M. D. Hendy and
N. S. Jeans The Jacobi--Perron Algorithm in Integer
Form . . . . . . . . . . . . . . . . . . 565--574
Svein Mossige Algorithms for computing the $h$-range
of the postage stamp problem . . . . . . 575--582
Masao Kishore On odd perfect, quasiperfect, and odd
almost perfect numbers . . . . . . . . . 583--586
David G. Cantor and
Hans Zassenhaus A new algorithm for factoring
polynomials over finite fields . . . . . 587--592
H. C. Williams A numerical investigation into the
length of the period of the continued
fraction expansion of $ \sqrt {D} $ . . 593--601
Moshe Goldberg and
Eitan Tadmor Scheme-independent stability criteria
for difference approximations of
hyperbolic initial-boundary value
problems. II . . . . . . . . . . . . . . 603--626
Richard P. Brent and
John M. Pollard Factorization of the Eighth Fermat
Number . . . . . . . . . . . . . . . . . 627--630
H. C. Williams Some Results Concerning Vorono\uì's
Continued Fraction Over $ \mathcal
{Q}(\sqrt [3]{D}) $ . . . . . . . . . . 631--652
W. W. Stothers Subgroups of finite index in a free
product with amalgamated subgroup . . . 653--662
James H. Bramble The Lagrange multiplier method for
Dirichlet's problem . . . . . . . . . . 1--11
Juhani Pitkäranta The finite element method with Lagrange
multipliers for domains with corners . . 13--30
M. Vogelius and
I. Babu\vska On a dimensional reduction method. I.
The optimal selection of basis functions 31--46
M. Vogelius and
I. Babu\vska On a dimensional reduction method. II.
Some approximation-theoretic results . . 47--68
D. L. Hicks Hydrocode Subcycling Stability . . . . . 69--78
Alan E. Berger and
Jay M. Solomon and
Melvyn Ciment An analysis of a uniformly accurate
difference method for a singular
perturbation problem . . . . . . . . . . 79--94
Athena Makroglou A block-by-block method for Volterra
integro-differential equations with
weakly-singular kernel . . . . . . . . . 95--99
M. Madalena Martins Note on irreducible diagonally dominant
matrices and the convergence of the AOR
iterative method . . . . . . . . . . . . 101--103
Y. Saad Krylov Subspace Methods for Solving
Large Unsymmetric Linear Systems . . . . 105--126
James A. Pennline Improving convergence rate in the method
of successive approximations . . . . . . 127--134
C. B. Dunham and
Jack Williams Rate of convergence of discretization in
Chebyshev approximation . . . . . . . . 135--139
P. Lancaster and
K. Salkauskas Surfaces Generated by Moving Least
Squares Methods . . . . . . . . . . . . 141--158
J. Marshall Ash and
Roger L. Jones Optimal numerical differentiation using
three function evaluations . . . . . . . 159--167
Bing Yuan Ting and
Yudell L. Luke Computation of integrals with
oscillatory and singular integrands . . 169--183
B. Mond On algorithmic equivalence in linear
fractional programming . . . . . . . . . 185--187
John P. Boyd The rate of convergence of Chebyshev
polynomials for functions which have
asymptotic power series about one
endpoint . . . . . . . . . . . . . . . . 189--195
J. P. Delahaye Automatic Selection of Sequence
Transformations . . . . . . . . . . . . 197--204
C. J. Smyth On the measure of totally real algebraic
integers. II . . . . . . . . . . . . . . 205--208
Rudolf A. Mathon and
Kevin T. Phelps and
Alexander Rosa A class of Steiner triple systems of
order $ 21 $ and associated Kirkman
systems . . . . . . . . . . . . . . . . 209--222
A. J. W. Duijvestijn and
P. Leeuw Lowest order squared rectangles and
squares with the largest element not on
the boundary . . . . . . . . . . . . . . 223--228
Robert Baillie and
G. Cormack and
H. C. Williams The problem of Sierpi\'nski concerning $
k \cdot 2^n + 1 $ . . . . . . . . . . . 229--231
Arne Fransén Addendum and corrigendum to:
``High-precision values of the gamma
function and of some related
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by Fransén and S. Wrigge . . . . . . . . 233--235
J. Thomas Beale and
Andrew Majda Rates of convergence for viscous
splitting of the Navier--Stokes
equations . . . . . . . . . . . . . . . 243--259
A. K. Aziz and
R. Bruce Kellogg Finite Element Analysis of a Scattering
Problem . . . . . . . . . . . . . . . . 261--272
D. Isaacson and
E. L. Isaacson and
D. Marchesin and
P. J. Paes-Leme Numerical analysis of spectral
properties of coupled oscillator
Schrödinger operators. I. Single and
double well anharmonic oscillators . . . 273--292
David Gottlieb and
Steven A. Orszag and
Eli Turkel Stability of pseudospectral and
finite-difference methods for variable
coefficient problems . . . . . . . . . . 293--305
A. Y. Le Roux Numerical Stability for Some Equations
of Gas Dynamics . . . . . . . . . . . . 307--320
Göran Starius Asymptotic expansions for a class of
elliptic difference schemes . . . . . . 321--326
Mingyou Huang and
Vidar Thomée Some Convergence Estimates for
Semidiscrete Type Schemes for
Time-Dependent Nonselfadjoint Parabolic
Equations . . . . . . . . . . . . . . . 327--346
David A. Field An algorithm for determining invertible
quadratic isoparametric finite element
transformations . . . . . . . . . . . . 347--360
M. Vogelius and
I. Babu\vska On a Dimensional Reduction Method. III.
A Posteriori Error Estimation and an
Adaptive Approach . . . . . . . . . . . 361--384
A. Jameson and
E. Turkel Implicit Schemes and $ {LU} $
Decompositions . . . . . . . . . . . . . 385--397
Giuseppe Piazza On the $ {BN} $ Stability of the
Runge--Kutta Methods . . . . . . . . . . 399--401
F. Locher Interpolation on uniform meshes by the
translates of one function and related
attenuation factors . . . . . . . . . . 403--416
Erica Jen and
R. P. Srivastav Cubic splines and approximate solution
of singular integral equations . . . . . 417--423
Ph. L. Toint A sparse quasi-Newton update derived
variationally with a nondiagonally
weighted Frobenius norm . . . . . . . . 425--433
F. Stummel Perturbation theory for evaluation
algorithms of arithmetic expressions . . 435--473
Arne Fransén Conjectures on the Taylor Series
Expansion Coefficients of the Jacobian
Elliptic Function $ \mathrm {sn}(x, k) $ 475--494
Staffan Wrigge A Note on the Taylor Series Expansion
Coefficients of the Jacobian Elliptic
Function $ \mathrm {sn}(x, k) $ . . . . 495--497
M. L. Glasser A Class of Bessel Summations . . . . . . 499--501
L. C. Hsu and
Y. S. Chou An asymptotic formula for a type of
singular oscillatory integrals . . . . . 503--507
R. Wong and
J. P. McClure On a method of asymptotic evaluation of
multiple integrals . . . . . . . . . . . 509--521
A. J. W. Duijvestijn and
P. J. Federico The number of polyhedral ($3$-connected
planar) graphs . . . . . . . . . . . . . 523--532
S. K. Winker and
L. Wos and
E. L. Lusk Semigroups, antiautomorphisms, and
involutions: a computer solution to an
open problem. I . . . . . . . . . . . . 533--545
Larissa Queen Modular Functions Arising from Some
Finite Groups . . . . . . . . . . . . . 547--580
W. G. Leavitt and
Albert A. Mullin Primes Differing by a Fixed Integer . . 581--585
Carl Pomerance On the Distribution of Pseudoprimes . . 587--593
Henry C. Thacher Book Review: \booktitleComputational
Analysis with the HP-25 Pocket
Calculator, by Peter Henrici . . . . . . 595--596
Henry E. Fettis Corrigendum: ``On some trigonometric
integrals'' . . . . . . . . . . . . . . 605--605
A. H. Schatz and
L. B. Wahlbin On the Quasi-Optimality in $ {L}_\infty
$ of the $ \overset {\circ
}{H}^1$-Projection into Finite Element
Spaces . . . . . . . . . . . . . . . . . 1--22
Douglas N. Arnold and
Ragnar Winther A superconvergent finite element method
for the Korteweg--de Vries equation . . 23--36
David Archer and
Julio César Díaz A collocation-Galerkin method for a
first order hyperbolic equation with
space and time dependent coefficient . . 37--53
Houde Han The finite element method in a family of
improperly posed problems . . . . . . . 55--65
C. Canuto and
A. Quarteroni Approximation results for orthogonal
polynomials in Sobolev spaces . . . . . 67--86
Peter Alfeld Fixed Point Iteration with Inexact
Function Values . . . . . . . . . . . . 87--98
Arieh Iserles Composite Exponential Approximations . . 99--112
M. J. Marsden Spline Interpolation at Knot Averages on
a Two-Sided Geometric Mesh . . . . . . . 113--126
Avram Sidi Numerical quadrature rules for some
infinite range integrals . . . . . . . . 127--142
T. H. Charles Chen Asymptotic error estimates for Gaussian
quadrature formulas . . . . . . . . . . 143--152
B. N. Parlett and
H. Simon and
L. M. Stringer On Estimating the Largest Eigenvalue
with the Lánczos Algorithm . . . . . . . 153--165
Ralph Kallman A method for finding permanents of $ 0,
\, 1 $ matrices . . . . . . . . . . . . 167--170
Annie A. M. Cuyt Numerical stability of the
Halley-iteration for the solution of a
system of nonlinear equations . . . . . 171--179
Richard Franke Scattered Data Interpolation: Tests of
Some Methods . . . . . . . . . . . . . . 181--200
C. M. Joshi and
J. P. Arya Inequalities for Certain Hypergeometric
Functions . . . . . . . . . . . . . . . 201--205
Shyam L. Kalla and
Salvador Conde and
Yudell L. Luke Integrals of Jacobi Functions . . . . . 207--214
Chih Bing Ling and
Ming Jing Wu Evaluation of integrals of Howland type
involving a Bessel function . . . . . . 215--222
V. Belevitch and
J. Boersma On Stieltjes integral transforms
involving $ {\Gamma } $-functions . . . 223--226
Harvey Cohn An explicit modular equation in two
variables and Hilbert's twelfth problem 227--236
G. Greaves An algorithm for the solution of certain
differential-difference equations of
advanced type . . . . . . . . . . . . . 237--247
Walter E. Beck and
Rudolph M. Najar A Lower Bound for Odd Triperfects . . . 249--251
Richard P. Brent Succinct proofs of primality for the
factors of some Fermat numbers . . . . . 253--255
Michael Laska An algorithm for finding a minimal
Weierstrass equation for an elliptic
curve . . . . . . . . . . . . . . . . . 257--260
H. C. Williams Determination of Principal Factors in $
\mathcal {Q}(\sqrt {D}) $ and $ \mathcal
{Q}(\sqrt [3]{D}) $ . . . . . . . . . . 261--274
Michael Pohst and
Hans Zassenhaus On Effective Computation of Fundamental
Units. I . . . . . . . . . . . . . . . . 275--291
Michael Pohst and
Peter Weiler and
Hans Zassenhaus On Effective Computation of Fundamental
Units. II . . . . . . . . . . . . . . . 293--329
Wilfrid Keller Table errata: ``New primes of the form $
k \cdot 2^n + 1 $'' [Math. Comp. 33
(1979), no. 148, 1333--1336], MR
80h:10009, by R. Baillie . . . . . . . . 335--335
Wilfrid Keller Table errata: ``Properties of the
sequence $ 3 \cdot 2^n + 1 $'' [Math.
Comp. \bf 30 (1976), no. 135, 657--663,
MR \bf 53 #7933] by S. W. Golomb . . . . 335--335
Wilfrid Keller Table errata: ``Some very large primes
of the form $ k \cdot 2^m + 1 $'' [Math.
Comp. \bf 35 (1980), no. 152,
1419--1421], MR 81i:10011 by G. V.
Cormack and H. C. Williams . . . . . . . 335--335
J. H. Davenport Table errata: \em Tables of indefinite
integrals [English translation, Dover,
New York, 1961, MR \bf 23 #A256] by G.
Petit Bois . . . . . . . . . . . . . . . 335--336
Henry E. Fettis Corrigendum: ``Table errata: \em Table
of integrals, series, and products by I.
S. Grad\vste\uìn and I. M. Ry\vzik''
[Math. Comp. \bf 36 (1981), no. 153,
317--318], MR 82a:65009 . . . . . . . . 337--337
Stanley Osher and
Fred Solomon Upwind difference schemes for hyperbolic
systems of conservation laws . . . . . . 339--374
Claes Johnson and
Juhani Pitkäranta Analysis of some mixed finite element
methods related to reduced integration 375--400
Arthur G. Werschulz Optimal error properties of finite
element methods for second order
elliptic Dirichlet problems . . . . . . 401--413
Laurence Halpern Absorbing boundary conditions for the
discretization schemes of the
one-dimensional wave equation . . . . . 415--429
M. R. Crisci and
E. Russo $ {A}$-stability of a class of methods
for the numerical integration of certain
linear systems of ordinary differential
equations . . . . . . . . . . . . . . . 431--435
Rolf Rannacher and
Ridgway Scott Some optimal error estimates for
piecewise linear finite element
approximations . . . . . . . . . . . . . 437--445
S. Kovvali and
G. K. Gupta Polynomial formulation of second
derivative multistep methods . . . . . . 447--458
J. E. Dennis, Jr. and
Earl S. Marwil Direct Secant Updates of Matrix
Factorizations . . . . . . . . . . . . . 459--474
James R. Bunch A Note on the Stable Decomposition of
Skew Symmetric Matrices . . . . . . . . 475--479
David A. Smith and
William F. Ford Numerical comparisons of nonlinear
convergence accelerators . . . . . . . . 481--499
Z. U. A. Warsi and
J. F. Thompson A noniterative method for the generation
of orthogonal coordinates in
doubly-connected regions . . . . . . . . 501--516
Avram Sidi The numerical evaluation of very
oscillatory infinite integrals by
extrapolation . . . . . . . . . . . . . 517--529
David Levin Procedures for computing one- and
two-dimensional integrals of functions
with rapid irregular oscillations . . . 531--538
S. Beighton and
B. Noble An error estimate for Stenger's
quadrature formula . . . . . . . . . . . 539--545
A. R. DiDonato Recurrence relations for the indefinite
integrals of the associated Legendre
functions . . . . . . . . . . . . . . . 547--551
Géza Németh and
Magda Zimányi Polynomial Type Padé Approximants . . . . 553--565
Staffan Wrigge and
Arne Fransén A General Method of Approximation. Part
I . . . . . . . . . . . . . . . . . . . 567--588
Ll. G. Chambers An upper bound for the first zero of
Bessel functions . . . . . . . . . . . . 589--591
Chih Bing Ling Evaluation of Generalized Howland
Integrals . . . . . . . . . . . . . . . 593--599
Jack Laderman and
Julian D. Laderman Simplified Forecasting by Polynomial
Regression with Equally Spaced Values of
the Independent Variable . . . . . . . . 601--610
David Lee Hilliker An algorithm for solving a certain class
of Diophantine equations. I . . . . . . 611--626
Horst Brunotte The computation of a certain metric
invariant of an algebraic number field 627--632
Patrick J. Costello Density problems involving $ p_r(n) $ 633--637
J. P. Buhler and
R. E. Crandall and
M. A. Penk Primes of the Form $ n! \pm 1 $ and $ 2
\cdot 3 \cdot 5 \cdots p \pm 1 $ . . . . 639--643
Gary B. Gostin and
Philip B. McLaughlin, Jr. Six New Factors of Fermat Numbers . . . 645--649
J. M. Blair Corrigenda: ``Rational Chebyshev
approximations for the Bickley functions
$ K i_n(x) $'' [Math. Comp. \bf 32
(1978), no. 143, 876--886 and C. A.
Edwards MR \bf 57 #10999] by the author
and J. H. Johnson . . . . . . . . . . . 657--657
Henry E. Fettis Corrigenda: ``Erratum: \em Table of
integrals, series, and products
[Academic Press, New York, 1965 and MR
\bf 33 #5952] by I. S. Gradshte\uìn and
I. M. Ryzhik'' [Math. Comp. \bf 27
(1973), 451--452, MR \bf 54 #4049] by A.
Ojo and J. Sadiku . . . . . . . . . . . 657--657
A. Hadjidimos Corrigenda: ``Optimum accelerated
overrelaxation method in a special
case'' [Math. Comp. \bf 36 (1981),
183--187, MR 82c:65016] by G. Avdelas
and the author . . . . . . . . . . . . . 657--657
J. Thomas Beale and
Andrew Majda Vortex Methods. I: Convergence in Three
Dimensions . . . . . . . . . . . . . . . 1--27
J. Thomas Beale and
Andrew Majda Vortex methods. II. Higher order
accuracy in two and three dimensions . . 29--52
Lars Eldén Time discretization in the backward
solution of parabolic equations. I . . . 53--68
Lars Eldén Time discretization in the backward
solution of parabolic equations. II . . 69--84
Todd Dupont Mesh Modification for Evolution
Equations . . . . . . . . . . . . . . . 85--107
L. F. Shampine Type-insensitive ODE codes based on
implicit $ {A}(\alpha)$-stable formulas 109--123
W. Bunse and
A. Bunse-Gerstner Computation of bounds for the positive
eigenvector of a nonnegative irreducible
matrix by monotone iteration . . . . . . 125--131
Claude Brezinski Some New Convergence Acceleration
Methods . . . . . . . . . . . . . . . . 133--145
H. Brunner and
E. Hairer and
S. P. Nòrsett Runge--Kutta theory for Volterra
integral equations of the second kind 147--163
S. H. Chang On certain extrapolation methods for the
numerical solution of
integro-differential equations . . . . . 165--171
Moshe Levin On the Evaluation of Double Integrals 173--177
K. S. Nagaraja and
G. R. Verma Evaluation of the Integral $ \int^p_0
u^n e^{-u^2}(u + x)^{-1} d u $ . . . . . 179--194
P. N. Shivakumar and
R. Wong Asymptotic expansion of the Lebesgue
constants associated with polynomial
interpolation . . . . . . . . . . . . . 195--200
John P. Boyd A Chebyshev polynomial
rate-of-convergence theorem for
Stieltjes functions . . . . . . . . . . 201--206
K. Mahler On the Zeros of a Special Sequence of
Polynomials . . . . . . . . . . . . . . 207--212
W. J. A. Colman The number of partitions of the integer
$ {N} $ into $ {M} $ nonzero positive
integers . . . . . . . . . . . . . . . . 213--224
H. C. Williams A $ p + 1 $ Method of Factoring . . . . 225--234
Andrew Bremner and
Patrick Morton The Integer Points on Three Related
Elliptic Curves . . . . . . . . . . . . 235--238
A. Rotkiewicz On Euler Lehmer pseudoprimes and strong
Lehmer pseudoprimes with parameters $
{L} $, $ {Q} $ in arithmetic
progressions . . . . . . . . . . . . . . 239--247
David W. Boyd The Sequence of Radii of the Apollonian
Packing . . . . . . . . . . . . . . . . 249--254
William Adams and
Daniel Shanks Strong Primality Tests that are Not
Sufficient . . . . . . . . . . . . . . . 255--300
Robert Baillie and
G. Cormack and
H. C. Williams Corrigenda: ``The problem of
Sierpi\'nski concerning $ k \cdot 2^n +
1 $'' [Math. Comp. \bf 37 (1981), no.
155, 229--231] . . . . . . . . . . . . . 308--308
Charles I. Goldstein A finite element method for solving
Helmholtz type equations in waveguides
and other unbounded domains . . . . . . 309--324
Laurent Véron Some remarks on the convergence of
approximate solutions of nonlinear
evolution equations in Hilbert spaces 325--337
Garth A. Baker and
Vassilios A. Dougalis and
Ohannes A. Karakashian On a higher order accurate fully
discrete Galerkin approximation to the
Navier--Stokes equations . . . . . . . . 339--375
Joseph W. Jerome and
Michael E. Rose Error estimates for the multidimensional
two-phase Stefan problem . . . . . . . . 377--414
J. Paine Correction of Sturm--Liouville
Eigenvalue Estimates . . . . . . . . . . 415--420
Peter A. Markowich Eigenvalue Problems on Infinite
Intervals . . . . . . . . . . . . . . . 421--441
Yves Jaccard and
Hugo Evéquoz Approximation of the spectrum of an
operator given by the
magnetohydrodynamic stability of a
plasma . . . . . . . . . . . . . . . . . 443--452
Randolph E. Bank and
Donald J. Rose Analysis of a multilevel iterative
method for nonlinear finite element
equations . . . . . . . . . . . . . . . 453--465
J. H. Freilich and
E. L. Ortiz Numerical solution of systems of
ordinary differential equations with the
Tau method: an error analysis . . . . . 467--479
Eckart Gekeler Linear Multistep Methods for Stable
Differential Equations $ y^{..} = A y +
{B}(t) y^. c(t) $ . . . . . . . . . . . 481--490
J. D. Day and
D. N. P. Murthy Two classes of internally $ {S}$-stable
generalized Runge--Kutta processes which
remain consistent with an inaccurate
Jacobian . . . . . . . . . . . . . . . . 491--509
C. J. Gladwin On optimal integration methods for
Volterra integral equations of the first
kind . . . . . . . . . . . . . . . . . . 511--518
Ivan G. Graham Galerkin methods for second kind
integral equations with singularities 519--533
M. Lax and
G. P. Agrawal Evaluation of Fourier integrals using $
{B}$-splines . . . . . . . . . . . . . . 535--548
Masaaki Sugihara and
Kazuo Murota A note on Haselgrove's method for
numerical integration . . . . . . . . . 549--554
H. Jager On the speed of convergence of the
nearest integer continued fraction . . . 555--558
H. A. Van der Vorst A generalized Lánczos scheme . . . . . . 559--561
Abraham Ziv Relative distance---an error measure in
round-off error analysis . . . . . . . . 563--569
Jeff Chow On the Uniqueness of Best $ {L}_2
\lbrack 0, 1 \rbrack $ Approximation by
Piecewise Polynomials with Variable
Breakpoints . . . . . . . . . . . . . . 571--585
B. Gabutti and
J. N. Lyness An acceleration method for the power
series of entire functions of order $1$ 587--597
U. Grothkopf and
G. Opfer Complex Chebyshev polynomials on
circular sectors with degree six or less 599--615
C. A. Wills and
J. M. Blair and
P. L. Ragde Rational Chebyshev approximations for
the Bessel functions $ {J}_0 (x) $, $
{J}_1 (x) $, $ {Y}_0 (x) $, $ {Y}_1 (x)
$ . . . . . . . . . . . . . . . . . . . 617--623
Keith R. Lassey On the computation of certain integrals
containing the modified Bessel function
$ {I}_0 (\xi) $ . . . . . . . . . . . . 625--637
Andrés Cruz and
Javier Sesma Zeros of the Hankel function of real
order and of its derivative . . . . . . 639--645
K. S. Kölbig Closed Expressions for $ \int^1_0 t^{-1}
\log^{n - 1}t \log^p(1 - t) d t $ . . . 647--654
Francis J. Murray Formulas for Factorial $ {N} $ . . . . . 655--662
Gregory Butler and
John J. Cannon Computing in Permutation and Matrix
Groups. I. Normal Closure, Commutator
Subgroups, Series . . . . . . . . . . . 663--670
Gregory Butler and
John J. Cannon Computing in permutation and matrix
groups. II. Backtrack algorithm . . . . 671--680
R. P. Brent and
J. van de Lune and
H. J. J. te Riele and
D. T. Winter On the zeros of the Riemann zeta
function in the critical strip. II . . . 681--688
P. Llorente and
A. V. Oneto On the Real Cubic Fields . . . . . . . . 689--692
F. J. van der Linden Class Number Computations of Real
Abelian Number Fields . . . . . . . . . 693--707
Don Zagier On the number of Markoff numbers below a
given bound . . . . . . . . . . . . . . 709--723
Richard H. Hudson and
Kenneth S. Williams Class Number Formulae of Dirichlet Type 725--732
John Brillhart Table errata: ``New primality criteria
and factorizations of $ 2^m \pm a n d 1
$'' [Math. Comp. 29 (1975), 620--647 and
D. H. Lehmer MR 52 #5546] by the author
and J. L. Selfridge . . . . . . . . . . 747--747
H. van Haeringen and
L. P. Kok Table errata: \em Table of integrals,
series, and products [corrected and 1980
enlarged edition, Academic Press, New
York and MR 81g:33001] by I. S.
Gradshteyn [I. S. Gradshte\uìn] and I. M.
Ryzhik . . . . . . . . . . . . . . . . . 747--757
Daniel Shanks Corrigendum: H. C. Williams, ``Some
primes with interesting digit patterns''
[Math. Comp. \bf 32 (1978), no. 144,
1306--1310, MR \bf 58 #484] . . . . . . 759--759
Daniel Michelson Stability theory of difference
approximations for multidimensional
initial-boundary value problems . . . . 1--45
A. H. Schatz and
L. B. Wahlbin On the finite element method for
singularly perturbed reaction-diffusion
problems in two and one dimensions . . . 47--89
Richard Sanders On convergence of monotone finite
difference schemes with variable spatial
differencing . . . . . . . . . . . . . . 91--106
Jim Douglas, Jr. and
Mary Fanett Wheeler Implicit, Time-dependent Variable Grid
Finite Difference Methods for the
Approximation of a Linear Waterflood . . 107--121
Peter A. Markowich and
Christian A. Ringhofer Collocation methods for boundary value
problems on ``long'' intervals . . . . . 123--150
Goong Chen and
Wendell H. Mills, Jr. and
Shun Hua Sun and
David A. Yost Sharp error estimates for a finite
element-penalty approach to a class of
regulator problems . . . . . . . . . . . 151--173
J. R. Cash Block Runge--Kutta Methods for the
Numerical Integration of Initial Value
Problems in Ordinary Differential
Equations. Part I. The Nonstiff Case . . 175--191
J. R. Cash Block Runge--Kutta Methods for the
Numerical Integration of Initial Value
Problems in Ordinary Differential
Equations. Part II. The Stiff Case . . . 193--206
G. J. Cooper and
A. Sayfy Additive Runge--Kutta methods for stiff
ordinary differential equations . . . . 207--218
O. Axelsson and
I. Gustafsson Preconditioning and two-level multigrid
methods of arbitrary degree of
approximation . . . . . . . . . . . . . 219--242
Thomas R. Lucas A posteriori improvements for
interpolating periodic splines . . . . . 243--251
Gregory M. Nielson A method for interpolating scattered
data based upon a minimum norm network 253--271
Moshe Levin On the Approximate Calculation of Double
Integrals . . . . . . . . . . . . . . . 273--282
Boris Mityagin Quadratic pencils and least-squares
piecewise-polynomial approximation . . . 283--300
P. H. M. Wolkenfelt Modified multilag methods for Volterra
functional equations . . . . . . . . . . 301--316
Angelo Lucia An explicit quasi-Newton update for
sparse optimization calculations . . . . 317--322
George Cybenko A general orthogonalization technique
with applications to time series
analysis and signal processing . . . . . 323--336
Walter Gautschi On the convergence behavior of continued
fractions with real elements . . . . . . 337--342
J. P. Coleman and
A. J. Monaghan Chebyshev expansions for the Bessel
function $ {J}_n(z) $ in the complex
plane . . . . . . . . . . . . . . . . . 343--366
F. M. Arscott and
P. J. Taylor and
R. V. M. Zahar On the numerical construction of
ellipsoidal wave functions . . . . . . . 367--380
G. Jaeschke On the smallest $k$ such that all $ k
\cdot 2^n + 1$ are composite . . . . . . 381--384
Samuel S. Wagstaff, Jr. Divisors of Mersenne Numbers . . . . . . 385--397
Peter Hagis, Jr. Sketch of a proof that an odd perfect
number relatively prime to $3$ has at
least eleven prime factors . . . . . . . 399--404
Masao Kishore Odd Perfect Numbers Not Divisible by
$3$. II . . . . . . . . . . . . . . . . 405--411
T. Charles Chen Table errata: \em Methods of numerical
integration [Academic Press, New York,
1975, MR \bf 56 #7119] by P. J. Davis
and P. Rabinowitz . . . . . . . . . . . 417--417
Garth A. Baker and
Vassilios A. Dougalis and
Ohannes A. Karakashian Convergence of Galerkin approximations
for the Korteweg--de Vries equation . . 419--433
Michael E. Rose Numerical methods for flows through
porous media. I . . . . . . . . . . . . 435--467
Randall J. LeVeque and
Joseph Oliger Numerical methods based on additive
splittings for hyperbolic partial
differential equations . . . . . . . . . 469--497
P. Keast and
G. Fairweather and
J. C. Diaz A computational study of finite element
methods for second order linear
two-point boundary value problems . . . 499--518
William E. Smith and
Ian H. Sloan and
Alex H. Opie Product integration over infinite
intervals. I. Rules based on the zeros
of Hermite polynomials . . . . . . . . . 519--535
Richard S. Falk Error estimates for the numerical
identification of a variable coefficient 537--546
A. Iserles and
S. P. Nòrsett Frequency Fitting of Rational
Approximations to the Exponential
Function . . . . . . . . . . . . . . . . 547--559
M. L. Glasser A Remarkable Property of Definite
Integrals . . . . . . . . . . . . . . . 561--563
K. S. Kölbig On the Integral $ \int^{\pi / 2}_0
\log^n \cos x \log^p \sin x d x $ . . . 565--570
Andrew Adler On the Bisection Method for Triangles 571--574
S. W. Ellacott Computation of Faber series with
application to numerical polynomial
approximation in the complex plane . . . 575--587
W. J. Thron and
Haakon Waadeland Truncation error bounds for limit
periodic continued fractions . . . . . . 589--597
Roy L. Streit and
Albert H. Nuttall A note on the semi-infinite programming
approach to complex approximation . . . 599--605
Robert Riley Applications of a computer
implementation of Poincaré's theorem on
fundamental polyhedra . . . . . . . . . 607--632
Matthew A. Grayson The orbit space of a Kleinian group:
Riley's modest example . . . . . . . . . 633--646
Allen H. Brady The Determination of the Value of Rado's
Noncomputable Function $ {\Sigma }(k) $
for Four-State Turing Machines . . . . . 647--665
Joseph L. Gerver Irregular sets of integers generated by
the greedy algorithm . . . . . . . . . . 667--676
Ronald J. Evans Twenty-Fourth Power Residue Difference
Sets . . . . . . . . . . . . . . . . . . 677--683
Theresa P. Vaughan The discriminant of a quadratic
extension of an algebraic field . . . . 685--707
M. C. Wunderlich A performance analysis of a simple
prime-testing algorithm . . . . . . . . 709--714
H. Schwindt Three Summation Criteria for Fermat's
Last Theorem . . . . . . . . . . . . . . 715--716
John M. Smith Table errata: \em Handbook of
mathematical functions with formulas,
graphs and mathematical tables [Nat.
Bur. Standards, Washington, D.C., 1964
and MR \bf 29 #4914] . . . . . . . . . . 723--724
Wilfred Keller Corrigendum: ``Primes of the form $ n!
\pm 1 $ and $ 2 \cdot 3 \cdot 5 \cdots p
\pm 1 $'' [Math. Comp. 38 (1982), no.
158, 639--643 and MR 83c:10006] by J. P.
Buhler, R. E. Crandall and M. A. Penk 727--727
D. M. Sloan Boundary conditions for a fourth order
hyperbolic difference scheme . . . . . . 1--11
Zi Cai Li and
Guo Ping Liang On the Simplified Hybrid-Combined Method 13--25
M. R. Crisci and
E. Russo An extension of Ortiz' recursive
formulation of the tau method to certain
linear systems of ordinary differential
equations . . . . . . . . . . . . . . . 27--42
S. F. McCormick and
J. W. Ruge Unigrid for Multigrid Simulation . . . . 43--62
Philip Rabinowitz Gauss--Kronrod integration rules for
Cauchy principal value integrals . . . . 63--78
N. I. Ioakimidis Further convergence results for the
weighted Galerkin method of numerical
solution of Cauchy-type singular
integral equations . . . . . . . . . . . 79--85
Ch. Lubich Runge--Kutta theory for Volterra and
Abel integral equations of the second
kind . . . . . . . . . . . . . . . . . . 87--102
John Lund Sinc function quadrature rules for the
Fourier integral . . . . . . . . . . . . 103--113
Seymour Haber Parameters for integrating periodic
functions of several variables . . . . . 115--129
Charles K. Chui and
Ren Hong Wang On Smooth Multivariate Spline Functions 131--142
Wolfgang A. Dahmen and
Charles A. Micchelli On the linear independence of
multivariate $ {B}$-splines. II.
Complete configurations . . . . . . . . 143--163
Nira Dyn and
Warren E. Ferguson, Jr. The numerical solution of equality
constrained quadratic programming
problems . . . . . . . . . . . . . . . . 165--170
K. S. Kölbig On the Integral $ \int^\infty_0 e^{- \mu
t}t^{\nu - 1} \log^m t d t $ . . . . . . 171--182
J. H. McCabe The quotient-difference algorithm and
the Padé table: an alternative form and a
general continued fraction . . . . . . . 183--197
D. S. Lubinsky and
A. Sharif On the largest zeroes of orthogonal
polynomials for certain weights . . . . 199--202
T. C. Benton Common Zeros of Two Bessel Functions.
Part II. Approximations and Tables . . . 203--217
L. B. Rall Representations of intervals and optimal
error bounds . . . . . . . . . . . . . . 219--227
Frank Gerth, III An application of matrices over finite
fields to algebraic number theory . . . 229--234
H. C. Williams and
G. W. Dueck and
B. K. Schmid A rapid method of evaluating the
regulator and class number of a pure
cubic field . . . . . . . . . . . . . . 235--286
Joseph L. Gerver Factoring Large Numbers with a Quadratic
Sieve . . . . . . . . . . . . . . . . . 287--294
R. J. Schoof Class Groups of Complex Quadratic Fields 295--302
Eric Seah and
Lawrence C. Washington and
Hugh C. Williams The calculation of a large cubic class
number with an application to real
cyclotomic fields . . . . . . . . . . . 303--305
H. van Haeringen and
L. P. Kok Table errata: \em Higher transcendental
functions, Vol. I [McGraw-Hill, New
York, 1955, F. Oberhettinger, MR \bf 16,
586] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 778--779
H. van Haeringen and
L. P. Kok Table errata: \em Higher transcendental
functions, Vol. II [McGraw-Hill, New
York, 1955, F. Oberhettinger, MR \bf 16,
586] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 778--778
H. van Haeringen and
L. P. Kok Table errata: \em Higher transcendental
functions, Vol. III [McGraw-Hill, New
York, 1955, F. Oberhettinger, MR \bf 16,
586] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 778--778
Eitan Tadmor The unconditional instability of
inflow-dependent boundary conditions in
difference approximations to hyperbolic
systems . . . . . . . . . . . . . . . . 309--319
Stanley Osher and
Richard Sanders Numerical approximations to nonlinear
conservation laws with locally varying
time and space grids . . . . . . . . . . 321--336
R. E. White A modified finite difference scheme for
the Stefan problem . . . . . . . . . . . 337--347
Douglas N. Arnold and
Wolfgang L. Wendland On the Asymptotic Convergence of
Collocation Methods . . . . . . . . . . 349--381
Douglas N. Arnold A spline-trigonometric Galerkin method
and an exponentially convergent boundary
integral method . . . . . . . . . . . . 383--397
J. Pitkäranta and
R. Stenberg Analysis of some mixed finite element
methods for plane elasticity equations 399--423
Milo\vs Zlámal A linear scheme for the numerical
solution of nonlinear quasistationary
magnetic fields . . . . . . . . . . . . 425--440
Jim Douglas, Jr. and
Jean E. Roberts Numerical Methods for a Model for
Compressible Miscible Displacement in
Porous Media . . . . . . . . . . . . . . 441--459
Luciano Galeone The use of positive matrices for the
analysis of the large time behavior of
the numerical solution of
reaction-diffusion systems . . . . . . . 461--472
H. D. Mittelmann An efficient algorithm for bifurcation
problems of variational inequalities . . 473--485
Robert E. Scheid, Jr. The accurate numerical solution of
highly oscillatory ordinary differential
equations . . . . . . . . . . . . . . . 487--509
Theodore S. Papatheodorou Block AOR Iteration for Nonsymmetric
Matrices . . . . . . . . . . . . . . . . 511--525
T. J. Ypma Local convergence of difference
Newton-like methods . . . . . . . . . . 527--536
Takemitsu Hasegawa and
Tatsuo Torii and
Ichizo Ninomiya Generalized Chebyshev interpolation and
its application to automatic quadrature 537--553
Vittorio Massidda Analytical calculation of a class of
integrals containing exponential and
trigonometric functions . . . . . . . . 555--557
Ralph Baker Kearfott A Sinc Approximation for the Indefinite
Integral . . . . . . . . . . . . . . . . 559--572
J. Ernest Wilkins, Jr. and
Theodore R. Hatcher The Maximum of a Quasi-Smooth Function 573--589
Richard F. King Anderson--Björck for Linear Sequences . . 591--596
Andrés Cruz and
Javier Sesma Modulus and phase of the reduced
logarithmic derivative of the Hankel
function . . . . . . . . . . . . . . . . 597--605
D. Kershaw Some extensions of W. Gautschi's
inequalities for the gamma function . . 607--611
Shigehiko Okui Some integrals relating to the $
{I}_e$-function . . . . . . . . . . . . 613--622
N. C. Albertsen and
G. Jacobsen and
S. B. Sòrensen Nonlinear transformations for
accelerating the convergence of $
{M}$-dimensional series . . . . . . . . 623--634
Aurel J. Zajta Solutions of the Diophantine equation $
{A}^4 + {B}^4 = {C}^4 + {D}^4 $ . . . . 635--659
Wilfrid Keller Factors of Fermat numbers and large
primes of the form $ k \cdot 2^n + 1 $ 661--673
Jean Lagrange Sets of $n$ squares of which any $ n -
1$ have their sum square . . . . . . . . 675--681
L. Alayne Parson A Lower Bound for the Norm of the Theta
Operator . . . . . . . . . . . . . . . . 683--685
Thorkil Naur New Integer Factorizations . . . . . . . 687--695
Paul A. Pritchard Eighteen Primes in Arithmetic
Progression . . . . . . . . . . . . . . 697--697
Leonard M. Adleman and
Andrew M. Odlyzko Irreducibility testing and factorization
of polynomials . . . . . . . . . . . . . 699--709
H. Cohn and
J. C. Lagarias On the Existence of Fields Governing the
$2$-Invariants of the Classgroup of $
{Q}(\sqrt {dp})$ as $p$ Varies . . . . . 711--730
Andrew Bremner and
Nicholas Tzanakis Integer Points on $ y^2 = x^3 - 7 x + 10
$ . . . . . . . . . . . . . . . . . . . 731--741
D. H. Lehmer and
Emma Lehmer Cyclotomy With Short Periods . . . . . . 743--758
J. van de Lune and
H. J. J. te Riele On the zeros of the Riemann zeta
function in the critical strip. III . . 759--767
H. van Haeringen and
L. P. Kok Table errata: \em Formulas and theorems
for the special functions of
mathematical physics [Springer, New
York, 1966 and F. Oberhettinger MR \bf
38 #1291] by W. Magnus and R. P. Soni 775--778
H. van Haeringen and
L. P. Kok Table errata: \em Tables of integral
transforms, Vol. I [McGraw-Hill, New
York 1954, F. Oberhettinger MR \bf 15,
868] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 778--779
H. van Haeringen and
L. P. Kok Table errata: \em Tables of integral
transforms, Vol. II [McGraw-Hill, New
York, 1954, F. Oberhettinger MR \bf 16,
468] by A. Erdélyi, W. Magnus and F. G.
Tricomi . . . . . . . . . . . . . . . . 779--780
H. van Haeringen and
L. P. Kok Table errata: \em Handbook of
mathematical functions, with formulas,
graphs, and mathematical tables [Dover,
New York, 1966 and MR \bf 34 #8606] . . 780--780
Ernst D. Krupnikov Table errata: \em Table of integrals,
series, and products [Academic Press,
New York, 1980 and MR 81g:33001] by I.
S. Gradshte\uìn and I. M. Ryzhik . . . . 780--783
I. M. Longman Table errata: \em Handbook of
mathematical functions with formulas,
graphs, and mathematical tables [U.S.
Government Printing Office, Washington,
D.C., 1964 and MR \bf 29 #4914] . . . . 783--783
Lars B. Wahlbin On the Sharpness of Certain Local
Estimates for $ \overset {\circ }{H}^1 $
Projections into Finite Element Spaces:
Influence of a Reentrant Corner . . . . 1--8
Rolf Stenberg Analysis of Mixed Finite Element Methods
for the Stokes Problem: a Unified
Approach . . . . . . . . . . . . . . . . 9--23
R. M. M. Mattheij and
G. W. M. Staarink On Optimal Shooting Intervals . . . . . 25--40
Richard Weiss An analysis of the box and trapezoidal
schemes for linear singularly perturbed
boundary value problems . . . . . . . . 41--67
Arthur G. Werschulz Does Increased Regularity Lower
Complexity? . . . . . . . . . . . . . . 69--93
Hermann Brunner Implicit Runge--Kutta methods of optimal
order for Volterra integro-differential
equations . . . . . . . . . . . . . . . 95--109
Yougun Huang and
Jack Williams A Note on An Algorithm for Interpolating
Rationals . . . . . . . . . . . . . . . 111--113
Horst D. Simon The Lánczos algorithm with partial
reorthogonalization . . . . . . . . . . 115--142
Daniel Boley and
Gene H. Golub A modified method for reconstructing
periodic Jacobi matrices . . . . . . . . 143--150
Han Lin Chen and
Tron Hvaring Approximation of complex harmonic
functions by complex harmonic splines 151--164
Masao Igarashi A termination criterion for iterative
methods used to find the zeros of
polynomials . . . . . . . . . . . . . . 165--171
Paul F. Byrd and
Lawrence Stalla Chebyshev quadrature rules for a new
class of weight functions . . . . . . . 173--181
D. M. E. Foster and
G. M. Phillips The Arithmetic-Harmonic Mean . . . . . . 183--191
Burnett Meyer Some Inequalities for Elementary Mean
Values . . . . . . . . . . . . . . . . . 193--194
R. Piessens A Series Expansion for the First
Positive Zero of the Bessel Functions 195--197
Morris Newman and
Daniel Shanks On a sequence arising in series for $
\pi $ . . . . . . . . . . . . . . . . . 199--217
Herman J. J. te Riele On Generating New Amicable Pairs from
Given Amicable Pairs . . . . . . . . . . 219--223
Hansraj Gupta Diophantine Equations in Partitions . . 225--229
Masao Kishore Odd Triperfect Numbers . . . . . . . . . 231--233
Manny Scarowsky and
Abraham Boyarsky A note on the Diophantine equation $ x^n
+ y^n + z^n = 3 $ . . . . . . . . . . . 235--237
M. L. Brown On the Diophantine equation $ \sum {X}_i
= \prod {X}_i $ . . . . . . . . . . . . 239--240
H. R. P. Ferguson and
R. D. Major and
K. E. Powell and
H. G. Throolin On Zeros of Mellin Transforms of $ {\rm
SL}_2 (\mathbf {Z}) $ Cusp Forms . . . . 241--255
A. Bremner and
J. W. S. Cassels On the Equation $ {Y}^2 = {X}({X}^2 + p)
$ . . . . . . . . . . . . . . . . . . . 257--264
Kevin S. McCurley Explicit estimates for the error term in
the prime number theorem for arithmetic
progressions . . . . . . . . . . . . . . 265--285
Kevin S. McCurley Explicit Estimates for $ \theta (x; 3,
l) $ and $ \psi (x; 3, l) $ . . . . . . 287--296
H. Cohen and
H. W. Lenstra, Jr. Primality Testing and Jacobi Sums . . . 297--330
H. W. Lenstra, Jr. Divisors in Residue Classes . . . . . . 331--340
Kenneth Eriksson and
Vidar Thomée Galerkin methods for singular boundary
value problems in one space dimension 345--367
David L. Brown A note on the numerical solution of the
wave equation with piecewise smooth
coefficients . . . . . . . . . . . . . . 369--391
Tunc Geveci On the convergence of Galerkin
approximation schemes for second-order
hyperbolic equations in energy and
negative norms . . . . . . . . . . . . . 393--415
Mitsuhiro Nakao A collocation-$ {H}^{-1}$-Galerkin
method for some elliptic equations . . . 417--426
Eugene C. Gartland, Jr. Accurate approximation of eigenvalues
and zeros of selected eigenfunctions of
regular Sturm--Liouville problems . . . 427--439
Ewa Weinmüller A difference method for a singular
boundary value problem of second order 441--464
Alan E. Berger and
Hou De Han and
R. Bruce Kellogg A priori estimates and analysis of a
numerical method for a turning point
problem . . . . . . . . . . . . . . . . 465--492
Zhong Ci Shi On the convergence properties of the
quadrilateral elements of Sander and
Beckers . . . . . . . . . . . . . . . . 493--504
Dietrich Braess The Convergence Rate of a Multigrid
Method with Gauss--Seidel Relaxation for
the Poisson Equation . . . . . . . . . . 505--519
Trond Steihaug On the sparse and symmetric least-change
secant update . . . . . . . . . . . . . 521--533
Tony F. Chan On the Existence and Computation of $
{LU}$-Factorizations with Small Pivots 535--547
Garry Rodrigue and
Donald Wolitzer Preconditioning By Incomplete Block
Cyclic Reduction . . . . . . . . . . . . 549--565
Youcef Saad Chebyshev Acceleration Techniques for
Solving Nonsymmetric Eigenvalue Problems 567--588
Luciano Misici Numerical Solution of Two Transcendental
Equations . . . . . . . . . . . . . . . 589--595
Andrea Laforgia Further Inequalities for the Gamma
Function . . . . . . . . . . . . . . . . 597--600
Arne Fransén and
Staffan Wrigge Calculation of the moments and the
moment generating function for the
reciprocal gamma distribution . . . . . 601--616
Staffan Wrigge A note on the moment generating function
for the reciprocal gamma distribution 617--621
Richard Mansfield A Complete Axiomatization of Computer
Arithmetic . . . . . . . . . . . . . . . 623--635
Joachim von zur Gathen Hensel and Newton methods in valuation
rings . . . . . . . . . . . . . . . . . 637--661
C. J. Smyth The Mean Values of Totally Real
Algebraic Integers . . . . . . . . . . . 663--681
H. C. Williams and
G. W. Dueck An analogue of the nearest integer
continued fraction for certain cubic
irrationalities . . . . . . . . . . . . 683--705
H. J. Godwin On quartic fields of signature one with
small discriminant. II . . . . . . . . . 707--711
Steve Schaffer Supplement to Higher Order Multi-Grid
Methods . . . . . . . . . . . . . . . . S1--S19
M. G. Crandall and
P. L. Lions Two approximations of solutions of
Hamilton--Jacobi equations . . . . . . . 1--19
J. M. Sanz-Serna Methods for the Numerical Solution of
the Nonlinear Schrödinger Equation . . . 21--27
A. Bendali Numerical Analysis of the Exterior
Boundary Value Problem for the
Time-Harmonic Maxwell Equations by a
Boundary Finite Element Method. Part 1:
The Continuous Problem . . . . . . . . . 29--46
A. Bendali Numerical Analysis of the Exterior
Boundary Value Problem for the
Time-Harmonic Maxwell Equations by a
Boundary Finite Element Method. Part 2:
The Discrete Problem . . . . . . . . . . 47--68
D. Goldfarb and
Ph. L. Toint Optimal estimation of Jacobian and
Hessian matrices that arise in finite
difference calculations . . . . . . . . 69--88
Steve Schaffer Higher Order Multi-Grid Methods . . . . 89--115, S1--19
Ciprian Foia\cs and
Roger Temam Determination of the solutions of the
Navier--Stokes equations by a set of
nodal values . . . . . . . . . . . . . . 117--133
Eric Schechter Sharp convergence rates for nonlinear
product formulas . . . . . . . . . . . . 135--155
U. Ascher and
R. Weiss Collocation for singular perturbation
problems. II. Linear first order systems
without turning points . . . . . . . . . 157--187
P. Onumanyi and
E. L. Ortiz Numerical solution of stiff and
singularly perturbed boundary value
problems with a segmented-adaptive
formulation of the tau method . . . . . 189--203
Wilhelm Werner Polynomial Interpolation: Lagrange
versus Newton . . . . . . . . . . . . . 205--217
D. S. Lubinsky and
P. Rabinowitz Rates of convergence of Gaussian
quadrature for singular integrands . . . 219--242
Norbert H. J. Lacroix On Common Zeros of Legendre's Associated
Functions . . . . . . . . . . . . . . . 243--245
Ay\cse Kiper Fourier series coefficients for powers
of the Jacobian elliptic functions . . . 247--259
J. Wróblewski A nonaveraging set of integers with a
large sum of reciprocals . . . . . . . . 261--262
Graeme L. Cohen Primitive $ \alpha $-abundant numbers 263--270
A. Rotkiewicz On the Congruence $ 2^{n - 2} \equiv 1
(\operatorname {mod} n) $ . . . . . . . 271--272
Fred H. Hao and
Charles J. Parry Generalized Bernoulli numbers and
$m$-regular primes . . . . . . . . . . . 273--288
C. P. Schnorr and
H. W. Lenstra, Jr. A Monte Carlo factoring algorithm with
linear storage . . . . . . . . . . . . . 289--311
Duncan A. Buell The expectation of success using a Monte
Carlo factoring method---some statistics
on quadratic class numbers . . . . . . . 313--327
William W. Adams Splitting of Quartic Polynomials . . . . 329--343
Henry E. Fettis Table errata: \em Formulas and theorems
for the special functions of
mathematical physics [second edition,
Springer, Berlin, 1948 and 38] by W.
Magnus MR \bf 10 and F. Oberhettinger.
(German) . . . . . . . . . . . . . . . . 346--346
Herbert E. Salzer Table errata: \em Table of sines and
cosines to ten decimal places at
thousandths of a degree [Pergamon, New
York, 1962 and MR \bf 26 #361] by Salzer
and N. Levine . . . . . . . . . . . . . 346--346
G. Fairweather Corrigenda: ``A computational study of
finite element methods for second-order
linear two-point boundary value
problems'' [Math. Comp. \bf 40 (1983),
no. 162, 499--518, MR 84c:65103] by
Fairweather, P. Keast and J. C. Diaz . . 347--347
M. Lax and
G. P. Agrawal Corrigenda: ``Evaluation of Fourier
integrals using $B$-splines'' [Math.
Comp. \bf 39 (1982), no. 160, 535--548,
MR 83i:65021] . . . . . . . . . . . . . 347--347
Laurence A. Bales Supplement to: ``Semidiscrete and single
step fully discrete approximations for
second order hyperbolic equations with
time-dependent coefficients'' . . . . . S1--S12
Walter Gautschi and
Jet Wimp In memoriam: Yudell L. Luke, June 26,
1918--May 6, 1983 . . . . . . . . . . . 349--352
Eitan Tadmor The large-time behavior of the scalar,
genuinely nonlinear Lax--Friedrichs
scheme . . . . . . . . . . . . . . . . . 353--368
Eitan Tadmor Numerical viscosity and the entropy
condition for conservative difference
schemes . . . . . . . . . . . . . . . . 369--381
Laurence A. Bales Semidiscrete and Single Step Fully
Discrete Approximations for Second Order
Hyperbolic Equations With Time-Dependent
Coefficients . . . . . . . . . . . . . . 383--414
Mark J. Friedman Finite element formulation of the
general magnetostatic problem in the
space of solenoidal vector functions . . 415--431
Joseph E. Pasciak A new scalar potential formulation of
the magnetostatic field problem . . . . 433--445
Mark J. Friedman and
Joseph E. Pasciak Spectral properties for the
magnetization integral operator . . . . 447--453
P. P. B. Eggermont Approximation properties of quadrature
methods for Volterra integral equations
of the first kind . . . . . . . . . . . 455--471
Werner C. Rheinboldt Differential-algebraic systems as
differential equations on manifolds . . 473--482
G. W. Stewart On the Asymptotic Behavior of Scaled
Singular Value and QR Decompositions . . 483--489
Stephen Demko and
William F. Moss and
Philip W. Smith Decay Rates for Inverses of Band
Matrices . . . . . . . . . . . . . . . . 491--499
A. McCurdy and
K. C. Ng and
B. N. Parlett Accurate computation of divided
differences of the exponential function 501--528
B. L. R. Shawyer Best Approximation of Positive Power
Series . . . . . . . . . . . . . . . . . 529--534
Nira Dyn Composite Hermite--Birkhoff quadrature
formulas of Gaussian type . . . . . . . 535--541
J. Kautský and
S. Elhay Gauss Quadratures and Jacobi Matrices
for Weight Functions Not of One Sign . . 543--550
J. N. Newman Approximations for the Bessel and Struve
functions . . . . . . . . . . . . . . . 551--556
Henry E. Fettis More Trigonometric Integrals . . . . . . 557--564
Enrico Spoletini Generation of permutations following
Lehmer and Howell . . . . . . . . . . . 565--572
W. Plesken and
W. Hanrath The Lattices of Six-Dimensional
Euclidean Space . . . . . . . . . . . . 573--587
Robert Grone and
Russell Merris An Algorithm for the Second Immanant . . 589--591
David W. Boyd Pisot numbers in the neighborhood of a
limit point. II . . . . . . . . . . . . 593--602
Richard H. Hudson Products and Sums of Powers of Binomial
Coefficients $ \operatorname {mod} p $
and Solutions of Certain Quaternary
Diophantine Systems . . . . . . . . . . 603--613
H. J. Godwin Corrigenda: ``On quartic fields of
signature one with small discriminant.
II'' . . . . . . . . . . . . . . . . . . 621--621
Theresa P. Vaughan Corrigenda: ``The discriminant of a
quadratic extension of an algebraic
field'' [Math. Comp. \bf 40 (1983), no.
162, 685--707, MR 84e:12006] . . . . . . 621--621
Walter Gautschi and
Gradimir V. Milovanovic Supplement to Gaussian Quadrature
Involving Einstein and Fermi Functions
with an Application to Summation of
Series . . . . . . . . . . . . . . . . . S1--S11
F. Graimain and
M. Weber Supplement to Computing an Arithmetic
Constant Related to the Ring of Gaussian
Integers . . . . . . . . . . . . . . . . S13--S16
Stanley Osher and
Mohamed Hafez and
Woodrow Whitlow, Jr. Entropy condition satisfying
approximations for the full potential
equation of transonic flow . . . . . . . 1--29
Maria E. Schonbek Second-order conservative schemes and
the entropy condition . . . . . . . . . 31--38
Jim Douglas, Jr. and
Jean E. Roberts Global estimates for mixed methods for
second order elliptic equations . . . . 39--52
A. K. Aziz and
R. B. Kellogg and
A. B. Stephens Least Squares Methods for Elliptic
Systems . . . . . . . . . . . . . . . . 53--70
Christine Bernardi and
Genevi\`eve Raugel Analysis of some finite elements for the
Stokes problem . . . . . . . . . . . . . 71--79
Robert E. Scheid, Jr. Difference methods for problems with
different time scales . . . . . . . . . 81--92
Frank de Hoog and
Richard Weiss The application of Runge--Kutta schemes
to singular initial value problems . . . 93--103
Beresford N. Parlett and
Derek R. Taylor and
Zhishun A. Liu A look-ahead Lánczos algorithm for
unsymmetric matrices . . . . . . . . . . 105--124
Alden H. Wright Finding all solutions to a system of
polynomial equations . . . . . . . . . . 125--133
L. Pasquini and
D. Trigiante A globally convergent method for
simultaneously finding polynomial roots 135--149
Richard I. Shrager A Rapid Robust Rootfinder . . . . . . . 151--165
J. F. Mahoney Partial fraction evaluation and
incomplete decomposition of a rational
function whose denominator contains a
repeated polynomial factor . . . . . . . 167--175
Walter Gautschi and
Gradimir V. Milovanovi\'c Gaussian quadrature involving Einstein
and Fermi functions with an application
to summation of series . . . . . . . . . 177--190
N. I. Ioakimidis On the uniform convergence of Gaussian
quadrature rules for Cauchy principal
value integrals and their derivatives 191--198
N. I. Ioakimidis Application of quadrature rules for
Cauchy-type integrals to the generalized
Poincaré-Bertrand formula . . . . . . . . 199--206
D. J. Newman A simplified version of the fast
algorithms of Brent and Salamin . . . . 207--210
N. Costa Pereira Estimates for the Chebyshev function $
\psi (x) - \theta (x) $ . . . . . . . . 211--221
Tom M. Apostol Formulas for higher derivatives of the
Riemann zeta function . . . . . . . . . 223--232
J. Lehner and
M. Sheingorn Computing self-intersections of closed
geodesics on finite-sheeted covers of
the modular surface . . . . . . . . . . 233--240
F. Gramain and
M. Weber Computing an arithmetic constant related
to the ring of Gaussian integers . . . . 241--250, S13--S16
Marvin C. Wunderlich Implementing the continued fraction
factoring algorithm on parallel machines 251--260
Masao Kishore Odd triperfect numbers are divisible by
eleven distinct prime factors . . . . . 261--263
J. W. S. Cassels A note on the Diophantine equation $ x^3
+ y^3 + z^3 = 3 $ . . . . . . . . . . . 265--266
Leo J. Alex On the Diophantine equation $ 1 + 2^a =
3^b 5^c + 2^d 3^e 5^f $ . . . . . . . . 267--278
Herbert E. Salzer and
Norman Levine Table errata: \em Tables of sines and
cosines to ten decimal places at
thousandths of a degree [Pergamon Press,
New York, 1962 and MR \bf 26 #361] . . . 281--281
Tony F. Chan Corrigendum: ``On the existence and
computation of $ L U$-factorizations
with small pivots'' [Math. Comp. \bf 42
(1984), no. 166, 535--547, MR 85i:65037] 282--282
Barbara Kok and
Tunc Geveci Supplement to the Convergence of
Galerkin Approximation Schemes for
Second-Order Hyperbolic Equations With
Dissipation . . . . . . . . . . . . . . S17--S25
R. E. Bank and
A. Weiser Some a posteriori error estimators for
elliptic partial differential equations 283--301
F. A. Milner Mixed finite element methods for
quasilinear second-order elliptic
problems . . . . . . . . . . . . . . . . 303--320
Kenneth Eriksson Improved accuracy by adapted
mesh-refinements in the finite element
method . . . . . . . . . . . . . . . . . 321--343
Kenneth Eriksson Finite element methods of optimal order
for problems with singular data . . . . 345--360
Moshe Goldberg and
Eitan Tadmor Convenient stability criteria for
difference approximations of hyperbolic
initial-boundary value problems . . . . 361--377
Barbara Kok and
Tunc Geveci The convergence of Galerkin
approximation schemes for second-order
hyperbolic equations with dissipation 379--390, S17--S25
H. M. Jones and
S. McKee Variable step size predictor-corrector
schemes for second kind Volterra
integral equations . . . . . . . . . . . 391--404
J. Bigge and
E. Bohl On the Steady States of Finitely Many
Chemical Cells . . . . . . . . . . . . . 405--415
Youcef Saad and
Martin H. Schultz Conjugate Gradient-like Algorithms for
Solving Nonsymmetric Linear Systems . . 417--424
Lothar Reichel On polynomial approximation in the
complex plane with application to
conformal mapping . . . . . . . . . . . 425--433
S. Lewanowicz On the differential-difference
properties of the extended Jacobi
polynomials . . . . . . . . . . . . . . 435--441
M. S. Milgram The Generalized Integro-Exponential
Function . . . . . . . . . . . . . . . . 443--458
Mark A. Heald Rational Approximations for the Fresnel
Integrals . . . . . . . . . . . . . . . 459--461
U. Fincke and
M. Pohst Improved methods for calculating vectors
of short length in a lattice, including
a complexity analysis . . . . . . . . . 463--471
Joe P. Buhler and
Benedict H. Gross and
Don B. Zagier On the conjecture of Birch and
Swinnerton-Dyer for an elliptic curve of
rank $3$ . . . . . . . . . . . . . . . . 473--481
René Schoof Elliptic Curves Over Finite Fields and
the Computation of Square Roots $
\operatorname {mod} p $ . . . . . . . . 483--494
Veikko Ennola and
Reino Turunen On Totally Real Cubic Fields . . . . . . 495--518
Peter L. Montgomery Modular Multiplication Without Trial
Division . . . . . . . . . . . . . . . . 519--521
C. D. Patterson and
H. C. Williams Some Periodic Continued Fractions With
Long Periods . . . . . . . . . . . . . . 523--532
D. R. Stinson and
H. Ferch $ 2 \, 000 \, 000 $ Steiner triple
systems of order $ 19 $ . . . . . . . . 533--535
J. C. Lagarias and
V. S. Miller and
A. M. Odlyzko Computing $ \pi (x) $: The
Meissel--Lehmer Method . . . . . . . . . 537--560
Richard H. Hudson Averaging effects on irregularities in
the distribution of primes in arithmetic
progressions . . . . . . . . . . . . . . 561--571
A. O. H. Axelsson and
J. G. Verwer Supplement to Boundary Value Techniques
for Initial Value Problems in Ordinary
Differential Equations . . . . . . . . . S1--S4
David W. Boyd Supplement to The Maximal Modulus of an
Algebraic Integer . . . . . . . . . . . S17--S20
W. Plesken and
M. Pohst Supplement to Constructing Integral
Lattices With Prescribed Minimum. I . . S5--S16
Juhani Pitkäranta and
Tuomo Saarinen A multigrid version of a simple finite
element method for the Stokes problem 1--14
Jonathan B. Goodman and
Randall J. LeVeque On the accuracy of stable schemes for
$2$D scalar conservation laws . . . . . 15--21
David Hoff A linearly implicit finite-difference
scheme for the one-dimensional porous
medium equation . . . . . . . . . . . . 23--33
David Hoff and
Joel Smoller Error bounds for finite-difference
approximations for a class of nonlinear
parabolic systems . . . . . . . . . . . 35--49
J. Descloux and
J. Rappaz and
R. Scholz On the rate of convergence for the
approximation of nonlinear problems . . 51--64
Laurence A. Bales and
Vassilios A. Dougalis and
Steven M. Serbin Cosine methods for second-order
hyperbolic equations with time-dependent
coefficients . . . . . . . . . . . . . . 65--89
J. Saranen and
W. L. Wendland On the asymptotic convergence of
collocation methods with spline
functions of even degree . . . . . . . . 91--108
Kenneth Eriksson High-order local rate of convergence by
mesh-refinement in the finite element
method . . . . . . . . . . . . . . . . . 109--142
J. M. Sanz-Serna and
C. Palencia A general equivalence theorem in the
theory of discretization methods . . . . 143--152
A. O. H. Axelsson and
J. G. Verwer Boundary value techniques for initial
value problems in ordinary differential
equations . . . . . . . . . . . . . . . 153--171, S1--S4
Krzysztof C. Kiwiel An algorithm for nonsmooth convex
minimization with errors . . . . . . . . 173--180
A. Neumaier and
A. Schäfer Divided differences, shift
transformations and Larkin's root
finding method . . . . . . . . . . . . . 181--196
Günter Meinardus Remark on a lemma: ``On a method of
asymptotic evaluation of multiple
integrals'' [Math. Comp. \bf 37 (1981),
no. 156, 509--521, MR 83b:41040] by R.
Wong and J. P. McClure . . . . . . . . . 197--198
B. A. Troesch On Shapiro's Cyclic Inequality for $ {N}
= 13 $ . . . . . . . . . . . . . . . . . 199--207
W. Plesken and
M. Pohst Constructing integral lattices with
prescribed minimum. I . . . . . . . . . 209--221, S5--S16
G. Dueck and
H. C. Williams Computation of the class number and
class group of a complex cubic field . . 223--231
Theresa P. Vaughan The construction of unramified cyclic
quartic extensions of $ {Q}(\sqrt m) $ 233--242
David W. Boyd The Maximal Modulus of an Algebraic
Integer . . . . . . . . . . . . . . . . 243--249, S17--S20
J. von zur Gathen and
E. Kaltofen Factorization of multivariate
polynomials over finite fields . . . . . 251--261
Paul A. Pritchard Long arithmetic progressions of primes:
some old, some new . . . . . . . . . . . 263--267
Philip Rabinowitz Correction: ``Gauss--Kronrod integration
rules for Cauchy principal value
integrals'' [Math. Comp. \bf 41 (1983),
no. 1, 63--78, MR 84i:65029] . . . . . . 277--277
P. J. van der Houwen and
H. J. J. te Riele Supplement to: ``Linear multistep
methods for Volterra integral and
integro-differential equations'' . . . . S21--S28
Lloyd N. Trefethen Stability of finite-difference models
containing two boundaries or interfaces 279--300
Marsha J. Berger Stability of Interfaces with Mesh
Refinement . . . . . . . . . . . . . . . 301--318
Endre Süli and
Bo\vsko Jovanovi\'c and
Lav Ivanovi\'c Finite difference approximations of
generalized solutions . . . . . . . . . 319--327
Vassilios A. Dougalis and
Ohannes A. Karakashian On some high-order accurate fully
discrete Galerkin methods for the
Korteweg--de Vries equation . . . . . . 329--345
Haroon Kheshgi and
Mitchell Luskin Analysis of the finite element variable
penalty method for Stokes equations . . 347--363
Rolf Jeltsch and
Klaus-Günther Strack Accuracy bounds for semidiscretizations
of hyperbolic problems . . . . . . . . . 365--376
M. N. Spijker Stepsize restrictions for stability of
one-step methods in the numerical
solution of initial value problems . . . 377--392
J. Bigge and
E. Bohl Deformations of the bifurcation diagram
due to discretization . . . . . . . . . 393--403
Heinz W. Engl and
Andreas Neubauer An improved version of Marti's method
for solving ill-posed linear integral
equations . . . . . . . . . . . . . . . 405--416
Hermann Brunner The numerical solution of weakly
singular Volterra integral equations by
collocation on graded meshes . . . . . . 417--437
P. J. van der Houwen and
H. J. J. te Riele Linear multistep methods for Volterra
integral and integro-differential
equations . . . . . . . . . . . . . . . 439--461
Ch. Lubich Fractional linear multistep methods for
Abel--Volterra integral equations of the
second kind . . . . . . . . . . . . . . 463--469
R. Fletcher and
S. P. J. Matthews A stable algorithm for updating
triangular factors under a rank one
change . . . . . . . . . . . . . . . . . 471--485
T. A. Porsching Estimation of the error in the reduced
basis method solution of nonlinear
equations . . . . . . . . . . . . . . . 487--496
C. de Boor and
R. DeVore A geometric proof of total positivity
for spline interpolation . . . . . . . . 497--504
J. F. Traub and
D. Lee Optimal integration for functions of
bounded variation . . . . . . . . . . . 505--512
G. Akrivis The error norm of certain Gaussian
quadrature formulae . . . . . . . . . . 513--519
Stanis\law Lewanowicz Recurrence relations for hypergeometric
functions of unit argument . . . . . . . 521--535
C. L. Frenzen and
R. Wong A note on asymptotic evaluation of some
Hankel transforms . . . . . . . . . . . 537--548
Henry E. Fettis Further Extensions of a Legendre
Function Integral . . . . . . . . . . . 549--552
J. H. McCabe and
G. M. Phillips Aitken sequences and generalized
Fibonacci numbers . . . . . . . . . . . 553--558
John F. Monahan Accuracy in Random Number Generation . . 559--568
Theresa P. Vaughan On computing the discriminant of an
algebraic number field . . . . . . . . . 569--584
Veikko Ennola and
Reino Turunen On Cyclic Cubic Fields . . . . . . . . . 585--589
V. Ennola and
S. Mäki and
R. Turunen On Real Cyclic Sextic Fields . . . . . . 591--611
Ezra Brown Sets in Which $ x y + k $ is Always a
Square . . . . . . . . . . . . . . . . . 613--620
Alice A. Deanin A counterexample to a conjecture of
Mahler on best $p$-adic Diophantine
approximation constants . . . . . . . . 621--632
G. Jaeschke Corrigendum: ``On the smallest $k$ such
that all $ k \cdot 2^n + 1$ are
composite'' [Math. Comp. \bf 40 (1983),
no. 161, 381--384, MR 84k:10006] . . . . 637--637
E. A. McIntyre, Jr. Supplement to Boundary Integral
Solutions of the Heat Equations . . . . S1--S14
C. Johnson and
J. Pitkäranta An analysis of the discontinuous
Galerkin method for a scalar hyperbolic
equation . . . . . . . . . . . . . . . . 1--26
Milo\vs Zlámal Finite element solution of the
fundamental equations of semiconductor
devices. I . . . . . . . . . . . . . . . 27--43
Jens Lorenz Convergence of Upwind Schemes for a
Stationary Shock . . . . . . . . . . . . 45--57
Bradley J. Lucier A moving mesh numerical method for
hyperbolic conservation laws . . . . . . 59--69
E. A. McIntyre, Jr. Boundary Integral Solutions of the Heat
Equation . . . . . . . . . . . . . . . . 71--79, S1--S14
Eugene O'Riordan and
Martin Stynes An analysis of a superconvergence result
for a singularly perturbed boundary
value problem . . . . . . . . . . . . . 81--92
Ewa Weinmüller On the numerical solution of singular
boundary value problems of second order
by a difference method . . . . . . . . . 93--117
M. Zennaro Natural continuous extensions of
Runge--Kutta methods . . . . . . . . . . 119--133
Lawrence F. Shampine Some Practical Runge--Kutta Formulas . . 135--150
Edward R. Vrscay Julia sets and Mandelbrot-like sets
associated with higher order Schröder
rational iteration functions: a computer
assisted study . . . . . . . . . . . . . 151--169
Eugene L. Allgower and
Phillip H. Schmidt Computing Volumes of Polyhedra . . . . . 171--174
Ph. L. Toint Numerical solution of large sets of
algebraic nonlinear equations . . . . . 175--189
D. Bini and
M. Capovani A class of cubic splines obtained
through minimum conditions . . . . . . . 191--202
Paolo Costantini On Monotone and Convex Spline
Interpolation . . . . . . . . . . . . . 203--214
J. L. Lavoie Some evaluations for the generalized
hypergeometric series . . . . . . . . . 215--218
Chih Bing Ling Evaluation of Howland-Type Integrals
Involving $ \tanh $ and $ \coth $
Functions . . . . . . . . . . . . . . . 219--223
Philip Rabinowitz On the definiteness of Gauss--Kronrod
integration rules . . . . . . . . . . . 225--227
D. S. Lubinsky and
Avram Sidi Convergence of product integration rules
for functions with interior and endpoint
singularities over bounded and unbounded
intervals . . . . . . . . . . . . . . . 229--245
J. M. Borwein and
P. B. Borwein More Quadratically Converging Algorithms
for $ \pi $ . . . . . . . . . . . . . . 247--253
D. J. Newman Computing When Multiplications Cost
Nothing . . . . . . . . . . . . . . . . 255--257
Paul Erd\Hos and
Carl Pomerance On the number of false witnesses for a
composite number . . . . . . . . . . . . 259--279
W. Borho and
H. Hoffmann Breeding Amicable Numbers in Abundance 281--293
Harvey Cohn and
Jesse Deutsch Use of a Computer Scan to Prove $
\mathbf {Q}(\sqrt {2 + \sqrt 2}) $ and $
\mathbf {Q}(\sqrt {3 + \sqrt 2}) $ are
Euclidean . . . . . . . . . . . . . . . 295--299
M. R. Darafsheh Computing the Irreducible Characters of
the Group $ \mathrm {GL}_6 (2) $ . . . . 301--319
Harold M. Fredricksen and
Alfred W. Hales and
Melvin M. Sweet A generalization of Swan's theorem . . . 321--331
M. Tennenhouse and
H. C. Williams A note on class-number one in certain
real quadratic and pure cubic fields . . 333--336
K. F. Ireland and
R. D. Small Class Numbers of Cyclotomic Function
Fields . . . . . . . . . . . . . . . . . 337--340
Robert Segal and
Robert L. Ward Weight distributions of some irreducible
cyclic codes . . . . . . . . . . . . . . 341--354
Helmut F. Bauer Supplement to Table of the Roots of the
Associated Legendre Function with
Respect to the Degree . . . . . . . . . S29--S41
J. Thomas Beale Supplement to A Convergent 3-D Vortex
Method with Grid-Free Stretching . . . . S15--S20
Klaus-Jurgen Forster and
Georg-Peter Ostermeyer Supplement to ``On Weighted
Chebyshev-Type Quadrature Formulas'' . . S21--S27
Hiroyoshi Yamaki Supplement to A Conjecture of Frobenius
and the Sporadic Simple Groups. II . . . S43--S46
James H. Bramble and
Joseph E. Pasciak and
Alfred H. Schatz An iterative method for elliptic
problems on regions partitioned into
substructures . . . . . . . . . . . . . 361--369
M. E. Cayco and
R. A. Nicolaides Finite element technique for optimal
pressure recovery from stream function
formulation of viscous flows . . . . . . 371--377
Ami Harten On a Large Time-Step High Resolution
Scheme . . . . . . . . . . . . . . . . . 379--399
J. Thomas Beale A convergent $3$-D vortex method with
grid-free stretching . . . . . . . . . . 401--424, S15--S20
Laurence Halpern Artificial boundary conditions for the
linear advection diffusion equation . . 425--438
S. F. McCormick and
J. W. Thomas The fast adaptive composite grid (FAC)
method for elliptic equations . . . . . 439--456
Arthur G. Werschulz Complexity of Indefinite Elliptic
Problems . . . . . . . . . . . . . . . . 457--477
Christian Schmeiser Approximate solution of boundary value
problems on infinite intervals by
collocation methods . . . . . . . . . . 479--490
Per Lötstedt and
Linda Petzold Numerical solution of nonlinear
differential equations with algebraic
constraints. I. Convergence results for
backward differentiation formulas . . . 491--516
Takuya Tsuchiya On two methods for approximating minimal
surfaces in parametric form . . . . . . 517--529
Ted Speevak An efficient algorithm for obtaining the
volume of a special kind of pyramid and
application to convex polyhedra . . . . 531--536
Nicholas J. Higham Newton's Method for the Matrix Square
Root . . . . . . . . . . . . . . . . . . 537--549
Gradimir V. Milovanovi\'c and
Staffan Wrigge Least Squares Approximation With
Constraints . . . . . . . . . . . . . . 551--565
Holger Mettke Convex Interpolation by Splines of
Arbitrary Degree . . . . . . . . . . . . 567--576
Reinhard Farwig Rate of convergence of Shepard's global
interpolation formula . . . . . . . . . 577--590
Klaus-Jürgen Förster and
Georg-Peter Ostermeyer On Weighted Chebyshev-Type Quadrature
Formulas . . . . . . . . . . . . . . . . 591--599, S21--S27
Helmut F. Bauer Tables of the roots of the associated
Legendre function with respect to the
degree . . . . . . . . . . . . . . . . . 601--602, S29--S41
D. P. McCarthy Effect of improved multiplication
efficiency on exponentiation algorithms
derived from addition chains . . . . . . 603--608
Hiroyoshi Yamaki A conjecture of Frobenius and the
sporadic simple groups. II . . . . . . . 609--611, S43--S46
David Easton Effective irrationality measures for
certain algebraic numbers . . . . . . . 613--622
Nicholas Tzanakis A Remark on a Theorem of W. E. H.
Berwick . . . . . . . . . . . . . . . . 623--625
Thomas J. Kretschmer Construction of Elliptic Curves with
Large Rank . . . . . . . . . . . . . . . 627--635
Markus A. Reichert Explicit determination of nontrivial
torsion structures of elliptic curves
over quadratic number fields . . . . . . 637--658
Günter Lettl A lower bound for the class number of
certain cubic number fields . . . . . . 659--666
J. van de Lune and
H. J. J. te Riele and
D. T. Winter On the zeros of the Riemann zeta
function in the critical strip. IV . . . 667--681
D. H. Lehmer and
K. Mahler and
A. J. van der Poorten Integers with digits $0$ or $1$ . . . . 683--689
G. C. Kurtz and
Daniel Shanks and
H. C. Williams Fast primality tests for numbers less
than $ 50 \cdot 10^9 $ . . . . . . . . . 691--701
Ray P. Steiner On Mordell's Equation $ y^2 - k = x^3 $:
a Problem of Stolarsky . . . . . . . . . 703--714
Mok-Kong Shen On the Congruence $ 2^{n - k} \equiv 1
(\operatorname {mod} n) $ . . . . . . . 715--716
D. R. Stinson and
E. Seah $ 284 \, 457 $ Steiner triple systems of
order $ 19 $ contain a subsystem of
order $9$ . . . . . . . . . . . . . . . 717--729
Richard Blecksmith and
John Brillhart and
Irving Gerst A computer-assisted investigation of
Ramanujan pairs . . . . . . . . . . . . 731--749
J. Lagrange and
J. Leech Two Triads of Squares . . . . . . . . . 751--758
Mark A. Heald Corrigenda: ``Rational approximations
for the Fresnel integrals'' [Math. Comp.
\bf 44 (1985), no. 170, 459--461, MR
86b:65017] . . . . . . . . . . . . . . . 771--771
Herman J. J. te Riele Corrigenda: ``On the zeros of the
Riemann zeta function in the critical
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P. Brent, J. van de Lune, te Riele and
D. T. Winter . . . . . . . . . . . . . . 771--771
Herman J. J. te Riele Corrigenda: ``On the zeros of the
Riemann zeta function in the critical
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van de Lune and te Riele . . . . . . . . 771--771
M. C. Delfour and
F. Dubeau Supplement to Discontinuous Polynomial
Approximations in the Theory of
One-Step, Hybrid and Multistep Methods
for Nonlinear Ordinary Differential
Equations . . . . . . . . . . . . . . . S1--S8
H. J. J. te Riele Supplement to Computation of All the
Amicable Pairs Below $ 10^10 $ . . . . . S9--S40
Claes Johnson and
Jukka Saranen Streamline diffusion methods for the
incompressible Euler and Navier--Stokes
equations . . . . . . . . . . . . . . . 1--18
Bradley J. Lucier On nonlocal monotone difference schemes
for scalar conservation laws . . . . . . 19--36
Randall J. LeVeque Intermediate boundary conditions for
time-split methods applied to hyperbolic
partial differential equations . . . . . 37--54
I. Lasiecka Galerkin approximations of abstract
parabolic boundary value problems with
rough boundary data---$ {L}_p $ theory 55--75
Ohannes A. Karakashian On Runge--Kutta methods for parabolic
problems with time-dependent
coefficients . . . . . . . . . . . . . . 77--101
James H. Bramble and
Joseph E. Pasciak and
Alfred H. Schatz The construction of preconditioners for
elliptic problems by substructuring. I 103--134
R. S. Falk and
P. B. Monk Logarithmic convexity for discrete
harmonic functions and the approximation
of the Cauchy problem for Poisson's
equation . . . . . . . . . . . . . . . . 135--149
F. Brezzi and
M. Fortin Numerical Approximation of
Mindlin--Reissner Plates . . . . . . . . 151--158
Ezio Venturino On solving singular integral equations
via a hyperbolic tangent quadrature rule 159--167
M. C. Delfour and
F. Dubeau Discontinuous Polynomial Approximations
in the Theory of One-Step, Hybrid and
Multistep Methods for Nonlinear Ordinary
Differential Equations . . . . . . . . . 169--189, S1--S8
Howard C. Elman A stability analysis of incomplete $
{LU} $ factorizations . . . . . . . . . 191--217
A. J. Hughes Hallett The Convergence of Accelerated
Overrelaxation Iterations . . . . . . . 219--223
Frank Stenger Explicit, nearly optimal, linear
rational approximation with preassigned
poles . . . . . . . . . . . . . . . . . 225--252
C. Underhill Some asymptotic properties of Padé
approximants to $ e^{-x} $ . . . . . . . 253--263
Ronald G. Mosier Root Neighborhoods of a Polynomial . . . 265--273
Coert Olmsted Two formulas for the general
multivariate polynomial which
interpolates a regular grid on a simplex 275--284
Claus Schneider and
Wilhelm Werner Some New Aspects of Rational
Interpolation . . . . . . . . . . . . . 285--299
Giovanni Monegato Quadrature formulas for functions with
poles near the interval of integration 301--312
J. N. Lyness and
G. Giunta A modification of the Weeks method for
numerical inversion of the Laplace
transform . . . . . . . . . . . . . . . 313--322
Paul N. Swarztrauber Symmetric FFTs . . . . . . . . . . . . . 323--346
E. Elizalde An asymptotic expansion for the first
derivative of the generalized Riemann
zeta function . . . . . . . . . . . . . 347--350
Peter Shiu Counting sums of two squares: the
Meissel--Lehmer method . . . . . . . . . 351--360
H. J. J. te Riele Computation of All the Amicable Pairs
Below $ 10^{10} $ . . . . . . . . . . . 361--368, S9--S40
Takemitsu Hasegawa Corrigendum: ``Generalized Chebyshev
interpolation and its application to
automatic quadrature'' [Math. Comp. \bf
41 (1983), no. 164, 537--553, MR
84m:65037] by Hasegawa, T. Torii and I.
Ninomiya . . . . . . . . . . . . . . . . 385--385
Franca Calio and
Walter Gautschi and
Elena Marchetti Supplement to On Computing
Gauss--Kronrod Quadrature Formulae . . . S57--S63
George Majda Supplement to Stability with Large Step
Sizes for Multistep Discretizations of
Stiff Ordinary Differential Equations S41--S44
Thomas A. Manteuffel and
Andrew B. White, Jr. Supplement to The Numerical Solution of
Second-Order Boundary Value Problems on
Nonuniform Meshes . . . . . . . . . . . S53--S55
Robert D. Skeel Supplement to Construction of
Variable-Stepsize Multistep Formulas . . S45--S52
Claude Greengard Convergence of the Vortex Filament
Method . . . . . . . . . . . . . . . . . 387--398
Harry Yserentant The Convergence of Multi-Level Methods
for Solving Finite-Element Equations in
the Presence of Singularities . . . . . 399--409
E. A. Socolovsky Difference schemes for degenerate
parabolic equations . . . . . . . . . . 411--420
Lloyd N. Trefethen and
Laurence Halpern Well-posedness of one-way wave equations
and absorbing boundary conditions . . . 421--435
Robert L. Higdon Absorbing boundary conditions for
difference approximations to the
multidimensional wave equation . . . . . 437--459
Arthur G. Werschulz What is the complexity of related
elliptic, parabolic, and hyperbolic
problems? . . . . . . . . . . . . . . . 461--472
George Majda Stability with large step sizes for
multistep discretizations of stiff
ordinary differential equations . . . . 473--502, S41--S44
Robert D. Skeel Construction of Variable-Stepsize
Multistep Formulas . . . . . . . . . . . 503--510, S45--S52
Thomas A. Manteuffel and
Andrew B. White, Jr. The numerical solution of second-order
boundary value problems on nonuniform
meshes . . . . . . . . . . . . . . . . . 511--535, S53--S55
H.-O. Kreiss and
T. A. Manteuffel and
B. Swartz and
B. Wendroff and
A. B. White, Jr. Supra-Convergent Schemes on Irregular
Grids . . . . . . . . . . . . . . . . . 537--554
Eugene O'Riordan and
Martin Stynes A uniformly accurate finite-element
method for a singularly perturbed
one-dimensional reaction-diffusion
problem . . . . . . . . . . . . . . . . 555--570
John Lund Symmetrization of the Sinc--Galerkin
method for boundary value problems . . . 571--588
I. H. Sloan and
A. Spence Integral equations on the half-line: a
modified finite-section approximation 589--595
W. McLean A spectral Galerkin method for a
boundary integral equation . . . . . . . 597--607
C. T. Kelley A Shamanski\u\i-like Acceleration Scheme
for Nonlinear Equations at Singular
Roots . . . . . . . . . . . . . . . . . 609--623
Philip Rabinowitz Rates of convergence of Gauss, Lobatto,
and Radau integration rules for singular
integrands . . . . . . . . . . . . . . . 625--638
Franca Cali\`o and
Walter Gautschi and
Elena Marchetti On Computing Gauss--Kronrod Quadrature
Formulae . . . . . . . . . . . . . . . . 639--650, S57--S63
J. I. Maeztu An Estimate of Goodness of Cubatures for
the Unit Circle in $ {R}^2 $ . . . . . . 651--658
Joaquin Bustoz and
Mourad E. H. Ismail On Gamma Function Inequalities . . . . . 659--667
S. Lewanowicz Properties of the polynomials associated
with the Jacobi polynomials . . . . . . 669--682
N. M. Temme A double integral containing the
modified Bessel function: asymptotics
and computation . . . . . . . . . . . . 683--691
R. Creutzburg and
M. Tasche Number-Theoretic Transforms of
Prescribed Length . . . . . . . . . . . 693--701
H. C. Williams and
Harvey Dubner The Primality of $ {R1031} $ . . . . . . 703--711
A. Pethö and
B. M. M. de Weger Products of Prime Powers in Binary
Recurrence Sequences. Part I: The
Hyperbolic Case, with an Application to
the Generalized Ramanujan--Nagell
Equation . . . . . . . . . . . . . . . . 713--727
B. M. M. de Weger Products of Prime Powers in Binary
Recurrence Sequences. Part II: The
Elliptic Case, with an Application to a
Mixed Quadratic-Exponential Equation . . 729--739
Lawrence C. Washington Some Remarks on Cohen--Lenstra
Heuristics . . . . . . . . . . . . . . . 741--747
H. van Haeringen and
L. P. Kok Table erratum: \em A table of series and
products [Prentice-Hall, Englewood
Cliffs, N.J., 1975] by E. R. Hansen . . 767--767
G. Solt Table erratum: \em Table of integrals,
series and products [Academic Press, New
York, 1980 and MR 81g:33001] by I. S.
Gradshte\uìn and I. M. Ryzhik . . . . . . 768--768
R. D. Skeel Corrigendum: ``Equivalent forms of
multistep formulas'' [Math. Comp. \bf 33
(1979), no. 148, 1229--1250, MR
80j:65027] . . . . . . . . . . . . . . . 769--769
H. Cohen and
A. K. Lenstra Supplement to Implementation of a New
Primality Test . . . . . . . . . . . . . s1--s4
William W. Adams Characterizing pseudoprimes for
third-order linear recurrences . . . . . 1--15
Leonard M. Adleman and
Dennis R. Estes and
Kevin S. McCurley Solving bivariate quadratic congruences
in random polynomial time . . . . . . . 17--28
Richard Blecksmith and
John Brillhart and
Irving Gerst Parity results for certain partition
functions and identities similar to
theta function identities . . . . . . . 29--38
Johannes Buchmann The computation of the fundamental unit
of totally complex quartic orders . . . 39--54
Johannes Buchmann and
H. C. Williams On principal ideal testing in totally
complex quartic fields and the
determination of certain cyclotomic
constants . . . . . . . . . . . . . . . 55--66
Nicholas Buck and
Lones Smith and
Blair K. Spearman and
Kenneth S. Williams The Cyclotomic Numbers of Order Fifteen.
With Microfiche Supplement . . . . . . . 67--83
Duncan A. Buell Class Groups of Quadratic Fields. II . . 85--93
David G. Cantor Computing in the Jacobian of a
Hyperelliptic Curve . . . . . . . . . . 95--101
H. Cohen and
A. K. Lenstra Implementation of a New Primality Test 103--121, S1--S4
H. Cohen and
J. Martinet Class Groups of Number Fields: Numerical
Heuristics . . . . . . . . . . . . . . . 123--137
Harvey Cohn and
Jesse Deutsch Application of symbolic manipulation to
Hecke transformations of modular forms
in two variables . . . . . . . . . . . . 139--146
T. W. Cusick and
Lowell Schoenfeld A table of fundamental pairs of units in
totally real cubic fields . . . . . . . 147--158
Daniel Gordon and
Douglas Grenier and
Audrey Terras Hecke Operators and the Fundamental
Domain for $ \mathrm {SL}(3, \mathbf
{Z}) $ . . . . . . . . . . . . . . . . . 159--178
Marie-Nicole Gras Special Units in Real Cyclic Sextic
Fields . . . . . . . . . . . . . . . . . 179--182
R. K. Guy and
C. B. Lacampagne and
J. L. Selfridge Primes at a Glance . . . . . . . . . . . 183--202
Neal Koblitz Elliptic Curve Cryptosystems . . . . . . 203--209
D. H. Lehmer and
Emma Lehmer Cyclotomic Resultants . . . . . . . . . 211--216
H. W. Lenstra, Jr. and
R. J. Schoof Primitive Normal Bases for Finite Fields 217--231
R. A. Mollin Class numbers of quadratic fields
determined by solvability of Diophantine
equations . . . . . . . . . . . . . . . 233--242
Peter L. Montgomery Speeding the Pollard and elliptic curve
methods of factorization . . . . . . . . 243--264
Morris Newman and
Robert C. Thompson Numerical Values of Goldberg's
Coefficients in the Series for $ \log
(e^x e^y) $. With Microfiche Supplement 265--271
A. M. Odlyzko On the distribution of spacings between
zeros of the zeta function . . . . . . . 273--308
M. Pohst On Computing Isomorphisms of Equation
Orders . . . . . . . . . . . . . . . . . 309--314
Carl Pomerance Very Short Primality Proofs . . . . . . 315--322
Herman J. J. te Riele On the Sign of the Difference $ \pi (x)
- \mathrm {li}(x) $ . . . . . . . . . . 323--328
Robert D. Silverman The Multiple Polynomial Quadratic Sieve 329--339
Jonathan W. Tanner and
Samuel S. Wagstaff, Jr. New Congruences for the Bernoulli
Numbers . . . . . . . . . . . . . . . . 341--350
Heinz M. Tschöpe and
Horst G. Zimmer Computation of the Néron--Tate height on
elliptic curves . . . . . . . . . . . . 351--370
Lawrence C. Washington Class Numbers of the Simplest Cubic
Fields . . . . . . . . . . . . . . . . . 371--384
H. C. Williams Effective primality tests for some
integers of the forms $ {A5}^n - 1 $ and
$ {A7}^n - 1 $ . . . . . . . . . . . . . 385--403
H. C. Williams and
M. C. Wunderlich On the parallel generation of the
residues for the continued fraction
factoring algorithm . . . . . . . . . . 405--423
Don Zagier Large Integral Points on Elliptic Curves 425--436
N. Costa Pereira Corrigendum: ``Estimates for the
Chebyshev function $ \psi (x) - \theta
(x) $'' [Math. Comp. \bf 44 (1985), no.
169, 211--221, MR 86k:11005] . . . . . . 447--447
Kendall Atkinson and
Alex Bogomolny Supplement to The Discrete Galerkin
Method for Integral Equations . . . . . S11--S15
Eugene C. Gartland, Jr. Supplement to Uniform High-Order
Difference Schemes for a Singularly
Perturbed Two-Point Boundary Value
Problem . . . . . . . . . . . . . . . . S5--S9
T. M. Hagstrom and
H. B. Keller Asymptotic boundary conditions and
numerical methods for nonlinear elliptic
problems on unbounded domains . . . . . 449--470
Winfried Auzinger Defect corrections for multigrid
solutions of the Dirichlet problem in
general domains . . . . . . . . . . . . 471--484
Jukka Saranen Local error estimates for some
Petrov--Galerkin methods applied to
strongly elliptic equations on curves 485--502
Moshe Goldberg and
Eitan Tadmor Convenient stability criteria for
difference approximations of hyperbolic
initial-boundary value problems. II . . 503--520
M. Crouzeix and
V. Thomée The Stability in $ {L}_p $ and $ {W}_p^1
$ of the $ {L}_2$-Projection onto Finite
Element Function Spaces . . . . . . . . 521--532
R. M. M. Mattheij On the computation of solutions of
boundary value problems on infinite
intervals . . . . . . . . . . . . . . . 533--549
Eugene C. Gartland, Jr. Uniform high-order difference schemes
for a singularly perturbed two-point
boundary value problem . . . . . . . . . 551--564, S5--S9
A. Neubauer Finite-dimensional approximation of
constrained Tikhonov-regularized
solutions of ill-posed linear operator
equations . . . . . . . . . . . . . . . 565--583
Sunil Kumar and
Ian H. Sloan A new collocation-type method for
Hammerstein integral equations . . . . . 585--593
Kendall Atkinson and
Alex Bogomolny The discrete Galerkin method for
integral equations . . . . . . . . . . . 595--616, S11--S15
Jean-Paul Berrut and
Manfred R. Trummer Equivalence of Nyström's method and
Fourier methods for the numerical
solution of Fredholm integral equations 617--623
C. J. Gladwin An algorithm for the construction of
optimal methods for the numerical
solution of Volterra integral equations
of the first kind . . . . . . . . . . . 625--632
Maarten de Gee Linear multistep methods for
functional-differential equations . . . 633--649
Youcef Saad On the Lánczos Method for Solving
Symmetric Systems with Several
Right-Hand Sides . . . . . . . . . . . . 651--662
Bahram Nour-Omid and
Beresford N. Parlett and
Thomas Ericsson and
Paul S. Jensen How to Implement the Spectral
Transformation . . . . . . . . . . . . . 663--673
Rong Qing Jia $ L^\infty $-boundedness of $ L^2
$-projections on splines for a multiple
geometric mesh . . . . . . . . . . . . . 675--690
Zhongqi Jing and
Adly T. Fam An algorithm for computing continuous
Chebyshev approximations . . . . . . . . 691--710
C. K. Chui and
K. Jetter and
J. D. Ward Cardinal Interpolation by Multivariate
Splines . . . . . . . . . . . . . . . . 711--724
Giuliana Criscuolo and
Giuseppe Mastroianni On the convergence of an interpolatory
product rule for evaluating Cauchy
principal value integrals . . . . . . . 725--735
Ben Johnsen and
Eldar Straume Counting binary matrices with given row
and column sums . . . . . . . . . . . . 737--750
Péter Kiss and
Bui Minh Phong On a Problem of A. Rotkiewicz . . . . . 751--755
Martin Seysen A probabilistic factorization algorithm
with quadratic forms of negative
discriminant . . . . . . . . . . . . . . 757--780
Kurt Girstmair On invariant polynomials and their
application in field theory . . . . . . 781--797
R. V. Moody and
J. Patera Computation of character decompositions
of class functions on compact semisimple
Lie groups . . . . . . . . . . . . . . . 799--827
J. R. Maclaurin Philip Table errata: ``The symmetrical
Euler-summation formula'' [Math. Sci.
\bf 6 (1981), no. 1, 35--41, MR
82g:40002] . . . . . . . . . . . . . . . 851--851
Stanis\law Lewanowicz Corrigendum: ``Recurrence relations for
hypergeometric functions of unit
argument'' [Math. Comp. \bf 45 (1985),
no. 172, 521--535, MR 86m:33004] . . . . 853--853
François Gramain Corrigendum: ``Computing an arithmetic
constant related to the ring of Gaussian
integers'' [Math. Comp. \bf 44 (1985),
no. 169, 241--250, MR 87a:11028] by
Gramain and M. Weber . . . . . . . . . . 854--854
G. V. Milovanovi\'c Corrigendum: ``Least squares
approximation with constraints'' . . . . 854--854
John P. Coleman and
Russel [sic] A. Smith Supplement to ``The Faber Polynomials
for Circular Sectors'' . . . . . . . . . S1--S4
James H. Bramble and
Joseph E. Pasciak and
Alfred H. Schatz The construction of preconditioners for
elliptic problems by substructuring, II 1--16
Ricardo G. Durán Quasi-optimal estimates for finite
element approximations using Orlicz
norms . . . . . . . . . . . . . . . . . 17--23
C. Johnson and
A. H. Schatz and
L. B. Wahlbin Crosswind smear and pointwise errors in
streamline diffusion finite element
methods . . . . . . . . . . . . . . . . 25--38
Björn Engquist and
Bertil Gustafsson Steady state computations for wave
propagation problems . . . . . . . . . . 39--64
Robert L. Higdon Numerical absorbing boundary conditions
for the wave equation . . . . . . . . . 65--90
Eitan Tadmor The numerical viscosity of entropy
stable schemes for systems of
conservation laws. I . . . . . . . . . . 91--103
Chi-Wang Shu TVB uniformly high-order schemes for
conservation laws . . . . . . . . . . . 105--121
Chi-Wang Shu TVB boundary treatment for numerical
solutions of conservation laws . . . . . 123--134
Stefan P. Spekreijse Multigrid solution of monotone
second-order discretizations of
hyperbolic conservation laws . . . . . . 135--155
Takuya Tsuchiya Discrete solution of the Plateau problem
and its convergence . . . . . . . . . . 157--165
Kenneth Eriksson and
Yi Yong Nie Convergence analysis for a nonsymmetric
Galerkin method for a class of singular
boundary value problems in one space
dimension . . . . . . . . . . . . . . . 167--186
R. Baker Kearfott Abstract Generalized Bisection and a
Cost Bound . . . . . . . . . . . . . . . 187--202
Zheng Yan Piecewise Cubic Curve Fitting Algorithm 203--213
R. C. Mjolsness and
Blair Swartz Some Plane Curvature Approximations . . 215--230
John P. Coleman and
Russell A. Smith The Faber Polynomials for Circular
Sectors . . . . . . . . . . . . . . . . 231--241, S1--S4
U. Banerjee and
L. J. Lardy and
A. Lutoborski Asymptotic expansions of integrals of
certain rapidly oscillating functions 243--249
Klaus-Jürgen Förster On Weight Functions Admitting Chebyshev
Quadrature . . . . . . . . . . . . . . . 251--258
G. E. Okecha Quadrature formulae for Cauchy principal
value integrals of oscillatory kind . . 259--268
J. L. Lavoie Some Summation Formulas for the Series
$_3 {F}_2 (1)$ . . . . . . . . . . . . . 269--274
Basil J. Stoyanov and
Richard A. Farrell On the Asymptotic Evaluation of $
\int^{\pi / 2}_0 {J}^2_0 (\gamma \sin x)
d x $ . . . . . . . . . . . . . . . . . 275--279
R. Ernvall and
T. Metsänkylä A method for computing the Iwasawa $
\lambda $-invariant . . . . . . . . . . 281--294
Juergen M. Cherubini and
Rolf V. Wallisser On the computation of all imaginary
quadratic fields of class number one . . 295--299
Hans-Georg Rück A Note on Elliptic Curves Over Finite
Fields . . . . . . . . . . . . . . . . . 301--304
B. C. Carlson Supplement to A Table of Elliptic
Integrals of the Second Kind . . . . . . S13--S17
Helmut Gfrerer Supplement to An A Posteriori Parameter
Choice for Ordinary and Iterated
Tikhonov Regularization of Ill-Posed
Problems Leading to Optimal Convergence
Rates . . . . . . . . . . . . . . . . . S5--S12
James H. Bramble and
Joseph E. Pasciak New Convergence Estimates for Multigrid
Algorithms . . . . . . . . . . . . . . . 311--329
Claes Johnson and
Stig Larsson and
Vidar Thomée and
Lars B. Wahlbin Error estimates for spatially discrete
approximations of semilinear parabolic
equations with nonsmooth initial data 331--357
Michel Crouzeix and
Vidar Thomée On the discretization in time of
semilinear parabolic equations with
nonsmooth initial data . . . . . . . . . 359--377
Georges H. Guirguis A third-order boundary condition for the
exterior Stokes problem in three
dimensions . . . . . . . . . . . . . . . 379--389
Zhong Ci Shi The F--E--M test for convergence of
nonconforming finite elements . . . . . 391--405
G. H. Cottet Convergence of a vortex in cell method
for the two-dimensional Euler equations 407--425
Claes Johnson and
Anders Szepessy On the convergence of a finite element
method for a nonlinear hyperbolic
conservation law . . . . . . . . . . . . 427--444
Daniel Michelson Convergence Theorem for Difference
Approximations of Hyperbolic
Quasi-Initial-Boundary Value Problems 445--459
Martin Costabel and
Ernst P. Stephan On the convergence of collocation
methods for boundary integral equations
on polygons . . . . . . . . . . . . . . 461--478
Goong Chen and
Ying-Liang Tsai The boundary element numerical method
for two-dimensional linear quadratic
elliptic problems. I. Neumann control 479--498
C. W. Groetsch and
C. R. Vogel Asymptotic theory of filtering for
linear operator equations with discrete
noisy data . . . . . . . . . . . . . . . 499--506
Helmut Gfrerer An a posteriori parameter choice for
ordinary and iterated Tikhonov
regularization of ill-posed problems
leading to optimal convergence rates . . 507--522, S5--S12
Chien-Cheng Chang Numerical solution of stochastic
differential equations with constant
diffusion coefficients . . . . . . . . . 523--542
A. Iserles and
S. P. Nòrsett Two-Step Methods and Bi-Orthogonality 543--552
U. Ananthakrishnaiah $ {P}$-stable Obrechkoff methods with
minimal phase-lag for periodic initial
value problems . . . . . . . . . . . . . 553--559
Nabil R. Nassif Eigenvalue finite difference
approximations for regular and singular
Sturm--Liouville problems . . . . . . . 561--580
J. Stoer and
R. A. Tapia On the characterization of
$q$-superlinear convergence of
quasi-Newton methods for constrained
optimization . . . . . . . . . . . . . . 581--584
R. M. Dudley Some Inequalities for Continued
Fractions . . . . . . . . . . . . . . . 585--593
B. C. Carlson A Table of Elliptic Integrals of the
Second Kind . . . . . . . . . . . . . . 595--606, S13--S17
Philip W. Kuchel and
Brian T. Bulliman and
Edward D. Fackerell Bi-cyclide and flat-ring cyclide
coordinate surfaces: correction of two
expressions . . . . . . . . . . . . . . 607--613
Kenneth Hardy and
R. H. Hudson and
D. Richman and
Kenneth S. Williams and
N. M. Holtz Calculation of the class numbers of
imaginary cyclic quartic fields . . . . 615--620
Daniel M. Gordon Perfect Multiple Error-Correcting
Arithmetic Codes . . . . . . . . . . . . 621--633
Duncan A. Buell Integer Squares with Constant Second
Difference . . . . . . . . . . . . . . . 635--644
John Brillhart and
Peter L. Montgomery and
Robert D. Silverman Supplement to Tables of Fibonacci and
Lucas Factorizations . . . . . . . . . . S1--S15
James H. Bramble and
Joseph E. Pasciak A preconditioning technique for
indefinite systems resulting from mixed
approximations of elliptic problems . . 1--17
Stanley Osher and
Eitan Tadmor On the convergence of difference
approximations to scalar conservation
laws . . . . . . . . . . . . . . . . . . 19--51
J. P. Vila High-order schemes and entropy condition
for nonlinear hyperbolic systems of
conservation laws . . . . . . . . . . . 53--73
Gerard R. Richter An optimal-order error estimate for the
discontinuous Galerkin method . . . . . 75--88
Jack K. Hale and
Xiao Biao Lin and
Genevi\`eve Raugel Upper semicontinuity of attractors for
approximations of semigroups and partial
differential equations . . . . . . . . . 89--123
G. A. Chandler and
I. G. Graham Product integration-collocation methods
for noncompact integral operator
equations . . . . . . . . . . . . . . . 125--138
Enrique Fernández-Cara and
Carlos Moreno Critical point approximation through
exact regularization . . . . . . . . . . 139--153
J. E. Dennis, Jr. and
Guang Ye Li A hybrid algorithm for solving sparse
nonlinear systems of equations . . . . . 155--166
Walter Zulehner A simple homotopy method for determining
all isolated solutions to polynomial
systems . . . . . . . . . . . . . . . . 167--177
A. Gerasoulis A Fast Algorithm for the Multiplication
of Generalized Hilbert Matrices with
Vectors . . . . . . . . . . . . . . . . 179--188
Alan Weiser and
Sergio E. Zarantonello A note on piecewise linear and
multilinear table interpolation in many
dimensions . . . . . . . . . . . . . . . 189--196
Thomas A. Grandine The stable evaluation of multivariate
simplex splines . . . . . . . . . . . . 197--205
R. E. Scraton A Comparison of Some Taylor and
Chebyshev Series . . . . . . . . . . . . 207--213
T. Iwaniec and
A. Lutoborski Asymptotic expansions of multiple
integrals of rapidly oscillating
functions . . . . . . . . . . . . . . . 215--228
R. Wong Asymptotic Expansion of $ \int^{\pi /
2}_0 {J}^2_\nu (\lambda \cos \theta) d
\theta $ . . . . . . . . . . . . . . . . 229--234
R. Kannan and
A. K. Lenstra and
L. Lovász Polynomial factorization and
nonrandomness of bits of algebraic and
some transcendental numbers . . . . . . 235--250
John Brillhart and
Peter L. Montgomery and
Robert D. Silverman Tables of Fibonacci and Lucas
Factorizations . . . . . . . . . . . . . 251--260, S1--S15
Jeff Young and
Duncan A. Buell The Twentieth Fermat Number is Composite 261--263
D. H. Lehmer The sum of like powers of the zeros of
the Riemann zeta function . . . . . . . 265--273
David H. Bailey Numerical results on the transcendence
of constants involving $ \pi $, $e$, and
Euler's constant . . . . . . . . . . . . 275--281
David H. Bailey The Computation of $ \pi $ to 29,360,000
Decimal Digits Using Borweins'
Quartically Convergent Algorithm . . . . 283--296
W. F. Lunnon Integer Sets with Distinct Subset-Sums 297--320
Pascual Llorente and
Jordi Quer On the 3-Sylow subgroup of the class
group of quadratic fields . . . . . . . 321--333
Francis J. Rayner Weak Uniform Distribution for Divisor
Functions. I . . . . . . . . . . . . . . 335--342
Anonymous Corrigendum . . . . . . . . . . . . . . 359--359
Kenneth Eriksson and
Claes Johnson An adaptive finite element method for
linear elliptic problems . . . . . . . . 361--383
Sunil Kumar Superconvergence of a collocation-type
method for simple turning points of
Hammerstein equations . . . . . . . . . 385--398
Andrew R. Conn and
Nicholas I. M. Gould and
Philippe L. Toint Testing a class of methods for solving
minimization problems with simple bounds
on the variables . . . . . . . . . . . . 399--430
D. Bini and
V. Pan Efficient Algorithms for the Evaluation
of the Eigenvalues of (Block) Banded
Toeplitz Matrices . . . . . . . . . . . 431--448
James W. Demmel The Probability That a Numerical
Analysis Problem is Difficult . . . . . 449--480
F. W. J. Olver Error Bounds for Linear Recurrence
Relations . . . . . . . . . . . . . . . 481--499
Jean-Francis Loiseau and
Jean-Pierre Codaccioni and
Régis Caboz Hyperelliptic integrals and multiple
hypergeometric series . . . . . . . . . 501--512
Henry L. Gray and
Nien fan Zhang On a New Definition of the Fractional
Difference . . . . . . . . . . . . . . . 513--529
Shu Tezuka On Optimal GFSR Pseudorandom Number
Generators . . . . . . . . . . . . . . . 531--533
Emma Lehmer Connection between Gaussian periods and
cyclic units . . . . . . . . . . . . . . 535--541
René Schoof and
Lawrence C. Washington Quintic Polynomials and Real Cyclotomic
Fields with Large Class Number . . . . . 543--556
Harvey Cohn and
Jesse Deutsch An Explicit Modular Equation in Two
Variables for $ {Q}(\sqrt 3) $ . . . . . 557--568
Johannes Buchmann and
H. C. Williams On the infrastructure of the principal
ideal class of an algebraic number field
of unit rank one . . . . . . . . . . . . 569--579
Pascual Llorente and
Jordi Quer On totally real cubic fields with
discriminant $ {D} < 10^7 $ . . . . . . . 581--594
Francis Buekenhout and
Sarah Rees The subgroup structure of the Mathieu
group $ {M}_{12} $ . . . . . . . . . . . 595--605
E. Seah and
D. R. Stinson On the enumeration of one-factorizations
of complete graphs containing prescribed
automorphism groups . . . . . . . . . . 607--618
A. J. Stephens and
H. C. Williams Some computational results on a problem
concerning powerful numbers . . . . . . 619--632
S. Battiato and
W. Borho Are there odd amicable numbers not
divisible by three . . . . . . . . . . . 633--637
J. H. Knight and
J. R. Philip Table errata: \em Tables of integral
transforms. Vol. 1 [McGraw-Hill, New
York, 1954; MR \bf 15, 868] by A.
Erdélyi, W. Magnus, F. Oberhettinger and
F. G. Tricomi . . . . . . . . . . . . . 653--653
J. H. Knight Table errata: \em Tables of Laplace
transforms [Springer, New York, 1973; MR
\bf 50 #5375] by F. Oberhettinger and L.
Badii . . . . . . . . . . . . . . . . . 653--654
Anonymous Table errata: \em The book of squares
[Academic Press, Boston, Mass., 1987, MR
88m:01021a] by L. P. Fibonacci . . . . . 654--654
Philip Rabinowitz Corrigenda: ``Gauss--Kronrod integration
rules for Cauchy principal value
integrals'' [Math. Comp. \bf 41 (1983),
no. 163, 63--78, MR 84i:65029] . . . . . 655--655
H. C. Williams Corrigenda: ``Computation of the class
number and class group of a complex
cubic field'' [Math. Comp. \bf 45
(1985), no. 171, 223--231, MR 86m:11078]
by G. W. Dueck and Williams . . . . . . 655--657
B. C. Carlson Supplement to A Table of Elliptic
Integrals of the Third Kind . . . . . . S1--S5
I. Babu\vska and
Manil Suri The $p$-version of the finite element
method for constraint boundary
conditions . . . . . . . . . . . . . . . 1--13
Roger Pierre Convergence properties and numerical
approximation of the solution of the
Mindlin plate bending problem . . . . . 15--25
Ricardo H. Nochetto and
Claudio Verdi An efficient linear scheme to
approximate parabolic free boundary
problems: error estimates and
implementation . . . . . . . . . . . . . 27--53
V. Girault Incompressible Finite Element Methods
for Navier--Stokes Equations with
Nonstandard Boundary Conditions in $
{R}^3 $ . . . . . . . . . . . . . . . . 55--74
Klaus Böhmer and
John Locker Asymptotic expansions for the
discretization error of least squares
solutions of linear boundary value
problems . . . . . . . . . . . . . . . . 75--91
Eugene C. Gartland, Jr. An Analysis of a Uniformly Convergent
Finite Difference/Finite Element Scheme
for a Model Singular-Perturbation
Problem . . . . . . . . . . . . . . . . 93--106
Mark A. Lukas Convergence Rates for Regularized
Solutions . . . . . . . . . . . . . . . 107--131
Bernard Bialecki and
Frank Stenger Sinc--Nyström method for numerical
solution of one-dimensional Cauchy
singular integral equation given on a
smooth arc in the complex plane . . . . 133--165
M. Costabel and
V. J. Ervin and
E. P. Stephan On the convergence of collocation
methods for Symm's integral equation on
open curves . . . . . . . . . . . . . . 167--179
Richard Tapia On secant updates for use in general
constrained optimization . . . . . . . . 181--202
Charles K. Chui and
Harvey Diamond and
Louise A. Raphael Interpolation by Multivariate Splines 203--218
Morten Dæhlen and
Tom Lyche Bivariate Interpolation with Quadratic
Box Splines . . . . . . . . . . . . . . 219--230
Walter Gautschi and
Sotirios E. Notaris An algebraic study of Gauss--Kronrod
quadrature formulae for Jacobi weight
functions . . . . . . . . . . . . . . . 231--248
Avram Sidi A user-friendly extrapolation method for
oscillatory infinite integrals . . . . . 249--266
B. C. Carlson A Table of Elliptic Integrals of the
Third Kind . . . . . . . . . . . . . . . 267--280, S1--S5
Jan Bohman and
Carl-Erik Fröberg The Stieltjes function---definition and
properties . . . . . . . . . . . . . . . 281--289
Lucy Garnett A computer algorithm for determining the
Hausdorff dimension of certain fractals 291--300
Richard Blecksmith and
John Brillhart and
Irving Gerst Some Infinite Product Identities . . . . 301--314
P. Erd\Hos and
P. Kiss and
A. Sárközy A Lower Bound for the Counting Function
of Lucas Pseudoprimes . . . . . . . . . 315--323
Pierre Goetgheluck On Prime Divisors of Binomial
Coefficients . . . . . . . . . . . . . . 325--329
Francis J. Rayner Weak uniform distribution for divisor
functions. II . . . . . . . . . . . . . 331--337
Joseph H. Silverman Computing Heights on Elliptic Curves . . 339--358
István Gaál On the resolution of inhomogeneous norm
form equations in two dominating
variables . . . . . . . . . . . . . . . 359--373
Don Zagier Addendum to: ``Large integral points on
elliptic curves'' [Math. Comp. \bf 48
(1987), no. 177, 425--436, MR 87k:11062] 375--375
A. J. Hughes-Hallett Corrigenda: ``The convergence of
accelerated overrelaxation iterations''
[Math. Comp. \bf 47 (1986), no. 175,
219--223, MR 87g:65046] . . . . . . . . 387--387
James H. Bramble and
Joseph E. Pasciak Corrigenda: ``A preconditioning
technique for indefinite systems
resulting from mixed approximations of
elliptic problems'' . . . . . . . . . . 387--388
Kathryn E. Brenan and
Bjorn E. Engquist Supplement to Backward Differentiation
Approximations of Nonlinear
Differential/Algebraic Systems . . . . . S7--S16
James H. Bramble and
Joseph E. Pasciak and
Jin Chao Xu The analysis of multigrid algorithms for
nonsymmetric and indefinite elliptic
problems . . . . . . . . . . . . . . . . 389--414
James H. Bramble and
Joseph E. Pasciak and
Alfred H. Schatz The construction of preconditioners for
elliptic problems by substructuring. III 415--430
Peter A. Markowich and
Milo\vs A. Zlámal Inverse-average-type finite element
discretizations of selfadjoint
second-order elliptic problems . . . . . 431--449
P. B. Monk An iterative finite element method for
approximating the biharmonic equation 451--476
X. Y. Liu and
Y. M. Chen Convergence of a generalized
pulse-spectrum technique (GPST) for
inverse problems of $1$-D diffusion
equations in space-time domain . . . . . 477--489
R. Durán and
R. H. Nochetto and
Jun Ping Wang Sharp maximum norm error estimates for
finite element approximations of the
Stokes problem in 2-D . . . . . . . . . 491--506
C. Chiu and
R. A. Nicolaides Convergence of a higher-order vortex
method for two-dimensional Euler
equations . . . . . . . . . . . . . . . 507--534
Richard Sanders A third-order accurate variation
nonexpansive difference scheme for
single nonlinear conservation laws . . . 535--558
Dalia Fishelov The spectrum and the stability of the
Chebyshev collocation operator for
transonic flow . . . . . . . . . . . . . 559--579
Thomas Hagstrom and
S. I. Hariharan Accurate boundary conditions for
exterior problems in gas dynamics . . . 581--597
D. Funaro and
D. Gottlieb A new method of imposing boundary
conditions in pseudospectral
approximations of hyperbolic equations 599--613
Claudio Canuto Spectral Methods and a Maximum Principle 615--629
Eugene C. Gartland, Jr. Graded-mesh difference schemes for
singularly perturbed two-point boundary
value problems . . . . . . . . . . . . . 631--657
Kathryn E. Brenan and
Björn E. Engquist Backward differentiation approximations
of nonlinear differential/algebraic
systems . . . . . . . . . . . . . . . . 659--676, S7--S16
M. van Veldhuizen Convergence Results for Invariant Curve
Algorithms . . . . . . . . . . . . . . . 677--697
Bengt Fornberg Generation of finite difference formulas
on arbitrarily spaced grids . . . . . . 699--706
Myong-Hi Kim On approximate zeros and rootfinding
algorithms for a complex polynomial . . 707--719
Ping Tak Peter Tang A fast algorithm for linear complex
Chebyshev approximations . . . . . . . . 721--739
Philip Rabinowitz Convergence results for piecewise linear
quadratures for Cauchy principal value
integrals . . . . . . . . . . . . . . . 741--747
Walter Gautschi and
Theodore J. Rivlin A Family of Gauss--Kronrod Quadrature
Formulae . . . . . . . . . . . . . . . . 749--754
G. W. Stewart A Curiosity Concerning the
Representation of Integers in Noninteger
Bases . . . . . . . . . . . . . . . . . 755--756
Jürgen Eichenauer and
Jürgen Lehn and
Alev Topuzo\vglu A nonlinear congruential pseudorandom
number generator with power of two
modulus . . . . . . . . . . . . . . . . 757--759
Gunter Malle Polynomials with Galois Groups $
\operatorname {Aut}({M}_{22}) $, $
{M}_{22} $, and $ \operatorname {PSL}_3
({\mathbb F}_4) \cdot 2_2 $ Over $
{\mathbb Q} $ . . . . . . . . . . . . . 761--768
Shigefumi Mori and
David R. Morrison and
Ian Morrison On Four-Dimensional Terminal Quotient
Singularities . . . . . . . . . . . . . 769--786
Harvey Cohn Fricke's Two-Valued Modular Equations 787--807
A. J. Stephens and
H. C. Williams Computation of real quadratic fields
with class number one . . . . . . . . . 809--824
Noam D. Elkies On $ {A}^4 + {B}^4 + {C}^4 = {D}^4 $ . . 825--835
J. A. Abbott and
J. H. Davenport Another surprising property of $ 42 $. A
remark on a paper by P. S. Wang:
``Factoring multivariate polynomials
over algebraic number fields'' [Math.
Comp. \bf 30 (1976), no. 134, 324--336,
MR \bf 58 #27887a] . . . . . . . . . . . 837--839
Johannes Buchmann and
Attila Petho Supplement to Computation of Independent
Units in Number Fields by Dirichlet's
Method . . . . . . . . . . . . . . . . . S1--S14
Susanne C. Brenner An optimal-order multigrid method for P1
nonconforming finite elements . . . . . 1--15
M. I. Comodi The Hellan--Herrmann--Johnson method:
some new error estimates and
postprocessing . . . . . . . . . . . . . 17--29
E. P. Stephan and
M. Suri On the convergence of the $p$-version of
the boundary element Galerkin method . . 31--48
A. Bellen and
Z. Jackiewicz and
R. Vermiglio and
M. Zennaro Natural continuous extensions of
Runge--Kutta methods for Volterra
integral equations of the second kind
and their applications . . . . . . . . . 49--63
Ivar Lie and
Syvert P. Nòrsett Superconvergence for Multistep
Collocation . . . . . . . . . . . . . . 65--79
Ian H. Sloan and
James N. Lyness The representation of lattice quadrature
rules as multiple sums . . . . . . . . . 81--94
Giuseppe Mastroianni On the convergence of product formulas
for the evaluation of certain
two-dimensional Cauchy principal value
integrals . . . . . . . . . . . . . . . 95--101
Giovanni Sacchi Landriani and
Hervé Vandeven Polynomial approximation of
divergence-free functions . . . . . . . 103--130
David M. Smith Efficient multiple-precision evaluation
of elementary functions . . . . . . . . 131--134
Harald Niederreiter The serial test for congruential
pseudorandom numbers generated by
inversions . . . . . . . . . . . . . . . 135--144
Jürgen Eichenauer-Herrmann and
Holger Grothe and
Jürgen Lehn On the period length of pseudorandom
vector sequences generated by matrix
generators . . . . . . . . . . . . . . . 145--148
Johannes Buchmann and
Attila Pethö Computation of independent units in
number fields by Dirichlet's method . . 149--159, S1--S14
Johannes Buchmann and
David Ford On the computation of totally real
quartic fields of small discriminant . . 161--174
R. J. Stroeker On Quartic Thue Equations with Trivial
Solutions . . . . . . . . . . . . . . . 175--187
R. Creutzburg and
M. Tasche Parameter determination for complex
number-theoretic transforms using
cyclotomic polynomials . . . . . . . . . 189--200
Eric Bach and
Jeffrey Shallit Factoring with Cyclotomic Polynomials 201--219
Jeff Young and
Aaron Potler First Occurrence Prime Gaps . . . . . . 221--224
François Morain On the $ \operatorname {lcm} $ of the
Differences of Eight Primes . . . . . . 225--229
Daniel M. Gordon On the Number of Elliptic Pseudoprimes 231--245
Laurence A. Bales and
Vassilios A. Dougalis Supplement to Cosine Methods for
Nonlinear Second-Order Hyperbolic
Equations . . . . . . . . . . . . . . . S15--S33
Blair Swartz Supplement to The Second-Order
Sharpening of Blurred Smooth Borders . . S35--S36
A. K. Aziz and
Peter Monk Continuous finite elements in space and
time for the heat equation . . . . . . . 255--274
I. Babu\vska and
J. E. Osborn Finite element-Galerkin approximation of
the eigenvalues and eigenvectors of
selfadjoint problems . . . . . . . . . . 275--297
Laurence A. Bales and
Vassilios A. Dougalis Cosine methods for nonlinear
second-order hyperbolic equations . . . 299--319, S15--S33
Alvin Bayliss and
Yanyan Li and
Cathleen Synge Morawetz Scattering by a Potential Using
Hyperbolic Methods . . . . . . . . . . . 321--338
James H. Bramble and
Joseph E. Pasciak and
Peter H. Sammon and
Vidar Thomée Incomplete iterations in multistep
backward difference methods for
parabolic problems with smooth and
nonsmooth data . . . . . . . . . . . . . 339--367
G. L. Browning and
H.-O. Kreiss Comparison of numerical methods for the
calculation of two-dimensional
turbulence . . . . . . . . . . . . . . . 369--388
Wei Cai and
David Gottlieb and
Chi-Wang Shu Essentially Nonoscillatory Spectral
Fourier Methods for Shock Wave
Calculations . . . . . . . . . . . . . . 389--410
Bernardo Cockburn and
Chi-Wang Shu TVB Runge--Kutta local projection
discontinuous Galerkin finite element
method for conservation laws. II.
General framework . . . . . . . . . . . 411--435
Michel Crouzeix and
Richard S. Falk Nonconforming finite elements for the
Stokes problem . . . . . . . . . . . . . 437--456
Vincenza Del Prete Quadratic Convergence of Vortex Methods 457--470
Randall L. Dougherty and
Alan S. Edelman and
James M. Hyman Nonnegativity-, monotonicity-, or
convexity-preserving cubic and quintic
Hermite interpolation . . . . . . . . . 471--494
Jim Douglas, Jr. and
Jun Ping Wang An absolutely stabilized finite element
method for the Stokes problem . . . . . 495--508
Björn Engquist and
Per Lötstedt and
Björn Sjögreen Nonlinear Filters for Efficient Shock
Computation . . . . . . . . . . . . . . 509--537
P. R. Garabedian Design of a large helical system for
magnetic fusion experiments . . . . . . 539--543
Alex Gelman and
Werner C. Rheinboldt On the computation of finite invariant
sets of mappings . . . . . . . . . . . . 545--551
David Isaacson and
Eli L. Isaacson Comment on A.-P. Calderón's paper: ``On
an inverse boundary value problem'' [in
\em Seminar on Numerical Analysis and
its Applications to Continuum Physics
(Rio de Janeiro, 1980), 65--73, Soc.
Brasil. Mat., Rio de Janeiro, 1980, MR
81k:35160] . . . . . . . . . . . . . . . 553--559
Stephen L. Keeling Galerkin/Runge--Kutta discretizations
for parabolic equations with
time-dependent coefficients . . . . . . 561--586
Marco Mosché Mostrel On some numerical schemes for transonic
flow problems . . . . . . . . . . . . . 587--613
Elbridge Gerry Puckett Convergence of a random particle method
to solutions of the Kolmogorov equation
$ u_t = \nu u_{xx} + u(1 - u) $ . . . . 615--645
Stephen Roberts Convergence of a random walk method for
the Burgers equation . . . . . . . . . . 647--673
Blair Swartz The second-order sharpening of blurred
smooth borders . . . . . . . . . . . . . 675--714, S35--S36
David W. Boyd Supplement to Reciprocal Polynomials
having Small Measure. II . . . . . . . . S1--S5
Richard P. Brent and
Graeme L. Cohen Supplement to A New Lower Bound for Odd
Perfect Numbers . . . . . . . . . . . . S7--S24
James H. Bramble and
Joseph E. Pasciak and
Alfred H. Schatz The construction of preconditioners for
elliptic problems by substructuring. IV 1--24
M. Crouzeix and
V. Thomée and
L. B. Wahlbin Error estimates for spatially discrete
approximations of semilinear parabolic
equations with initial data of low
regularity . . . . . . . . . . . . . . . 25--41
T. Geveci On the convergence of a time
discretization scheme for the
Navier--Stokes equations . . . . . . . . 43--53
Michelle Schatzman and
Michel Bercovier Numerical approximation of a wave
equation with unilateral constraints . . 55--79
W. H. Hundsdorfer and
J. G. Verwer Stability and convergence of the
Peaceman--Rachford ADI method for
initial-boundary value problems . . . . 81--101
Wilhelm Heinrichs Improved Condition Number for Spectral
Methods . . . . . . . . . . . . . . . . 103--119
Vidar Thomée and
Nai Ying Zhang Error estimates for semidiscrete finite
element methods for parabolic
integro-differential equations . . . . . 121--139
Christoph Börgers On the numerical solution of the
regularized Birkhoff equations . . . . . 141--156
P. P. B. Eggermont Uniform error estimates of Galerkin
methods for monotone Abel--Volterra
integral equations on the half-line . . 157--189
George Marsaglia and
Arif Zaman and
John C. W. Marsaglia Numerical solution of some classical
differential-difference equations . . . 191--201
D. J. Evans and
C. Li Determination of the $ {D}^{1 / 2}$-norm
of the SOR iterative matrix for the
unsymmetric case . . . . . . . . . . . . 203--218
Charles K. Chui and
Tian Xiao He On the Dimension of Bivariate
Superspline Spaces . . . . . . . . . . . 219--234
G. Meinardus and
G. Nürnberger and
M. Sommer and
H. Strauss Algorithms for piecewise polynomials and
splines with free knots . . . . . . . . 235--247
Ömer E\ugecio\uglu and
Cetin K. Koc A fast algorithm for rational
interpolation via orthogonal polynomials 249--264
Bernd Fischer and
Lothar Reichel Newton interpolation in Fejér and
Chebyshev points . . . . . . . . . . . . 265--278
P. Rabinowitz and
D. S. Lubinsky Noninterpolatory integration rules for
Cauchy principal value integrals . . . . 279--295
Yuan Xu Weight Functions for Chebyshev
Quadrature . . . . . . . . . . . . . . . 297--302
F. Locher A Family of Generalized Jacobi
Polynomials . . . . . . . . . . . . . . 303--309
J. M. Borwein and
P. B. Borwein On the Mean Iteration $ (a, b)
\leftarrow \big (\frac {a + 3b}{4},
\frac {\sqrt {ab} + b}{2} \big) $ . . . 311--326
B. C. Carlson A Table of Elliptic Integrals: Cubic
Cases . . . . . . . . . . . . . . . . . 327--333
J. F. Loiseau and
J. P. Codaccioni and
R. Caboz Incomplete hyperelliptic integrals and
hypergeometric series . . . . . . . . . 335--342
Lothar Afflerbach and
Rainer Weilbächer The exact determination of rectangle
discrepancy for linear congruential
pseudorandom numbers . . . . . . . . . . 343--354
David W. Boyd Reciprocal Polynomials having Small
Measure. II . . . . . . . . . . . . . . 355--357, S1--S5
David J. Rusin The Cohomology of the Groups of Order $
32 $ . . . . . . . . . . . . . . . . . . 359--385
J. Buchmann and
M. Pohst and
J. von Schmettow On the computation of unit groups and
class groups of totally real quartic
fields . . . . . . . . . . . . . . . . . 387--397
János Pintz and
William L. Steiger and
Endre Szemerédi Infinite sets of primes with fast
primality tests and quick generation of
large primes . . . . . . . . . . . . . . 399--406
Wayne L. McDaniel Some pseudoprimes and related numbers
having special forms . . . . . . . . . . 407--409
H. Dubner A new method for producing large
Carmichael numbers . . . . . . . . . . . 411--414
Ian Miyamoto and
M. Ram Murty Elliptic Pseudoprimes . . . . . . . . . 415--430
Richard P. Brent and
Graeme L. Cohen A New Lower Bound for Odd Perfect
Numbers . . . . . . . . . . . . . . . . 431--437, S7--S24
Landon Curt Noll and
David I. Bell $n$-clusters for $ 1 < n < 7$ . . . . . . 439--444
Ricardo H. Nochetto A stable extrapolation method for
multidimensional degenerate parabolic
problems . . . . . . . . . . . . . . . . 455--470
Milan Miklav\vci\vc Approximations for weakly nonlinear
evolution equations . . . . . . . . . . 471--484
P. Degond and
S. Mas-Gallic The Weighted Particle Method for
Convection-Diffusion Equations. Part 1:
The Case of an Isotropic Viscosity . . . 485--507
P. Degond and
S. Mas-Gallic The Weighted Particle Method for
Convection-Diffusion Equations. Part 2:
The Anisotropic Case . . . . . . . . . . 509--525
Anders Szepessy Convergence of a shock-capturing
streamline diffusion finite element
method for a scalar conservation law in
two space dimensions . . . . . . . . . . 527--545
P. Dutt Stability and convergence of spectral
methods for hyperbolic initial-boundary
value problems . . . . . . . . . . . . . 547--561
Glenn R. Luecke Numerical approximation of minimum norm
solutions of $ K f = g $ for special $
{K} $ . . . . . . . . . . . . . . . . . 563--569
Hermann Brunner Collocation methods for nonlinear
Volterra integro-differential equations
with infinite delay . . . . . . . . . . 571--587
D. D. Ang and
John Lund and
Frank Stenger Complex variable and regularization
methods of inversion of the Laplace
transform . . . . . . . . . . . . . . . 589--608
Ch. Großmann and
H.-G. Roos Uniform Enclosure of High Order for
Boundary Value Problems by Monotone
Discretization . . . . . . . . . . . . . 609--617
Gene H. Golub and
Mark D. Kent Estimates of Eigenvalues for Iterative
Methods . . . . . . . . . . . . . . . . 619--626
J. N. Lyness and
I. H. Sloan Some properties of rank-$2$ lattice
rules . . . . . . . . . . . . . . . . . 627--637
Claude Brezinski Procedures for estimating the error in
Padé approximation . . . . . . . . . . . 639--648
David H. Bailey and
Helaman R. P. Ferguson Numerical results on relations between
fundamental constants using a new
algorithm . . . . . . . . . . . . . . . 649--656
B. A. Troesch The validity of Shapiro's cyclic
inequality . . . . . . . . . . . . . . . 657--664
Jean-Pierre Massias and
Jean-Louis Nicolas and
Guy Robin Effective bounds for the maximal order
of an element in the symmetric group . . 665--678
Johannes Buchmann and
H. C. Williams On the computation of the class number
of an algebraic number field . . . . . . 679--688
I. Gaál and
N. Schulte Computing All Power Integral Bases of
Cubic Fields . . . . . . . . . . . . . . 689--696
Erich Kaltofen and
Heinrich Rolletschek Computing Greatest Common Divisors and
Factorizations in Quadratic Number
Fields . . . . . . . . . . . . . . . . . 697--720
Su Hee Kim and
Carl Pomerance The probability that a random probable
prime is composite . . . . . . . . . . . 721--741
Jonathan W. Tanner and
Samuel S. Wagstaff, Jr. New bound for the first case of Fermat's
last theorem . . . . . . . . . . . . . . 743--750
Günter Löh Long Chains of Nearly Doubled Primes . . 751--759
François Morain Corrigenda: ``On the $ \operatorname
{lcm} $ of the differences of eight
primes'' [Math. Comput. 52 (1989), no.
185, 225--229] . . . . . . . . . . . . . 911--911
Peter Shiu Corrigendum to ``Counting sums of two
squares: the Meissel--Lehmer method'' 2935--2938