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Mervin E. Muller A Note on a Method for Generating Points
Uniformly on $N$-Dimensional Spheres . . 19--20
Preston C. Hammer and
Howard H. Wicke Quadrature Formulas Involving
Derivatives of the Integrand . . . . . . 3--7
George Struble Tables for Use in Quadrature Formulas
Involving Derivatives of the Integrand 8--12
J. C. P. Miller Numerical Quadrature Over a Rectangular
Domain in Two or More Dimensions: Part
1. Quadrature over a Square, Using up to
Sixteen Equally Spaced Points . . . . . 13--20
A. H. Stroud Numerical Integration Formulas of Degree
Two . . . . . . . . . . . . . . . . . . 21--26
Thomas S. Walton and
Harry Polachek Calculation of Transient Motion of
Submerged Cables . . . . . . . . . . . . 27--46
Philip Rabinowitz Abscissas and Weights for Lobatto
Quadrature of High Order . . . . . . . . 47--52
I. M. Longman A Method for the Numerical Evaluation of
Finite Integrals of Oscillatory
Functions . . . . . . . . . . . . . . . 53--59
Joseph Gillis and
George Weiss Products of Laguerre Polynomials . . . . 60--63
F. L. Bauer The Formula-Controlled Logical Computer
``Stanislaus'' (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 64--67
Chih-Bing Ling Evaluation at Half Periods of
Weierstrass' Elliptic Function With
Rectangular Primitive
Period-Parallelogram . . . . . . . . . . 67--70
Raymond B. Killgrove A Note on the Nonexistence of Certain
Projective Planes of Order Nine . . . . 70--71
Robert W. Floyd A Note on Rational Approximation . . . . 72--73
K. R. Isemanger The Complete Factorization of $2^{132} +
1$ . . . . . . . . . . . . . . . . . . . 73--74
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 75--95
A. S. Householder Book Review: L. V. Kantorovich & V. I.
Krylov, \booktitleApproximate Methods of
Higher Analysis, Translated from the
third Russian edition by Curtis D.
Benster, Interscience Publishers, Inc.,
New York, 1958, xv + 681 p., 24 cm.
Price \$17.00} . . . . . . . . . . . . . 90--91
Anonymous Table Erratum . . . . . . . . . . . . . 96--96
Anonymous Corrigenda . . . . . . . . . . . . . . . 97--97
J. D. Swift Construction of Galois Fields of
Characteristic Two and Irreducible
Polynomials . . . . . . . . . . . . . . 99--103
Stig Comet Improved Methods to Calculate the
Characters of the Symmetric Group . . . 104--117
E. T. Kirkpatrick Tables of Values of the Modified Mathieu
Functions . . . . . . . . . . . . . . . 118--129
J. C. P. Miller Numerical Quadrature over a Rectangular
Domain in Two or More Dimensions . . . . 130--138
Arnold N. Lowan On the Propagation of Round-Off Errors
in the Numerical Integration of the Heat
Equation . . . . . . . . . . . . . . . . 139--146
Peter Wynn The Rational Approximation of Functions
which are Formally Defined by a Power
Series Expansion . . . . . . . . . . . . 147--186
I. M. Longman On the Utility of Newton's Method for
Computing Complex Roots of Equations (in
Technical Notes and Short Papers) . . . 187--189
Gordon Pall and
Esther Seiden A Problem in Abelian Groups, with
Application to the Transposition of a
Matrix on an Electronic Computer (in
Technical Notes and Short Papers) . . . 189--192
Charles Walmsley and
Arthur S. G. Grant The Fourier Transform of $\lbrack c^{2k}
+ (x - x^{-1})^{2k} \rbrack^{-1}$
Arising from Study of Tuned Circuit
Spectra (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 193--195
H. A. Lang On the Evaluation of Certain Complex
Elliptic Integrals (in Technical Notes
and Short Papers) . . . . . . . . . . . 195--199
D. Scheffler and
R. Ondrejka The Numerical Evaluation of the
Eighteenth Perfect Number (in Technical
Notes and Short Papers) . . . . . . . . 199--200
Daniel Shanks A Note on Gaussian Twin Primes (in
Technical Notes and Short Papers) . . . 201--203
Anonymous Corrigenda . . . . . . . . . . . . . . . 222--222
Arnold N. Lowan On the Propagation of Round-Off Errors
in the Numerical Treatment of the Wave
Equation . . . . . . . . . . . . . . . . 223--228
Michael Goldberg Rotors in Polygons and Polyhedra . . . . 229--239
J. C. P. Miller Numerical Quadrature Over a Rectangular
Domain in Two or More Dimensions. Part
3: Quadrature of a Harmonic Integrand 240--248
Milton E. Rose A Method for Calculating Solutions of
Parabolic Equations with a Free Boundary 249--256
Herbert E. Salzer Alternative Formulas for Osculatory and
Hyperosculatory Inverse Interpolation 257--261
Paul J. Nikolai Permanents of Incidence Matrices (in
Technical Notes and Short Papers) . . . 262--266
Arnold N. Lowan On the Numerical Treatment of Heat
Conduction Problems with Mixed Boundary
Conditions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 266--270
I. E. Perlin and
J. R. Garrett High Precision Calculation of
$\operatorname{Arcsin} x$,
$\operatorname{Arccos} x$, and
$\operatorname{Arctan} x$ (in Technical
Notes and Short Papers) . . . . . . . . 270--274
A. Rotenberg The Calculation of Toroidal Harmonics
(in Technical Notes and Short Papers) 274--276
J. R. M. Radok Transcendental Equation for the
Schrödinger Equation (in Technical Notes
and Short Papers) . . . . . . . . . . . 276--278
A. Gloden A Note on Factors of $n^4 + 1$ (in
Technical Notes and Short Papers) . . . 278--279
Herbert E. Salzer A Note on the Solution of Quartic
Equations (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 279--281
D. A. Magula A Conjugate Factor Method for the
Solution of a Cubic (in Technical Notes
and Short Papers) . . . . . . . . . . . 281--283
Anonymous Corrigendum . . . . . . . . . . . . . . 310--310
R. Sherman Lehman On Liouville's Function . . . . . . . . 311--320
Daniel Shanks On the Conjecture of Hardy & Littlewood
concerning the ``Number of Primes of the
Form $n^2 + a$'' . . . . . . . . . . . . 321--332
Arnold N. Lowan On the Propagation of Errors in the
Inversion of Certain Tridiagonal
Matrices . . . . . . . . . . . . . . . . 333--338
Daniel C. Fielder Tabulation of Coefficients for
Operations on Taylor Series . . . . . . 339--345
Marcia Ascher Explicit Solutions of the
One-Dimensional Heat Equation for a
Composite Wall . . . . . . . . . . . . . 346--353
David A. Pope A Method of ``Alternating Corrections''
for the Numerical Solution of Two-Point
Boundary Value Problems . . . . . . . . 354--361
E. Dempsey and
G. C. Benson Note on the Asymptotic Expansion of the
Modified Bessel Function of the Second
Kind (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 362--365
John Brillhart and
G. D. Johnson On the Factors of Certain Mersenne
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 365--369
John W. Wrench, Jr. Further Evaluation of Khintchine's
Constant (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 370--371
H. E. Fettis Note on $\int\sp \infty\sb 0 e\sp{-x}
{J}\sb 0 \left(\frac{\eta
x}{\epsilon}\right) {J}\sb
1\left(\frac{x}{\epsilon}\right)
x\sp{-n} dx$ . . . . . . . . . . . . . . 372--374
Henry E. Fettis Note on $\int^\infty_0 e^{-x}{J}_0
\Big(\frac{\eta x}{\xi}\Big) {J}_1
\Big(\frac{x}{\xi}\Big) x^{-n} dx$ (in
Technical Notes and Short Papers) . . . 372--374
R. D. Lord Integrals of Products of Laguerre
Polynomials (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 375--376
Irwin Greenberg The Evaluation of Certain Probability
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 376--378
Sidney Kravitz The Congruence $2^{p-1} \equiv 1
(\operatorname{mod} p^2) \text{for} p <
100,000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 378--378
Kasaburo Harumi and
Shigetoshi Katsura and
John W. Wrench, Jr. Values of $\frac{2}{\pi} \int^\infty_0
\Big(\frac{\sin t}{t}\Big)^n dt$ (in
Technical Notes and Short Papers) . . . 379--379
J. Boersma Computation of Fresnel Integrals (in
Technical Notes and Short Papers) . . . 380--380
George Shortley Book Review: \em The $3$-j and $6$-j
Symbols, by Manuel Rotenberg, R. Bivins,
N. Metropolis, and John K. Wooten, Jr. 382--383
O. Shisha The Chebyshev polynomial of best
approximation to a given function on an
interval . . . . . . . . . . . . . . . . 266--271
Murlan S. Corrington Applications of the Complex Exponential
Integral . . . . . . . . . . . . . . . . 1--6
Richard Barakat Evaluation of the Incomplete Gamma
Function of Imaginary Argument by
Chebyshev Polynomials . . . . . . . . . 7--11
C. W. Nelson New Tables of Howland's and Related
Integrals . . . . . . . . . . . . . . . 12--18
Gilbert C. Best Two Theorem Tables of Matrix Algebra . . 19--22
Herbert E. Salzer and
Genevieve M. Kimbro Improved Formulas for Complete and
Partial Summation of Certain Series . . 23--39
Henry Stone Approximation of Curves by Line Segments 40--47
F. C. Ledsham Numerical Integration Using Sums of
Exponential Functions (in Technical
Notes and Short Papers) . . . . . . . . 48--51
Edgar Karst New Factors of Mersenne Numbers (in
Technical Notes and Short Papers) . . . 51--51
A. H. Stroud A Bibliography on Approximate
Integration (in Surveys and Expository
Papers) . . . . . . . . . . . . . . . . 52--80
Anonymous Corrigenda . . . . . . . . . . . . . . . 113--114
William J. Kammerer Polynomial Approximations to Finitely
Oscillating Functions . . . . . . . . . 115--119
Herbert E. Salzer and
Norman Levine Table of a Weierstrass Continuous
Non-Differentiable Function . . . . . . 120--130
J. G. Jones On the Numerical Solution of Convolution
Integral Equations and Systems of Such
Equations . . . . . . . . . . . . . . . 131--142
A. H. Stroud Numerical Integration Formulas of Degree
$3$ for Product Regions and Cones . . . 143--150
P. Wynn The Epsilon Algorithm and Operational
Formulas of Numerical Analysis . . . . . 151--158
A. M. Arthurs and
R. McCarroll Expansion of Spherical Bessel Functions
in a Series of Chebyshev Polynomials . . 159--162
Harry A. Rothmann Gaussian Quadrature with Weight Function
$x^n$ on the Interval $(-1, 1)$ . . . . 163--168
Harry Weingarten and
A. R. Di Donato A Table of Generalized Circular Error 169--173
Jet Wimp Polynomial Approximations to Integral
Transforms . . . . . . . . . . . . . . . 174--178
Arnold N. Lowan On Stability Criteria of Explicit
Difference Schemes for Certain Heat
Conduction Problems with Uncommon
Boundary Conditions . . . . . . . . . . 179--185
Daniel Shanks On Numbers of the Form $n^4 + 1$ . . . . 186--189
Henry B. Mann On Modular Computation (in Technical
Notes and Short Papers) . . . . . . . . 190--192
Mark B. Wells Generation of Permutations by
Transposition (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 192--195
Helmut Werner and
Robert Collinge Chebyshev Approximations to the Gamma
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 195--197
J. C. Butcher A Partition Test for Pseudo-Random
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 198--199
Anonymous Corrigenda . . . . . . . . . . . . . . . 225--225
Walter Gautschi Recursive Computation of the Repeated
Integrals of the Error Function . . . . 227--232
Yudell L. Luke and
Richard L. Coleman Expansion of Hypergeometric Functions in
Series of Other Hypergeometric Functions 233--237
A. R. Mitchell Solution of the von Mises Boundary Layer
Equation Using a High-Speed Computer . . 238--242
M. M. Pennell and
L. M. Delves The Numerical Solution of Coupled
Integro-Differential Equations . . . . . 243--249
Hidehiko Yamabe and
David Pope A Computational Approach to the
Four-Color Problem . . . . . . . . . . . 250--253
Jack Levine Some Applications of High-Speed
Computers to the Case $n = 2$ of
Algebraic Cryptography . . . . . . . . . 254--260
L. Filler and
H. F. Ludloff Stability Analysis and Integration of
the Viscous Equations of Motion . . . . 261--274
A. Lazarkiewicz and
W. Balasinski A Simple Experimental Computer with
Negative Basis . . . . . . . . . . . . . 275--285
Stephen M. Robinson and
A. H. Stroud The Approximate Solution of an Integral
Equation Using High-Order Gaussian
Quadrature Formulas (in Technical Notes
and Short Papers) . . . . . . . . . . . 286--288
Ferdinand Freudenstein Bi-Variate, Rectangular,
Optimum-Interval Interpolation (in
Technical Notes and Short Papers) . . . 288--291
Sidney Kravitz Divisors of Mersenne Numbers $10,000 < p <
15,000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 292--293
R. T. Ostrowski and
K. D. Van Duren On a Theorem of Mann on Latin Squares
(in Technical Notes and Short Papers) 293--295
K. R. Isemonger Complete Factorization of $2^{159} - 1$
(in Technical Notes and Short Papers) 295--296
J. Boersma Two Formulas Relating to Elliptic
Integrals of the Third Kind (in
Technical Notes and Short Papers) . . . 296--298
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 299--318
A. S. Householder Book Review: A. Korganoff, with the
collaboration of L. Bossett, J. L.
Groboillot & J. Johnson,
\booktitleMéthodes de Calcul Numérique,
Tome I: Alg\`ebre non linéaire, Dunod,
Paris, 1961, xxvii + 375 p., 25 cm.
Price 58 NF . . . . . . . . . . . . . . 312--313
Anonymous Table Errata . . . . . . . . . . . . . . 319--321
C. B. Haselgrove A Method for Numerical Integration . . . 323--337
Feodor Theilheimer and
William Starkweather The Fairing of Ship Lines on a
High-Speed Computer . . . . . . . . . . 338--355
G. J. Habetler and
E. L. Wachspress Symmetric Successive Overrelaxation In
Solving Diffusion Difference Equations 356--362
J. W. Cooley An Improved Eigenvalue Corrector Formula
for Solving the Schrödinger Equation for
Central Fields . . . . . . . . . . . . . 363--374
A. R. DiDonato and
M. P. Jarnagin Integration of the General Bivariate
Gaussian Distribution over an Offset
Circle . . . . . . . . . . . . . . . . . 375--382
Martin Greenberger An a Priori Determination of Serial
Correlation in Computer Generated Random
Numbers . . . . . . . . . . . . . . . . 383--389
Jerry L. Fields and
Jet Wimp Expansions of Hypergeometric Functions
in Hypergeometric Functions . . . . . . 390--395
John W. Wrench, Jr. Evaluation of Artin's Constant and the
Twin-Prime Constant . . . . . . . . . . 396--398
Henry C. Thacher, Jr. Iterated Square Root Expansions for the
Inverse Cosine and Inverse Hyperbolic
Cosine . . . . . . . . . . . . . . . . . 399--403
J. S. Dranoff An Eigenvalue Problem Arising In Mass
and Heat Transfer Studies . . . . . . . 403--409
Kurt Spielberg Efficient Continued Fraction
Approximations To Elementary Functions 409--417
N. Ream Note on ``Approximation of Curves by
Line Segments'' . . . . . . . . . . . . 418--419
G. A. Paxson The Compositeness of the Thirteenth
Fermat Number . . . . . . . . . . . . . 420--420
Anonymous Corrigenda . . . . . . . . . . . . . . . 436--436
J. Kampe de Feriet and
François N. Frenkiel Correlations and Spectra for
Non-Stationary Random Functions . . . . 1--21
Arnold Nordsieck On Numerical Integration of Ordinary
Differential Equations . . . . . . . . . 22--49
J. Gillis and
M. Shimshoni Triple Product Integrals of Laguerre
Functions . . . . . . . . . . . . . . . 50--62
V. D. Barnett The Behavior of Pseudo-Random Sequences
Generated on Computers by the
Multiplicative Congruential Method . . . 63--69
Milton Lees A Note on the Convergence of Alternating
Direction Methods . . . . . . . . . . . 70--75
Daniel Shanks and
John W. Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals 76--99
T. Tamir Characteristic Exponents of Mathieu
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 100--106
Robert D. Stalley An Algorithm for Solving Certain
Polynomial Equations with Coefficient
Parameters (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 106--109
Bernard Epstein A Remark Concerning the Solution of the
Dirichlet Problem by Finite Differences
(in Technical Notes and Short Papers) 110--112
Anonymous Corrigenda . . . . . . . . . . . . . . . 126--126
Harvey Cohn A Numerical Study of the Relative Class
Numbers of Real Quadratic Integral
Domains . . . . . . . . . . . . . . . . 127--140
D. G. Cantor and
G. Estrin and
A. S. Fraenkel and
R. Turn A Very High-Speed Digital Number Sieve 141--154
R. P. Pearce and
A. R. Mitchell On Finite Difference Methods of Solution
of the Transport Equation . . . . . . . 155--169
W. M. Harper Quadrature Formulas for Infinite
Integrals . . . . . . . . . . . . . . . 170--175
E. K. Blum A Modification of the Runge--Kutta
Fourth-Order Method . . . . . . . . . . 176--187
R. K. Pathria A Statistical Study of Randomness Among
the First $10,000$ Digits of $\pi$ . . . 188--197
John F. Bridge and
Stanley W. Angrist An Extended Table of Roots of ${J}_n'(x)
{Y}_n'(\beta x) - {J}_n'(\beta x)
{Y}_n'(x) = 0$ . . . . . . . . . . . . . 198--204
Kurt Spielberg Polynomial and Continued-Fraction
Approximations for Logarithmic Functions 205--217
H. S. Shapiro Some Remarks on Modular Arithmetic and
Parallel Computation (in Technical Notes
and Short Papers) . . . . . . . . . . . 218--222
Frank Harary Permutations with Restricted Position
(in Technical Notes and Short Papers) 222--226
L. Jackson Laslett and
William Lewish Evaluation of the Zeros of Cross-Product
Bessel Functions (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 226--232
J. Boersma On the Computation of Lommel's Functions
of Two Variables (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 232--238
A. Gloden Additions to Cunningham's Factor Table
of $n^4 + 1$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 239--241
Gary Lotto On the Generation of All Possible
Stepwise Combinations (in Technical
Notes and Short Papers) . . . . . . . . 241--243
John R. Howell Generation of Permutations by Addition
(in Technical Notes and Short Papers) 243--244
Herbert E. Salzer Multiple Quadrature with Central
Differences on One Line (in Technical
Notes and Short Papers) . . . . . . . . 244--248
Alexander Hurwitz New Mersenne Primes (in Technical Notes
and Short Papers) . . . . . . . . . . . 249--251
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 252--260
G. Miller Clark Corrections to Mervin E. Muller, \em A
Note on a Method for Generating Points
Uniformly on $N$-Dimensional Spheres . . 261--261
Anonymous Corrigenda . . . . . . . . . . . . . . . 262--263
Eldon R. Hansen and
Merrell L. Patrick Some Relations and Values for the
Generalized Riemann Zeta Function . . . 265--274
Donald E. Knuth Euler's Constant to $1271$ Places . . . 275--281
W. Fraser and
C. C. Gotlieb A Calculation of the Number of Lattice
Points in the Circle and Sphere . . . . 282--290
K. M. Brown and
P. Henrici Sign Wave Analysis in Matrix Eigenvalue
Problems . . . . . . . . . . . . . . . . 291--300
P. Wynn Acceleration Techniques for Iterated
Vector and Matrix Problems . . . . . . . 301--322
J. Schröder Computing Error Bounds in Solving Linear
Systems . . . . . . . . . . . . . . . . 323--337
M. R. Osborne A Note on Finite Difference Methods for
Solving the Eigenvalue Problems of
Second-Order Differential Equations . . 338--346
A. R. DiDonato and
M. P. Jarnagin A Method for Computing the Circular
Coverage Function . . . . . . . . . . . 347--355
Herbert E. Salzer Optimum-Point Formulas for Osculatory
and Hyperosculatory Interpolation . . . 356--362
Paul T. Bateman and
Roger A. Horn A Heuristic Asymptotic Formula
Concerning the Distribution of Prime
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 363--367
E. J. Watson Primitive polynomials (mod $2$) . . . . 368--369
E. J. Watson Primitive Polynomials
$(\operatorname{Mod} 2)$ (in Technical
Notes and Short Papers) . . . . . . . . 368--369
H. H. Denman and
R. C. W. Ettinger Note on Latent Roots and Vectors of
Segments of the Hilbert Matrix (in
Technical Notes and Short Papers) . . . 370--371
Y. K. Lin and
F. A. Lee Expansions of Jacobian Elliptic
Functions in Powers of the Modulus (in
Technical Notes and Short Papers) . . . 372--375
Anonymous Corrigendum . . . . . . . . . . . . . . 406--406
D. H. Lehmer and
E. Lehmer and
W. H. Mills and
J. L. Selfridge Machine Proof of a Theorem on Cubic
Residues . . . . . . . . . . . . . . . . 407--415
Jack Levine and
R. E. Dalton Minimum Periods, Modulo $p$, of
First-Order Bell Exponential Integers 416--423
John Brillhart Concerning the Numbers $2^{2p} + 1, p$
Prime . . . . . . . . . . . . . . . . . 424--430
Anthony Ralston Runge--Kutta Methods with Minimum Error
Bounds . . . . . . . . . . . . . . . . . 431--437
Gene H. Golub Bounds for Eigenvalues of Tridiagonal
Symmetric Matrices Computed by the LR
Method . . . . . . . . . . . . . . . . . 438--445
Jet Wimp Polynomial Expansions of Bessel
Functions and Some Associated Functions 446--458
S. Muroga and
I. Toda and
M. Kondo Majority Decision Functions of up to Six
Variables . . . . . . . . . . . . . . . 459--472
R. Bellman and
B. Kotkin On the Numerical Solution of a
Differential-Difference Equation Arising
in Analytic Number Theory (in Technical
Notes and Short Papers) . . . . . . . . 473--475
L. Carlitz The Coefficients of the Lemniscate
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 475--478
H. Riesel All Factors $q < 10^8$ in All Mersenne
Numbers $2^p - 1, p \text{Prime} < 10^4$
(in Technical Notes and Short Papers) 478--482
M. Wunderlich Certain Properties of Pyramidal and
Figurate Numbers (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 482--486
Herbert E. Salzer Note on Osculatory Rational
Interpolation (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 486--491
Charlotte Froese On Solving $y'' = fy + g$ with a
Boundary Condition at Infinity (in
Technical Notes and Short Papers) . . . 492--494
A. L. Dulmage and
N. S. Mendelsohn On the Inversion of Sparse Matrices (in
Technical Notes and Short Papers) . . . 494--496
R. I. Jennrich Missing Data Correlation Computations
(in Technical Notes and Short Papers) 496--497
F. D. Burgoyne Polynomial Approximations to ${I}_0(x),
{I}_1(x)$ and Related Functions (in
Technical Notes and Short Papers) . . . 497--498
F. D. Burgoyne A Note on the Curve Fitting of Discrete
Data by Economization (in Technical
Notes and Short Papers) . . . . . . . . 498--499
Anonymous Corrigendum . . . . . . . . . . . . . . 513--513
W. V. Petryshyn On a General Iterative Method for the
Approximate Solution of Linear Operator
Equations . . . . . . . . . . . . . . . 1--10
John R. B. Whittlesey Incomplete Gamma Functions for
Evaluating Erlang Process Probabilities 11--17
J. Descloux Note on the Round-Off Errors in
Iterative Processes . . . . . . . . . . 18--27
Joel N. Franklin Deterministic Simulation of Random
Processes . . . . . . . . . . . . . . . 28--59
H. Polachek and
T. S. Walton and
R. Mejia and
C. Dawson Transient Motion of an Elastic Cable
Immersed in a Fluid . . . . . . . . . . 60--63
J. N. Newman and
W. Frank An Integral Containing the Square of a
Bessel Function . . . . . . . . . . . . 64--70
Jim Douglas, Jr. and
James E. Gunn Two High-Order Correct Difference
Analogues for the Equation of
Multidimensional Heat Flow . . . . . . . 71--80
T. A. Porsching Matrix Assignments and an Associated Min
Max Problem (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 81--84
James Miller Formulas for Integrals of Products of
Associated Legendre or Laguerre
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 84--87
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 88--99
A. S. Householder Book Review: John Todd, Editor,
\booktitleA Survey of Numerical
Analysis, McGraw-Hill Book Co., 1962,
23.5 cm., xvi + 589 p. Price \$12.50} 89--89
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 88--99
Anonymous Table Errata . . . . . . . . . . . . . . 100--103
Anonymous Table Errata . . . . . . . . . . . . . . 100--103
Anonymous Corrigenda . . . . . . . . . . . . . . . 104--104
A. H. Stroud and
Don Secrest Approximate Integration Formulas for
Certain Spherically Symmetric Regions 105--135
Daniel Shanks and
John W. Wrench, Jr. The Calculation of Certain Dirichlet
Series . . . . . . . . . . . . . . . . . 136--154
Richard Bellman and
Robert Kalaba and
Bella Kotkin Polynomial Approximation --- a New
Computational Technique in Dynamic
Programming: Allocation Processes . . . 155--161
Thomas Erber and
Alan Gordon Tabulation of the Functions
$\frac{\partial I_\nu(z)}{\partial \nu},
\nu = \pm \frac{1}{3}$ . . . . . . . . . 162--169
Dura W. Sweeney On the Computation of Euler's Constant 170--178
David C. Mapes Fast Method for Computing the Number of
Primes Less than a Given Limit . . . . . 179--185
Gene H. Golub On a Lower Bound for the Rank of a
Partitioned Square Matrix . . . . . . . 186--188
Daniel Shanks Supplementary Data and Remarks
Concerning a Hardy--Littlewood
Conjecture . . . . . . . . . . . . . . . 188--193
H. Werner and
G. Raymann An Approximation to the Fermi Integral
${F}_{1/2}(x)$ . . . . . . . . . . . . . 193--194
Erna H. Pearson On the Congruences $(p - 1)! \equiv - 1$
and $2^{p-1} \equiv (\operatorname{mod}
p^2)$ . . . . . . . . . . . . . . . . . 194--195
F. D. Burgoyne The Non-Existence of Certain
Laguerre--Chebyshev Quadrature Formulas 196--197
Donald W. Grace Search for Largest Polyhedra . . . . . . 197--199
Herbert S. Wilf Calculations Relating to a Conjecture of
Polya and Schoenberg . . . . . . . . . . 200--201
Anonymous Reviews and Descriptions of Tables and
Books . . . . . . . . . . . . . . . . . 202--213
A. S. Householder Book Review: Centre Belge de Recherches
Mathématiques, \booktitleColloque sur
l'Analyse Numérique, Gauthier-Villars,
Paris, 1961, 214 p., 25 cm. . . . . . . 209--210
Anonymous Table Errata . . . . . . . . . . . . . . 214--215
Anonymous Corrigenda . . . . . . . . . . . . . . . 215--215
James H. Bramble Fourth-Order Finite Difference Analogues
of the Dirichlet Problem for Poisson's
Equation in Three and Four Dimensions 217--222
H. B. Keller and
J. R. Swenson Experiments on the Lattice Problem of
Gauss . . . . . . . . . . . . . . . . . 223--230
R. W. Preisendorfer and
B. W. Roos On the Best Fit to Experimental Data
Curves Using Homogeneous Two-Parameter
Functions . . . . . . . . . . . . . . . 231--236
H. H. Michels Abscissas and Weight Coefficients for
Lobatto Quadrature . . . . . . . . . . . 237--244
P. Concus and
D. Cassatt and
G. Jaehnig and
E. Melby Tables for the Evaluation of
$\int^\infty_0 x^\beta e^{-x}f(x) dx$ by
Gauss--Laguerre Quadrature . . . . . . . 245--256
F. Ginsberg On the Cauchy Problem for the
One-Dimensional Heat Equation . . . . . 257--269
D. D. Stancu Evaluation of the Remainder Term in
Approximation Formulas by Bernstein
Polynomials . . . . . . . . . . . . . . 270--278
J. Douglas, Jr. and
R. B. Kellogg and
R. S. Varga Alternating Direction Iteration Methods
for $n$ Space Variables (in Technical
Notes and Short Papers) . . . . . . . . 279--282
Selmer M. Johnson Generation of Permutations by Adjacent
Transposition (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 282--285
R. W. Preisendorfer and
B. W. Roos and
W. C. Sangren Determinants by Means of Solutions of
Linear Equations (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 285--289
A. H. Stroud Coefficients in Quadrature Formulas (in
Technical Notes and Short Papers) . . . 289--291
M. H. McAndrew A Partition Problem (in Technical Notes
and Short Papers) . . . . . . . . . . . 291--295
F. D. Burgoyne Approximations to Kelvin Functions (in
Technical Notes and Short Papers) . . . 295--298
F. D. Burgoyne Quadrature Formulas over Infinite
Intervals in Terms of Differences (in
Technical Notes and Short Papers) . . . 298--301
Anonymous Corrigenda . . . . . . . . . . . . . . . 335--335
Israel Navot The Euler--Maclaurin Functional for
Functions with a Quasi-Step
Discontinuity . . . . . . . . . . . . . 337--345
Bart J. Daly The Stability Properties of a Coupled
Pair of Non-Linear Partial Difference
Equations . . . . . . . . . . . . . . . 346--360
A. D. McLaren Optimal Numerical Integration on a
Sphere . . . . . . . . . . . . . . . . . 361--383
D. D. Stancu and
A. H. Stroud Quadrature Formulas with Simple Gaussian
Nodes and Multiple Fixed Nodes . . . . . 384--394
Y. L. Luke and
J. Wimp Jacobi Polynomial Expansions of a
Generalized Hypergeometric Function over
a Semi-Infinite Ray . . . . . . . . . . 395--404
George W. Batten, Jr. Second-Order Correct Boundary Conditions
for the Numerical Solution of the Mixed
Boundary Problem for Parabolic Equations 405--413
R. Sankar and
V. Malini A Note on the Relative Merits of Padé and
Maehly's Diagonal Convergents in
Computing $e^x$ . . . . . . . . . . . . 414--418
R. E. von Holdt and
R. J. Howerton The Definite Integral of the Product of
Linear Functions . . . . . . . . . . . . 419--425
A. R. Mitchell and
R. P. Pearce Explicit Difference Methods for Solving
the Cylindrical Heat Conduction Equation 426--432
C. Donald La Budde The Reduction of an Arbitrary Real
Square Matrix to Tri-Diagonal Form Using
Similarity Transformations (in Technical
Notes and Short Papers) . . . . . . . . 433--437
J. T. Day A Gaussian Quadrature Method for the
Numerical Solution of the Characteristic
Initial Value Problem $u_{xy} = f(x, y,
u)$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 438--441
George Shapiro Gauss Elimination for Singular Matrices
(in Technical Notes and Short Papers) 441--445
A. Schinzel A Remark on a Paper of Bateman and Horn
(in Technical Notes and Short Papers) 445--447
John Brillhart Some Miscellaneous Factorizations (in
Technical Notes and Short Papers) . . . 447--450
S. R. Cavior A Note on Octic Permutation Polynomials
(in Technical Notes and Short Papers) 450--452
A. C. R. Newbery Multistep Integration Formulas (in
Technical Notes and Short Papers) . . . 452--455
M. Wunderlich On the Non-Existence of Fibonacci
Squares (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 455--457
Hans Riesel A Factor of the Fermat Number ${F}_{19}$
(in Technical Notes and Short Papers) 458--458
Anonymous Corrigenda . . . . . . . . . . . . . . . 487--488
John Gray On Certain Finite Difference Schemes for
Hyperbolic Systems . . . . . . . . . . . 1--18
A. K. Aziz and
B. E. Hubbard Bounds on the Truncation Error by Finite
Differences for the Goursat Problem . . 19--35
M. Stuart Lynn On the Round-Off Error in the Method of
Successive Over-Relaxation . . . . . . . 36--49
J. C. Butcher Implicit Runge--Kutta Processes . . . . 50--64
F. W. J. Olver Error Analysis of Miller's Recurrence
Algorithm . . . . . . . . . . . . . . . 65--74
Daniel Shanks The Second-Order Term in the Asymptotic
Expansion of ${B}(x)$ . . . . . . . . . 75--86
John Brillhart On the Factors of Certain Mersenne
Numbers, II . . . . . . . . . . . . . . 87--92
Donald B. Gillies Three New Mersenne Primes and a
Statistical Theory . . . . . . . . . . . 93--97
W. R. Wilcox Asymptotic Computation of the Repeated
Integrals of the Error Function
Complement . . . . . . . . . . . . . . . 98--105
J. H. Cadwell An Approximation to the Integral of the
Circular Gaussian Distribution over an
Offset Ellipse . . . . . . . . . . . . . 106--112
J. W. Layman A Finite Difference Exponential
Approximation Method (in Technical Notes
and Short Papers) . . . . . . . . . . . 113--118
C. Donald La Budde A New Algorithm for Diagonalizing a Real
Symmetric Matrix (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 118--123
D. B. Hunter The Calculation of Certain Bessel
Functions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 123--128
Helmut F. Bauer Tables of Zeros of Cross Product Bessel
Functions ${J}_p'(\xi){Y}_p'(k\xi) -
{J}_p'(k\xi){Y}_p'(\xi) = 0$ (in
Technical Notes and Short Papers) . . . 128--135
C. G. Broyden On Convergence Criteria for the Method
of Successive Over-Relaxation (in
Technical Notes and Short Papers) . . . 136--141
Jean L. Lavoie On Inverses of Finite Segments of the
Generalized Hilbert Matrix (in Technical
Notes and Short Papers) . . . . . . . . 141--143
Rosemarie M. Stemmler The Ideal Waring Theorem for Exponents
$401$--$200,000$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 144--146
J. L. Selfridge and
Alexander Hurwitz Fermat Numbers and Mersenne Numbers (in
Technical Notes and Short Papers) . . . 146--148
Sidney Kravitz and
Murray Berg Lucas' Test for Mersenne Numbers, $6000 <
p < 7000$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 148--149
Hans Riesel Note on the Congruence $a^{p-1} \equiv 1
(\operatorname{mod} p^2)$ (in Technical
Notes and Short Papers) . . . . . . . . 149--150
Milton E. Rose Finite Difference Schemes for
Differential Equations . . . . . . . . . 179--195
Bert K. Larkin Some Stable Explicit Difference
Approximations to the Diffusion Equation 196--202
R. B. Kellogg Difference Equations on a Mesh Arising
from a General Triangulation . . . . . . 203--210
David L. Jagerman The Autocorrelation and Joint
Distribution Functions of the Sequences
$\bigg\{\frac{a}{m}j^2\bigg\},
\bigg\{\frac{a}{m}(j + \tau)^2\bigg\}$ 211--232
J. C. Butcher Integration Processes Based on Radau
Quadrature Formulas . . . . . . . . . . 233--244
T. W. Sag and
G. Szekeres Numerical Evaluation of High-Dimensional
Integrals . . . . . . . . . . . . . . . 245--253
Irwin Roman Controlled Quadrature . . . . . . . . . 254--263
A. C. Ahlin A Bivariate Generalization of Hermite's
Interpolation Formula . . . . . . . . . 264--273
David Elliott The Evaluation and Estimation of the
Coefficients in the Chebyshev Series
Expansion of a Function . . . . . . . . 274--284
Richard Steck A Dynamic Programming Strategy for the
Two Machine Problem . . . . . . . . . . 285--291
A. K. Rigler An Application of Cyclic Reduction to
Ritz Type Difference Equations (in
Technical Notes and Short Papers) . . . 292--296
P. J. Eberlein A Two Parameter Test Matrix (in
Technical Notes and Short Papers) . . . 296--298
B. Mond Multivariate Polynomial Approximation
for Equidistant Data (in Technical Notes
and Short Papers) . . . . . . . . . . . 298--301
Friedrich Gebhardt Generating Normally Distributed Random
Numbers by Inverting the Normal
Distribution Function (in Technical
Notes and Short Papers) . . . . . . . . 302--306
T. E. Hull and
R. L. Johnston Optimum Runge--Kutta Methods (in
Technical Notes and Short Papers) . . . 306--310
Gilbert C. Best Helpful Formulas for Integrating
Polynomials in Three Dimensions (in
Technical Notes and Short Papers) . . . 310--312
Seymour Haber A Note on Some Quadrature Formulas for
the Interval $(-\infty, \infty)$ (in
Technical Notes and Short Papers) . . . 313--314
F. D. Burgoyne Generalized Trigonometric Functions (in
Technical Notes and Short Papers) . . . 314--316
David G. Hummer Expansions of Dawson's Function in a
Series of Chebyshev Polynomials (in
Technical Notes and Short Papers) . . . 317--319
Henry Gerber First One Hundred Zeros of ${J}_0(x)$
Accurate to 19 Significant Figures (in
Technical Notes and Short Papers) . . . 319--322
Daniel Shanks Polylogarithms, Dirichlet Series, and
Certain Constants (in Technical Notes
and Short Papers) . . . . . . . . . . . 322--324
Claude P. Wrathall New Factors of Fermat Numbers (in
Technical Notes and Short Papers) . . . 324--325
D. S. Book Review: \booktitleThe Theory of
Linear Graphs with Applications to the
Theory of the Virial Development of the
Properties of Gases by G. E. Uhlenbeck,
G. W. Ford . . . . . . . . . . . . . . . 338--338
Anonymous Corrigendum . . . . . . . . . . . . . . 348--348
James H. Bramble and
Bert E. Hubbard New Monotone Type Approximations for
Elliptic Problems . . . . . . . . . . . 349--367
John McNamee Error-Bounds for the Evaluation of
Integrals by the Euler--Maclaurin
Formula and by Gauss-Type Formulae . . . 368--381
D. G. Moursund Chebyshev Approximations of a Function
and Its Derivatives . . . . . . . . . . 382--389
John R. Rice On the Computation of ${L}_1$
Approximations by Exponentials,
Rationals, and Other Functions . . . . . 390--396
John Brillhart and
D. H. Lehmer and
Emma Lehmer Bounds for Pairs of Consecutive Seventh
and Higher Power Residues . . . . . . . 397--407
V. L. Gardiner and
R. B. Lazarus and
P. R. Stein Solutions of the Diophantine Equation
$x^3 + y^3 = z^3 - d$ . . . . . . . . . 408--413
M. S. Cheema Vector Partitions and Combinatorial
Identities . . . . . . . . . . . . . . . 414--420
A. H. Van Tuyl The Evaluation of Some Definite
Integrals Involving Bessel Functions
Which Occur in Hydrodynamics and
Elasticity . . . . . . . . . . . . . . . 421--432
Chih-Bing Ling and
Chen-Peng Tsai Evaluation at Half Periods of
Weierstrass' Elliptic Function with
Rhombic Primitive Period-Parallelogram 433--440
Boris Podolsky and
Harry H. Denman Conditions on Minimization Criteria for
Smoothing . . . . . . . . . . . . . . . 441--448
M. H. Lietzke and
R. W. Stoughton and
Marjorie P. Lietzke A Comparison of Several Methods for
Inverting Large Symmetric Positive
Definite Matrices . . . . . . . . . . . 449--456
Paul A. White and
Robert R. Brown A Comparison of Methods for Computing
the Eigenvalues and Eigenvectors of a
Real Symmetric Matrix . . . . . . . . . 457--463
Beresford N. Parlett Laguerre's Method Applied to the Matrix
Eigenvalue Problem . . . . . . . . . . . 464--485
George E. Forsythe Tests of Parlett's ALGOL Eigenvalue
Procedure $Eig 3$ (in Technical Notes
and Short Papers) . . . . . . . . . . . 486--487
Richard Bellman and
Robert Kalaba and
Bella Kotkin Differential Approximation Applied to
the Solution of Convolution Equations
(in Technical Notes and Short Papers) 487--491
Henry E. Fettis On the Numerical Solution of Equations
of the Abel Type (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 491--496
W. H. Witty A New Method of Numerical Integration of
Differential Equations (in Technical
Notes and Short Papers) . . . . . . . . 497--500
H. H. Wang and
R. T. Gregory On the Reduction of an Arbitrary Real
Square Matrix to Tridiagonal Form (in
Technical Notes and Short Papers) . . . 501--505
Beresford Parlett A Note on La Budde's Algorithm (in
Technical Notes and Short Papers) . . . 505--506
E. T. Parker and
R. B. Killgrove A Note on Projective Planes of Order
Nine (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 506--508
E. Karst and
U. Karst The First Power of $2$ With $8$
Consecutive Zeros (in Technical Notes
and Short Papers) . . . . . . . . . . . 508--508
Anonymous Corrigenda . . . . . . . . . . . . . . . 536--536
N. G. de Bruijn Some Direct Decompositions of the Set of
Integers . . . . . . . . . . . . . . . . 537--546
Raphael M. Robinson Algebraic Equations with Span Less than
$4$ . . . . . . . . . . . . . . . . . . 547--559
Joel N. Franklin Equidistribution of Matrix-Power
Residues Modulo One . . . . . . . . . . 560--568
Philip J. Davis Triangle Formulas in the Complex Plane 569--577
D. Mustard Numerical Integration over the
$n$-Dimensional Spherical Shell . . . . 578--589
A. H. Stroud Approximate Integration Formulas of
Degree $3$ for Simplexes . . . . . . . . 590--597
T. S. Shao and
T. C. Chen and
R. M. Frank Tables of Zeros and Gaussian Weights of
Certain Associated Laguerre Polynomials
and the Related Generalized Hermite
Polynomials . . . . . . . . . . . . . . 598--616
John R. Rice On the ${L}_\infty$ Walsh Arrays for
${\Gamma}(x)$ and $\mathrm{Erfc}(x)$ . . 617--626
Wyman Fair Padé Approximation to the Solution of the
Ricatti Equation . . . . . . . . . . . . 627--634
A. B. Otis, Jr. and
M. P. Barnett Surface Harmonic Expansions of Products
of Cartesian Coordinates . . . . . . . . 635--643
P. Erd\Hos On a Problem in Elementary Number Theory
and a Combinatorial Problem (in
Technical Notes and Short Papers) . . . 644--646
Daniel Shanks On Maximal Gaps between Successive
Primes (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 646--651
Lester J. Senechalle Iteration of Triangular Matrices (in
Technical Notes and Short Papers) . . . 651--653
Jean L. Lavoie On the Evaluation of Certain
Determinants (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 653--659
R. W. Klopfenstein Conditional Least Squares Polynomial
Approximation (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 659--662
D. van Z. Wadsworth Improved Asymptotic Expansion for the
Error Function with Imaginary Argument
(in Technical Notes and Short Papers) 662--664
J. T. Day A One-Step Method for the Numerical
Solution of Second Order Linear Ordinary
Differential Equations (in Technical
Notes and Short Papers) . . . . . . . . 664--668
Donald D. Fisher Minimum Ellipsoids (in Technical Notes
and Short Papers) . . . . . . . . . . . 669--673
R. P. Boas, Jr. and
Virginia C. Klema A Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 674--674
R. W. Hamming Book Review: Edward L. Stiefel,
\booktitleAn Introduction to Numerical
Mathematics, Academic Press, Inc., New
York, 1963, x + 286 p., 24 cm . . . . . 684--684
Anonymous Corrigendum . . . . . . . . . . . . . . 688--688
Olof B. Widlund On the Stability of Parabolic Difference
Schemes . . . . . . . . . . . . . . . . 1--13
M. Z. Nashed On General Iterative Methods for the
Solutions of a Class of Nonlinear
Operator Equations . . . . . . . . . . . 14--24
David Elliott and
George Szekeres Some Estimates of the Coefficients in
the Chebyshev Series Expansion of a
Function . . . . . . . . . . . . . . . . 25--32
Francis J. Smith An Algorithm for Summing Orthogonal
Polynomial Series and their Derivatives
with Applications to Curve-Fitting and
Interpolation . . . . . . . . . . . . . 33--36
W. V. Petryshyn On the Extrapolated Jacobi or
Simultaneous Displacements Method in the
Solution of Matrix and Operator
Equations . . . . . . . . . . . . . . . 37--55
A. J. Hoffman On the Nonsingularity of Real Matrices 56--61
N. A. Derzko and
A. M. Pfeffer Bounds for the Spectral Radius of a
Matrix . . . . . . . . . . . . . . . . . 62--67
M. H. McAndrew An Algorithm for Solving a Polynomic
Congruence, and its Application to
Error-Correcting Cods . . . . . . . . . 68--72
Harry S. Hayashi Computer Investigation of Difference
Sets . . . . . . . . . . . . . . . . . . 73--78
Don Secrest Best Approximate Integration Formulas
and Best Error Bounds . . . . . . . . . 79--83
Hans J. Stetter Stabilizing Predictors for Weakly
Unstable Correctors . . . . . . . . . . 84--89
Robert R. Brown and
James D. Riley and
Morris M. Bennett Stability Properties of Adams--Moulton
Type Methods . . . . . . . . . . . . . . 90--96
Henry E. Fettis Calculation of Elliptic Integrals of the
Third Kind by Means of Gauss'
Transformation . . . . . . . . . . . . . 97--104
W. J. Cody Chebyshev Approximations for the
Complete Elliptic Integrals ${K}$ and
${E}$ . . . . . . . . . . . . . . . . . 105--112
R. G. Medhurst and
J. H. Roberts Evaluation of the Integral ${I}_n(b) =
\frac{2}{\pi} \int^\infty_0
\bigg(\frac{\sin x}{x}\bigg)^n \cos (bx)
dx$ . . . . . . . . . . . . . . . . . . 113--117
A. H. Heatley An Extension of the Table of the Toronto
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 118--123
Chih-Bing Ling Tables of Values of $\sigma_{2s}$
Relating to Weierstrass' Elliptic
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 123--127
Otto Neall Strand A Method for the Computation of the
Error Function of a Complex Variable (in
Technical Notes and Short Papers) . . . 127--129
P. Razelos A New Integral Representation of the
Bessel Coefficients (in Technical Notes
and Short Papers) . . . . . . . . . . . 130--133
Y. T. Lo and
S. W. Lee and
B. Sun On Davis' Method of Estimating
Quadrature Errors (in Technical Notes
and Short Papers) . . . . . . . . . . . 133--138
Donald W. L. Sprung and
D. J. Hughes Gauss Weights and Ordinates for
$\int^1_0 f(x)x^2 \, dx$ (in Technical
Notes and Short Papers) . . . . . . . . 139--142
Alan G. Konheim Mantissa Distributions (in Technical
Notes and Short Papers) . . . . . . . . 143--144
A Gloden New Primes of the Form $n^4 + 1$ (in
Technical Notes and Short Papers) . . . 144--145
K. R. Isemonger Some Additional Factorizations of $2^n
\pm 1$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 145--146
A. S. H. Book Review: \booktitleError Propagation
for Difference Methods, by Peter Henrici 152--152
Anonymous Corrigenda . . . . . . . . . . . . . . . 175--175
J. F. Traub Generalized Sequences with Applications
to the Discrete Calculus . . . . . . . . 177--200
Robert C. Tausworthe Random Numbers Generated by Linear
Recurrence Modulo Two . . . . . . . . . 201--209
Raphael M. Robinson Some Conjectures About Cyclotomic
Integers . . . . . . . . . . . . . . . . 210--217
Burton Wendroff Bounds for Eigenvalues of Some
Differential Operators by the
Rayleigh--Ritz Method . . . . . . . . . 218--224
Lloyd D. Fosdick Approximation of a Class of Wiener
Integrals . . . . . . . . . . . . . . . 225--233
David Elliott Truncation Errors in Two Chebyshev
Series Approximations . . . . . . . . . 234--248
W. J. Cody Chebyshev Polynomial Expansions of
Complete Elliptic Integrals . . . . . . 249--259
J. N. Lyness Symmetric Integration Rules for
Hypercubes I. Error Coefficients . . . . 260--276
E. L. Whitney Estimates of Weights in Gauss-Type
Quadrature . . . . . . . . . . . . . . . 277--286
C. R. Cassity Abscissas, Coefficients, and Error Term
for the Generalized Gauss--Laguerre
Quadrature Formula Using the Zero
Ordinate . . . . . . . . . . . . . . . . 287--296
James W. Cooley and
John W. Tukey An Algorithm for the Machine Calculation
of Complex Fourier Series . . . . . . . 297--301
A. K. Rigler Estimation of the Successive
Over-Relaxation Factor (in Technical
Notes and Short Papers) . . . . . . . . 302--307
H. S. Price A Practical Application of Block
Diagonally Dominant Matrices (in
Technical Notes and Short Papers) . . . 307--313
John Gary Hyman's Method Applied to the General
Eigenvalue Problem (in Technical Notes
and Short Papers) . . . . . . . . . . . 314--316
A. D. Keedwell A Search for Projective Planes of a
Special Type with the Aid of a Digital
Computer (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 317--322
Nancy Lee and
A. H. Stroud Approximate Integration Formulas for
Ellipses (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 322--327
Donald van Zelm Wadsworth Improved Asymptotic Expansion for the
Exponential Integral with Positive
Argument (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 327--328
Irving H. Siegel Deferment of Computation in the Method
of Least Squares (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 329--331
Daniel Shanks Review of: Marshall Hall, Jr. and James
K. Senior, ``The Groups of Order $2^n (n
\le 6)$'' . . . . . . . . . . . . . . . 335--337
John Gary Computing Eigenvalues of Ordinary
Differential Equations by Finite
Differences . . . . . . . . . . . . . . 365--379
L. M. Delves Variation Principles for an Arbitrary
Operator. III . . . . . . . . . . . . . 380--386
W. E. Simon Numerical Technique for Solution and
Error Estimate for the Initial Value
Problem . . . . . . . . . . . . . . . . 387--393
J. N. Lyness Symmetric Integration Rules for
Hypercubes II. Rule Projection and Rule
Extension . . . . . . . . . . . . . . . 394--407
J. C. Butcher On the Attainable Order of Runge--Kutta
Methods . . . . . . . . . . . . . . . . 408--417
D. L. Jagerman Some Theorems Concerning Pseudo-Random
Numbers . . . . . . . . . . . . . . . . 418--426
M. L. Stein and
P. R. Stein Experimental Results on Additive
$2$-Bases . . . . . . . . . . . . . . . 427--434
N. Metropolis and
R. L. Ashenhurst Radix Conversion in an Unnormalized
Arithmetic System . . . . . . . . . . . 435--441
L. D. Baumert and
Marshall Hall, Jr. Hadamard Matrices of the Williamson Type 442--447
R. B. Kellogg and
J. Spanier On Optimal Alternating Direction
Parameters for Singular Matrices (in
Technical Notes and Short Papers) . . . 448--452
Adi Ben-Israel An Iterative Method for Computing the
Generalized Inverse of an Arbitrary
Matrix (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 452--455
C. H. Yang A Note on the Maximum Value of
Determinants Over the Complex Field (in
Technical Notes and Short Papers) . . . 455--456
John D. Lambert and
Brian Shaw On the Numerical Solution of $y' = f(x,
y)$ by a Class of Formulae Based on
Rational Approximation (in Technical
Notes and Short Papers) . . . . . . . . 456--462
Theodore R. Goodman The Numerical Solution of Eigenvalue
Problems (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 462--466
V. O. S. Olunloyo A Special Technique for the
Determination of Eigenvalues (in
Technical Notes and Short Papers) . . . 466--471
J. N. Lyness Integration Rules of Hypercubic Symmetry
Over a Certain Spherically Symmetric
Space (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 471--476
Donald G. Anderson Gaussian Quadrature Formulae for
$\int^1_0 -ln(x)f(x) dx$ (in Technical
Notes and Short Papers) . . . . . . . . 477--481
Lawrence F. Shampine Quadrature Formulas Using Derivatives
(in Technical Notes and Short Papers) 481--482
Jacqueline Wells and
Joseph Muskat On the Number of Solutions of Certain
Trinomial Congruences (in Technical
Notes and Short Papers) . . . . . . . . 483--487
Chih-Bing Ling and
Hsien-Chueh Wu Tables of Values of Three Infinite
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 487--494
Charles H. Franke Numerical Evaluation of the Elliptic
Integral of the Third Kind (in Technical
Notes and Short Papers) . . . . . . . . 494--496
Wendy James and
P. Jarratt The Generation of Square Roots on a
Computer with Rapid Multiplication
Compared with Division (in Technical
Notes and Short Papers) . . . . . . . . 497--500
Robert F. Church On a Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 501--501
Yudell L. Luke and
Wyman Fair and
Gerald ine Coombs and
Rosemary Moran On a Constant in the Theory of
Trigonometric Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 501--502
R. W. Hamming Book Review: \booktitleElements of
Numerical Analysis, by Peter Henrici . . 516--517
John R. Rice Book Review: Günter Meinardus,
\booktitleApproximation von Funktionen
und ihre numerische Behandlung,
Springer-Verlag, Berlin, 1964, viii +
180 pp., 23 cm. Price DM 49 . . . . . . 517--517
Anonymous Errata . . . . . . . . . . . . . . . . . 527--528
Anonymous Corrigendum . . . . . . . . . . . . . . 529--529
R. J. Aumann and
B. Peleg and
P. Rabinowitz A Method for Computing the Kernel of
$n$-Person Games . . . . . . . . . . . . 531--551
Joel N. Franklin Difference Methods for Stochastic
Ordinary Differential Equations . . . . 552--561
H. M. Sternberg and
J. B. Diaz Computation of the Riemann Function for
the Operator $\partial^n/ \partial
x_1\partial x_2 \cdots \partial x_n +
a(x_1, x_2, \cdots, x_n)$ . . . . . . . 562--569
Carl E. Pearson Impulsive End Condition for Diffusion
Equation . . . . . . . . . . . . . . . . 570--576
C. G. Broyden A Class of Methods for Solving Nonlinear
Simultaneous Equations . . . . . . . . . 577--593
Harvey Cohn A Numerical Survey of the Floors of
Various Hilbert Fundamental Domains . . 594--605
Jerry L. Fields Rational Approximations to Generalized
Hypergeometric Functions . . . . . . . . 606--624
J. N. Lyness Symmetric Integration Rules for
Hypercubes III. Construction of
Integration Rules Using Null Rules . . . 625--637
J. N. Lyness Limits on the Number of Function
Evaluations Required by Certain
High-Dimensional Integration Rules of
Hypercubic Symmetry . . . . . . . . . . 638--643
B. H. Mayoh A Graph Technique for Inverting Certain
Matrices (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 644--646
Stephan Ormonde and
Jerald S. Dick A Method of Calculation of Integrals of
Products of Radial Atomic Wave Functions
(in Technical Notes and Short Papers) 647--650
Jerry Allan Roberts Computation of Moments of
${K}_\nu(t)/{I}_\nu(t)$ (in Technical
Notes and Short Papers) . . . . . . . . 651--654
Lawrence R. Mack Bessel-Function Identities Needed for
the Theory of Axisymmetric Gravity Waves
(in Technical Notes and Short Papers) 654--657
Chih-Bing Ling Evaluation at Half Periods of
Weierstrass' Elliptic Functions with
Double Periods $1$ and $e^{i\alpha}$ (in
Technical Notes and Short Papers) . . . 658--661
G. T. Thompson The Asymptotic Expansion of the
Integrals Psi and Chi in Terms of
Tchebycheff Polynomials (in Technical
Notes and Short Papers) . . . . . . . . 661--663
Arun Verma A Class of Expansions of ${G}$-Functions
and the Laplace Transform (in Technical
Notes and Short Papers) . . . . . . . . 664--666
L. Carlitz The Irreducibility of the Bernoulli
Polynomial ${B}_{14}(x)$ (in Technical
Notes and Short Papers) . . . . . . . . 667--670
H. C. Williams and
R. A. German and
C. R. Zarnke Solution of the Cattle Problem of
Archimedes (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 671--674
Selmer M. Johnson An Elementary Remark on Maximal Gaps
Between Successive Primes (in Technical
Notes and Short Papers) . . . . . . . . 675--676
Bogumil Leszczynski On the Sum of the Series
$\sum^\infty_{\nu = 0} (t^\nu/\lbrack
u\nu + m \rbrack!)$ (in Technical Notes
and Short Papers) . . . . . . . . . . . 677--679
Daniel Shanks Review of Paul T. Bateman and Roger A.
Horn, ``Primes Represented by
irreducible polynomials in one
variable'', in \em Theory of Numbers,
pp. 119--132, in particular Tables II--V 684--686
Anonymous Errata . . . . . . . . . . . . . . . . . 705--706
Anonymous Corrigendum . . . . . . . . . . . . . . 706--706
J. C. Butcher On the Convergence of Numerical
Solutions to Ordinary Differential
Equations . . . . . . . . . . . . . . . 1--10
J. D. Lambert and
B. Shaw A Method for the Numerical Solution of
$y' = f(x, y)$ Based on a Self-Adjusting
Non-Polynomial Interpolant . . . . . . . 11--20
E. Baylis Shanks Solutions of Differential Equations by
Evaluations of Functions . . . . . . . . 21--38
Charles E. Treanor A Method for the Numerical Integration
of Coupled First-Order Differential
Equations with Greatly Different Time
Constants . . . . . . . . . . . . . . . 39--45
Jay A. Leavitt Methods and Applications of Power Series 46--52
Bert Hubbard Some Locally One-Dimensional Difference
Schemes for Parabolic Equations in an
Arbitrary Region . . . . . . . . . . . . 53--59
Moshe Mangad Bounds for the Two-Dimensional Discrete
Harmonic Green's Function . . . . . . . 60--67
C. S. Duris A Simplex Sufficiency Condition for
Quadrature Formulas . . . . . . . . . . 68--78
D. Jagerman Investigation of a Modified Mid-Point
Quadrature Formula . . . . . . . . . . . 79--89
A. H. Stroud Some Fifth Degree Integration Formulas
for Symmetric Regions . . . . . . . . . 90--97
Chikara Sato Correction of Stability Curves in
Hill--Meissner's Equation . . . . . . . 98--106
I. Borosh and
A. S. Fraenkel Exact Solutions of Linear Equations with
Rational Coefficients by Congruence
Techniques . . . . . . . . . . . . . . . 107--112
J. F. Traub A Class of Globally Convergent Iteration
Functions for the Solution of Polynomial
Equations . . . . . . . . . . . . . . . 113--138
Saburo Uchiyama A Note on a Theorem of J. N. Franklin
(in Technical Notes and Short Papers) 139--140
Joseph B. Muskat On Divisors of Odd Perfect Numbers (in
Technical Notes and Short Papers) . . . 141--144
M. Lal and
W. J. Blundon Solutions of the Diophantine Equations
$x^2 + y^2 = l^2, y^2 + z^2 = m^2, z^2 +
x^2 = n^2$ (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 144--147
C. H. Yang Some Designs for Maximal $(+1,
-1)$-Determinant of Order $n \equiv 2
(\operatorname{mod} 4)$ (in Technical
Notes and Short Papers) . . . . . . . . 147--148
David J. Edelblute Matrix Inversion by Rank Annihilation
(in Technical Notes and Short Papers) 149--151
Arun Verma Certain Expansions of the Basic
Hypergeometric Functions (in Technical
Notes and Short Papers) . . . . . . . . 151--157
Shih-Hsiung Tung Boundedness of Difference Kernels of
Bessel and Fourier Series (in Technical
Notes and Short Papers) . . . . . . . . 157--163
Robert G. Voigt On a Numerical Solution of an Integral
Equation with Singularities (in
Technical Notes and Short Papers) . . . 163--166
W. J. Cody Corrigenda: ``Chebyshev Approximations
for the Complete Elliptic Integrals
${K}$ and ${E}$'' . . . . . . . . . . . 207--207
Walter Gautschi Computation of Successive Derivatives of
$f(z)/z$ . . . . . . . . . . . . . . . . 209--214
Boro Doring Complex Zeros of Cylinder Functions . . 215--222
W. J. Nellis and
B. C. Carlson Reduction and Evaluation of Elliptic
Integrals . . . . . . . . . . . . . . . 223--231
A. I. van de Vooren and
H. J. van Linde Numerical Calculation of Integrals with
Strongly Oscillating Integrand . . . . . 232--245
L. M. Delves Exponential Differences . . . . . . . . 246--256
Harry H. Denman Minimax Polynomial Approximation . . . . 257--265
O. Shisha The Chebyshev Polynomial of Best
Approximation to a Given Function on an
Interval . . . . . . . . . . . . . . . . 266--271
K. V. Roberts and
N. O. Weiss Convective Difference Schemes . . . . . 272--299
W. C. Mitchell The Number of Lattice Points in a
$k$-Dimensional Hypersphere . . . . . . 300--310
D. H. Moore A Division Algebra for Sequences Defined
on all the Integers . . . . . . . . . . 311--317
Ian Barrodale A Note on Equal Sums of Like Powers (in
Technical Notes and Short Papers) . . . 318--322
M. Lal and
M. F. Jones and
W. J. Blundon Numerical Solutions of the Diophantine
Equation $y^3 - x^2 = k$ (in Technical
Notes and Short Papers) . . . . . . . . 322--325
John R. Rice Experiments on Gram--Schmidt
Orthogonalization (in Technical Notes
and Short Papers) . . . . . . . . . . . 325--328
J. W. Moon and
L. Moser A Matrix Reduction Problem (in Technical
Notes and Short Papers) . . . . . . . . 328--330
Rory Thompson Evaluation of ${I}_n(b) = 2\pi^{-1}
\int^\infty_0 \big(\frac{sin x}{x}\big)
^n \cos (bx) dx$ and of Similar
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 330--332
M. L. Glasser Evaluation of Some Integrals Involving
the $\psi$-Function (in Technical Notes
and Short Papers) . . . . . . . . . . . 332--333
Anonymous Corrigendum . . . . . . . . . . . . . . 344--344
Alan Solomon Some Remarks on the Stefan Problem . . . 347--360
Seymour Haber A Modified Monte-Carlo Quadrature . . . 361--368
Shmuel Kaniel Estimates for Some Computational
Techniques in Linear Algebra . . . . . . 369--378
F. G. Lether The Use of Richardson Extrapolation in
One-Step Methods with Variable Step Size 379--385
Richard King Runge--Kutta Methods with Constrained
Minimum Error Bounds . . . . . . . . . . 386--391
David J. Fyfe Economical Evaluation of Runge--Kutta
Formulae . . . . . . . . . . . . . . . . 392--398
M. Godart An Iterative Method for the Solution of
Eigenvalue Problems . . . . . . . . . . 399--406
Fr. Mechel Calculation of the Modified Bessel
Functions of the Second Kind with
Complex Argument . . . . . . . . . . . . 407--412
Arun Verma A Note on an Expansion of Hypergeometric
Functions of Two Variables . . . . . . . 413--417
Bruce S. Berger Inversion of the ${N}$-Dimensional
Laplace Transform (in Technical Notes
and Short Papers) . . . . . . . . . . . 418--421
R. D. Low On the First Positive Zero of
${P}^{(-m)}_{\nu-1/2} (\cos \theta)$,
Considered as a Function of $\nu$ (in
Technical Notes and Short Papers) . . . 421--424
Van E. Wood Some Integrals of Ramanujan and Related
Contour Integrals (in Technical Notes
and Short Papers) . . . . . . . . . . . 424--429
Philip Rudnick Note on the Calculation of Fourier
Series (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 429--430
H. P. Decell, Jr. and
L. F. Guseman, Jr. and
R. N. Lea Concerning the Numerical Solution of
Differential Equations (in Technical
Notes and Short Papers) . . . . . . . . 431--434
P. Jarratt Some Fourth Order Multipoint Iterative
Methods for Solving Equations (in
Technical Notes and Short Papers) . . . 434--437
J. M. Varah Certification of Parlett's ALGOL
Eigenvalue Procedure
$\operatorname{Eig}$ 3 (in Technical
Notes and Short Papers) . . . . . . . . 437--438
Adi Ben-Israel A Note on an Iterative Method for
Generalized Inversion of Matrices (in
Technical Notes and Short Papers) . . . 439--440
James W. Burrows Maximization of a Second-Degree
Polynomial on the Unit Sphere (in
Technical Notes and Short Papers) . . . 441--444
John W. Wrench, Jr. and
Daniel Shanks Questions Concerning Khintchine's
Constant and the Efficient Computation
of Regular Continued Fractions (in
Technical Notes and Short Papers) . . . 444--448
Sidney Kravitz Distributions of Mersenne Divisors (in
Technical Notes and Short Papers) . . . 448--449
L. J. Lander and
T. R. Parkin Equal Sums of Biquadrates (in Technical
Notes and Short Papers) . . . . . . . . 450--451
Anonymous Errata . . . . . . . . . . . . . . . . . 468--471
Achi Brandt Estimates for Difference Quotients of
Solutions of Poisson Type Difference
Equations . . . . . . . . . . . . . . . 473--499
Olof B. Widlund On the Rate of Convergence of an
Alternating Direction Implicit Method in
a Noncommutative Case . . . . . . . . . 500--515
Milton Lees A Linear Three-Level Difference Scheme
for Quasilinear Parabolic Equations . . 516--522
R. Sherman Lehman Separation of Zeros of the Riemann
Zeta-Function . . . . . . . . . . . . . 523--541
Robert Spira Zeros of Sections of the Zeta Function.
I . . . . . . . . . . . . . . . . . . . 542--550
Daniel Shanks and
Larry P. Schmid Variations on a Theorem of Landau. Part
I . . . . . . . . . . . . . . . . . . . 551--569
Guy de Balbine and
Joel N. Franklin The Calculation of Fourier Integrals . . 570--589
Arun Verma Expansions Involving Hypergeometric
Functions of Two Variables . . . . . . . 590--596
A. C. R. Newbery Interpolation by Algebraic and
Trigonometric Polynomials (in Technical
Notes and Short Papers) . . . . . . . . 597--599
J. T. Day A Note on Best Approximation in ${E}^n$
(in Technical Notes and Short Papers) 599--600
Roger G. Hart A Close Approximation Related to the
Error Function (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 600--602
Wyman Fair and
Yudell L. Luke Rational Approximations to the Solution
of the Second Order Riccati Equation (in
Technical Notes and Short Papers) . . . 602--606
Roy Takenaga On the Evaluation of the Incomplete
Gamma Function (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 606--610
Van E. Wood and
R. P. Kenan and
M. L. Glasser Doppler Broadening Integrals (in
Technical Notes and Short Papers) . . . 610--611
Beresford N. Parlett Singular and Invariant Matrices Under
the ${QR}$ Transformation (in Technical
Notes and Short Papers) . . . . . . . . 611--615
Anonymous Corrigenda . . . . . . . . . . . . . . . 643--643
G. Fairweather and
A. R. Gourlay Some Stable Difference Approximations to
a Fourth-Order Parabolic Partial
Differential Equation . . . . . . . . . 1--11
James D. Riley and
Morris M. Bennett and
Emily McCormick Numerical Integration of Variational
Equations . . . . . . . . . . . . . . . 12--17
I. Gargantini and
P. Henrici A Continued Fraction Algorithm for the
Computation of Higher Transcendental
Functions in the Complex Plane . . . . . 18--29
W. J. Cody and
Henry C. Thacher, Jr. Rational Chebyshev Approximations for
Fermi--Dirac Integrals of Orders
$-\frac{1}{2}, \frac{1}{2}$ and
$\frac{3}{2}$ . . . . . . . . . . . . . 30--40
Robert Spira Zeros of Approximate Functional
Approximations . . . . . . . . . . . . . 41--48
Alan G. Konheim and
Willard L. Miranker Numerical Evaluation of Wiener Integrals 49--65
R. E. Barnhill and
J. A. Wixom Quadratures with Remainders of Minimum
Norm. I . . . . . . . . . . . . . . . . 66--75
Harvey Cohn A Numerical Study of Topological
Features of Certain Hilbert Fundamental
Domains . . . . . . . . . . . . . . . . 76--86
John Brillhart and
J. L. Selfridge Some Factorizations of $2^n \pm 1$ and
Related Results . . . . . . . . . . . . 87--96
Daniel Shanks and
Sidney Kravitz On the Distribution of Mersenne Divisors
(in Technical Notes and Short Notices) 97--101
L. J. Lander and
T. R. Parkin A Counterexample to Euler's Sum of
Powers Conjecture (in Technical Notes
and Short Notices) . . . . . . . . . . . 101--103
M. F. Jones and
M. Lal and
W. J. Blundon Statistics on Certain Large Primes (in
Technical Notes and Short Notices) . . . 103--107
Arun Verma A Note on Expansions Involving Meijer's
${G}$-Functions (in Technical Notes and
Short Notices) . . . . . . . . . . . . . 107--112
William T. Moody Approximations for the
$\operatorname{Psi}$ (Digamma) Function
(in Technical Notes and Short Notices) 112--112
F. D. Burgoyne Practical ${L}^p$ Polynomial
Approximation (in Technical Notes and
Short Notices) . . . . . . . . . . . . . 113--115
Anonymous Corrigenda . . . . . . . . . . . . . . . 130--130
M. R. Osborne Minimising Truncation Error in Finite
Difference Approximations to Ordinary
Differential Equations . . . . . . . . . 133--145
C. W. Gear The Numerical Integration of Ordinary
Differential Equations . . . . . . . . . 146--156
H. R. Lewis, Jr. and
E. J. Stovall, Jr. Comments on a Floating-Point Version of
Nordsieck's Scheme for the Numerical
Integration of Differential Equations 157--161
H. R. Lewis, Jr. and
E. F. Stovall, Jr. Comments on a floating-point version of
Nordsieck's scheme for the numerical
integration of differential equations 157--161
J. N. Lyness and
B. W. Ninham Numerical Quadrature and Asymptotic
Expansions . . . . . . . . . . . . . . . 162--178
J. T. Day A Starting Method for Solving Nonlinear
Volterra Integral Equations . . . . . . 179--188
Jerry L. Fields Confluent Expansions . . . . . . . . . . 189--197
W. J. Cody and
K. E. Hillstrom Chebyshev Approximations for the Natural
Logarithm of the Gamma Function . . . . 198--203
L. D. Baumert and
H. Fredricksen The Cyclotomic Numbers of Order Eighteen
with Applications to Difference Sets . . 204--219
John Gary On Convergence Rates for Line
Overrelaxation (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 220--223
Beresford Parlett Canonical Decomposition of Hessenberg
Matrices (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 223--227
Leopold B. Willner An Elimination Method for Computing the
Generalized Inverse (in Technical Notes
and Short Papers) . . . . . . . . . . . 227--229
R. Langel An Algorithm for Certain Double Sums of
Polynomial Series (in Technical Notes
and Short Papers) . . . . . . . . . . . 230--232
Arun Verma A Note on the Summation of the
Generalised Hypergeometric Functions (in
Technical Notes and Short Papers) . . . 232--236
G. D. Bergland The Fast Fourier Transform Recursive
Equations for Arbitrary Length Records
(in Technical Notes and Short Papers) 236--238
E. O. Tuck A Simple ``Filon-Trapezoidal'' Rule (in
Technical Notes and Short Papers) . . . 239--241
J. Alanen and
Ò. Òre and
J. Stemple Systematic Computations on Amicable
Numbers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 242--245
M. Lal Primes of the Form $n^4 + 1$ (in
Technical Notes and Short Papers) . . . 245--247
Robert Bowen The Generation of Minimal Triangle
Graphs (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 248--250
Robert Bowen and
Stephen Fisk Generation of Triangulations of the
Sphere (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 250--252
J. Schonheim Conversion of Modular Numbers to their
Mixed Radix Representation by Matrix
Formula (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 253--257
Anonymous Corrigenda . . . . . . . . . . . . . . . 296--296
C. Ballester and
V. Pereyra On the Construction of Discrete
Approximations to Linear Differential
Expressions . . . . . . . . . . . . . . 297--302
Willard L. Miranker and
Werner Liniger Parallel Methods for the Numerical
Integration of Ordinary Differential
Equations . . . . . . . . . . . . . . . 303--320
R. Bruce Simpson A Fundamental Solution for a Biharmonic
Finite-Difference Operator . . . . . . . 321--339
Paul Concus Numerical Solution of the Minimal
Surface Equation . . . . . . . . . . . . 340--350
A. R. Gourlay and
A. R. Mitchell Split Operator Methods for Hyperbolic
Systems in $p$ Space Variables . . . . . 351--354
A. Solomon A Steady State Phase Change Problem . . 355--359
John Greenstadt On the Relative Efficiencies of Gradient
Methods . . . . . . . . . . . . . . . . 360--367
C. G. Broyden Quasi-Newton Methods and their
Application to Function Minimisation . . 368--381
R. E. Barnhill and
J. A. Wixom Quadratures with Remainders of Minimum
Norm. II . . . . . . . . . . . . . . . . 382--387
Seymour Haber A Modified Monte-Carlo Quadrature. II 388--397
David Elliott Truncation Errors in Padé Approximations
to Certain Functions: An Alternative
Approach . . . . . . . . . . . . . . . . 398--406
J. E. Kilpatrick and
Shigetoshi Katsura and
Yuji Inoue Calculations of Integrals of Products of
Bessel Functions . . . . . . . . . . . . 407--412
Charles E. McQueary and
Lawrence R. Mack Bessel-Function Integrals Needed for Two
Classes of Physical Problems . . . . . . 413--417
Wyman G. Fair and
Yudell L. Luke Rational Approximations to the
Incomplete Elliptic Integrals of the
First and Second Kinds . . . . . . . . . 418--422
Moshe Mangad Some Limiting Values and Two Error
Estimation Procedures for Power Series
Approximations . . . . . . . . . . . . . 423--430
Henry E. Fettis and
James C. Caslin Eigenvalues and Eigenvectors of Hilbert
Matrices of Order $3$ Through $10$ . . . 431--441
Raymond G. Ayoub A Note on the Class Number of Imaginary
Quadratic Fields . . . . . . . . . . . . 442--445
L. J. Lander and
T. R. Parkin and
J. L. Selfridge A Survey of Equal Sums of Like Powers 446--459
Edward L. Cohen On the Sum of the Squares of Two
Consecutive Integers . . . . . . . . . . 460--465
Thomas R. Parkin and
Daniel Shanks On the Distribution of Parity in the
Partition Function . . . . . . . . . . . 466--480
Morris Newman Note on Partitions Modulo $5$ (in
Technical Notes and Short Papers) . . . 481--482
L. J. Lander and
T. R. Parkin On First Appearance of Prime Differences
(in Technical Notes and Short Papers) 483--488
L. J. Lander and
T. R. Parkin Consecutive Primes in Arithmetic
Progression (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 489--489
A. C. R. Newbery Convergence of Successive Substitution
Starting Procedures (in Technical Notes
and Short Papers) . . . . . . . . . . . 489--491
Jay A. Leavitt A Polynomial Approximation Converging in
a Lens-Shaped Region (in Technical Notes
and Short Papers) . . . . . . . . . . . 491--493
Van E. Wood Chebyshev Expansions for Integrals of
the Error Function (in Technical Notes
and Short Papers) . . . . . . . . . . . 494--496
James D. Lear and
James E. Sturm An Integral Representation for the
Modified Bessel Function of the Third
Kind, Computable for Large, Imaginary
Order (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 496--498
J. W. Layman Mixed Algebraic-Exponential
Interpolation Using Finite Differences
(in Technical Notes and Short Papers) 498--500
W. J. Cody and
Henry C. Thacher, Jr. Corrigendum: ``Rational Chebyshev
approximations for Fermi--Dirac
integrals of orders $-1/2$, $1/2$, and
$3/2$'' . . . . . . . . . . . . . . . . 525--525
Stefan Bergman and
Bruce Chalmers A Procedure for Conformal Mapping of
Triply-Connected Domains . . . . . . . . 527--542
L. M. Delves and
J. N. Lyness A Numerical Method for Locating the
Zeros of an Analytic Function . . . . . 543--560
J. N. Lyness and
L. M. Delves On Numerical Contour Integration Round a
Closed Contour . . . . . . . . . . . . . 561--577
Philip J. Davis A Construction of Nonnegative
Approximate Quadratures . . . . . . . . 578--582
W. D. Murphy Numerical Analysis of Boundary-Layer
Problems in Ordinary Differential
Equations . . . . . . . . . . . . . . . 583--596
G. J. Cooper A Class of Single-Step Methods for
Systems of Nonlinear Differential
Equations . . . . . . . . . . . . . . . 597--610
Masaya Yamaguti Some Remarks on the Lax--Wendroff
Finite-Difference Scheme for
Nonsymmetric Hyperbolic Systems . . . . 611--619
Dale U. von Rosenberg Numerical Solution for Flux Components
in Potential Flow . . . . . . . . . . . 620--628
R. Tait Error Analysis of Recurrence Equations 629--638
Jet Wimp The Asymptotic Representation of a Class
of ${G}$-Functions for Large Parameter 639--646
Alex Reichel Error Estimates in Simple Quadrature
with Voigt Functions . . . . . . . . . . 647--651
A. R. DiDonato and
M. P. Jarnagin The Efficient Calculation of the
Incomplete Beta-Function Ratio for
Half-Integer Values of the Parameters
$a, b$ . . . . . . . . . . . . . . . . . 652--662
Donald E. Knuth and
Thomas J. Buckholtz Computation of Tangent, Euler, and
Bernoulli Numbers . . . . . . . . . . . 663--688
Daniel Shanks Generalized Euler and Class Numbers . . 689--694
S. S. Wagstaff, Jr. On Sequences of Integers with No $4$, or
No $5$ Numbers in Arithmetical
Progression . . . . . . . . . . . . . . 695--699
John R. Ehrman The Number of Prime Divisors of Certain
Mersenne Numbers . . . . . . . . . . . . 700--704
Daniel Shanks Lal's Constant and Generalizations (in
Technical Notes and Short Papers) . . . 705--707
Friedrich Gebhardt Generating Pseudo-Random Numbers by
Shuffling a Fibonacci Sequence (in
Technical Notes and Short Papers) . . . 708--709
Guy de Balbine Note on Random Permutations (in
Technical Notes and Short Papers) . . . 710--712
L. J. Bass and
S. R. Schubert On Finding the Disc of Minimum Radius
Containing a Given Set of Points (in
Technical Notes and Short Papers) . . . 712--714
S. Charmonman An Efficient Algorithm for Inverting a
Block-Symmetric Matrix (in Technical
Notes and Short Papers) . . . . . . . . 715--717
Fred T. Krogh A Note on the Effect of Conditionally
Stable Correctors (in Technical Notes
and Short Papers) . . . . . . . . . . . 717--719
Seymour Haber Midpoint Quadrature Formulas (in
Technical Notes and Short Papers) . . . 719--721
Joyce Weil and
Tadepalli S. Murty and
Desiraju B. Rao Zeros of
${J}_n(\lambda){Y}_n(\eta\lambda) -
{J}_n(\eta\lambda){Y}_n(\lambda)$ (in
Technical Notes and Short Papers) . . . 722--727
Henry E. Fettis More on the Calculation of the Integral
${I}_n(b) =
\frac{2}{\pi}\int^\infty_0\big(\frac{\sin x}{x}\big)^n \cos bx dx$ (in Technical Notes and Short Papers) 727--730
Anonymous Corrigendum . . . . . . . . . . . . . . 751--751
Heinz-Otto Kreiss and
Einar Lundqvist On Difference Approximations with Wrong
Boundary Values . . . . . . . . . . . . 1--12
S. Bergman and
J. G. Herriot and
T. G. Kurtz On Numerical Calculation of Transonic
Flow Patterns . . . . . . . . . . . . . 13--27
A. R. Gourlay and
J. Ll. Morris Finite-Difference Methods for Nonlinear
Hyperbolic Systems . . . . . . . . . . . 28--39
Blair K. Swartz Explicit ${O}(h^2)$ Bounds on the
Eigenvalues of the Half-${L}$ . . . . . 40--59
L. A. Hageman and
R. B. Kellogg Estimating Optimum Overrelaxation
Parameters . . . . . . . . . . . . . . . 60--68
G. J. Cooper Interpolation and Quadrature Methods for
Ordinary Differential Equations . . . . 69--76
Lloyd D. Fosdick A Special Case of the Filon Quadrature
Formula . . . . . . . . . . . . . . . . 77--81
M. M. Chawla and
M. K. Jain Error Estimates for Gauss Quadrature
Formulas for Analytic Functions . . . . 82--90
M. M. Chawla and
M. K. Jain Asymptotic Error Estimates for the Gauss
Quadrature Formula . . . . . . . . . . . 91--97
Robert E. Barnhill An Error Analysis for Numerical Multiple
Integration. I . . . . . . . . . . . . . 98--109
Richard A. Valentin The Use of the Hypercircle Inequality in
Deriving a Class of Numerical
Approximation Rules for Analytic
Functions . . . . . . . . . . . . . . . 110--117
John R. Rice and
Karl H. Usow The Lawson Algorithm and Extensions . . 118--127
R. P. Kelisky and
T. J. Rivlin A Rational Approximation to the
Logarithm . . . . . . . . . . . . . . . 128--136
C. Chiarella and
A. Reichel On the Evaluation of Integrals Related
to the Error Function . . . . . . . . . 137--143
Anthony J. Strecok On the Calculation of the Inverse of the
Error Function . . . . . . . . . . . . . 144--158
David Osborn and
Richard Madey The Incomplete Beta Function and its
Ratio to the Complete Beta Function . . 159--162
Robert Spira Zeros of Sections of the Zeta Function.
II . . . . . . . . . . . . . . . . . . . 163--173
C. H. Yang On Designs of Maximal $(+1,
-1)$-Matrices of Order $n \equiv 2
(\operatorname{mod} 4)$ . . . . . . . . 174--180
Elvin J. Lee Amicable Numbers and the Bilinear
Diophantine Equation . . . . . . . . . . 181--187
Z. A. Melzak Numerical Evaluation of an Isoperimetric
Constant . . . . . . . . . . . . . . . . 188--190
Herbert E. Salzer and
Norman Levine Proof that Every Integer $\leq
452,479,659$ is a Sum of Five Numbers of
the Form $\mathscr{Q}_x \equiv (x^3 +
5x)/6, x \geq 0$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 191--192
W. F. Lunnon A Map-Folding Problem (in Technical
Notes and Short Papers) . . . . . . . . 193--199
M. S. Cheema and
H. Gupta The Maxima of ${P}_r(n_1, n_2)$ (in
Technical Notes and Short Papers) . . . 199--200
W. R. Schucany and
H. L. Gray A New Approximation Related to the Error
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 201--202
Fr. Mechel Improvement in Recurrence Techniques for
the Computation of Bessel Functions of
Integral Order (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 202--205
Peter H. Wilcox The Zeros of ${P}^1_\nu (\cos \theta)$
and $\frac{\partial}{\partial \theta}
{P}^1_\mu (\cos \theta)$ (in Technical
Notes and Short Papers) . . . . . . . . 205--208
R. G. Buschman Substitution Formulas for Laplace
Transformations (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 209--211
Anonymous Corrigenda . . . . . . . . . . . . . . . 246--247
Carson Flammer Addendum . . . . . . . . . . . . . . . . 249--249
Walter Gautschi Construction of Gauss--Christoffel
Quadrature Formulas . . . . . . . . . . 251--270
A. H. Stroud Extensions of Symmetric Integration
Formulas . . . . . . . . . . . . . . . . 271--274
G. D. Bergland A Fast Fourier Transform Algorithm Using
Base $8$ Iterations . . . . . . . . . . 275--279
P. M. Hirsch Evaluation of Orthogonal Polynomials and
Relationship to Evaluating Multiple
Integrals . . . . . . . . . . . . . . . 280--285
Robert E. Barnhill An Error Analysis for Numerical Multiple
Integration. II . . . . . . . . . . . . 286--292
Christopher A. Feuchter Numerical Integration Over a Sphere . . 293--297
R. W. Dickey An Improved Method for the Numerical
Solution of the Suspension Bridge
Deflection Equations . . . . . . . . . . 298--303
D. O. Banks and
G. J. Kurowski Computation of Eigenvalues of Singular
Sturm--Liouville Systems . . . . . . . . 304--310
Robert E. Lynch and
John R. Rice Convergence Rates of ADI Methods with
Smooth Initial Error . . . . . . . . . . 311--335
C. M. Campbell and
P. Keast The Stability of Difference
Approximations to a Self-Adjoint
Parabolic Equation, Under Derivative
Boundary Conditions . . . . . . . . . . 336--346
Dennis Eisen Consistency Conditions for Difference
Schemes with Singular Coefficients . . . 347--351
J. N. Lyness Differentiation Formulas for Analytic
Functions . . . . . . . . . . . . . . . 352--362
Jet Wimp Recursion Formulae of Hypergeometric
Functions . . . . . . . . . . . . . . . 363--373
Eldon R. Hansen On Solving Systems of Equations Using
Interval Arithmetic . . . . . . . . . . 374--384
R. M. Baer and
P. Brock Natural Sorting Over Permutation Spaces 385--410
W. C. Mitchell An Evaluation of Golomb's Constant . . . 411--415
A. O. L. Atkin Explicit Gap Series at Cusps of
${\Gamma}(p)$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 416--419
H. C. Williams and
C. R. Zarnke A Report on Prime Numbers of the Forms
${M} = (6a + 1)2^{2m-1} - 1$ and ${M}' =
(6a - 1)2^{2m} - 1$ (in Technical Notes
and Short Papers) . . . . . . . . . . . 420--422
W. Gross and
R. Vacca Distribution of the Figures $0$ and $1$
in the Various Orders of Binary
Representations of $k$th Powers of
Integers (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 423--427
S. Charmonman and
R. S. Julius Explicit Inverses and Condition Numbers
of Certain Circulants (in Technical
Notes and Short Papers) . . . . . . . . 428--430
Philip Rabinowitz Error Bounds in Gaussian Integration of
Functions of Low-Order Continuity (in
Technical Notes and Short Papers) . . . 431--434
H. A. Luther An Explicit Sixth-Order Runge--Kutta
Formula (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 434--436
Paul Gordon A Note on a Maximum Principle for the
DuFort--Frankel Difference Equation (in
Technical Notes and Short Papers) . . . 437--439
D. B. Hunter The Evaluation of a Class of Functions
Defined by an Integral (in Technical
Notes and Short Papers) . . . . . . . . 440--444
M. L. Glasser Some Integrals of the Arctangent
Function (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 445--447
Robert F. Tooper and
John Mark Simplified Calculation of $Ei(x)$ for
Positive Arguments, and a Short Table of
$\operatorname{Shi}(x)$ (in Technical
Notes and Short Papers) . . . . . . . . 448--449
W. J. Cody Chebyshev Approximations for the Fresnel
Integrals (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 450--453
K. B. Oldham Approximations for the $x \exp x^2
\operatorname{erfc} x$ Function (in
Technical Notes and Short Papers) . . . 454--454
Anonymous Corrigenda . . . . . . . . . . . . . . . 474--474
Pierre Jamet Finite Difference Methods for the
Computation of the ``Poisson Kernel'' of
Elliptic Operators . . . . . . . . . . . 477--488
Harvey S. Price Monotone and Oscillation Matrices
Applied to Finite Difference
Approximations . . . . . . . . . . . . . 489--516
Chul-Hee Kim and
R. E. Gilbert Evaluation of a Kernel Associated with
Laminar Flow Tubular Catalytic Reactors 517--523
Mats Y. T. Apelkrans On Difference Schemes for Hyperbolic
Equations with Discontinuous Initial
Values . . . . . . . . . . . . . . . . . 525--539
John Miller On the Resolvent of a Linear Operator
Associated with a Well-Posed Cauchy
Problem . . . . . . . . . . . . . . . . 541--548
A. R. Gourlay and
J. Ll. Morris Finite-Difference Methods for Nonlinear
Hyperbolic Systems. II . . . . . . . . . 549--556
R. W. Klopfenstein and
R. S. Millman Numerical Stability of a One-Evaluation
Predictor-Corrector Algorithm for
Numerical Solution of Ordinary
Differential Equations . . . . . . . . . 557--564
Erwin H. Bareiss Sylvester's Identity and Multistep
Integer-Preserving Gaussian Elimination 565--578
T. L. Jordan Experiments on Error Growth Associated
with some Linear Least-squares
Procedures . . . . . . . . . . . . . . . 579--588
F. D. Burgoyne Bivariate Interpolation of Potential
Functions . . . . . . . . . . . . . . . 589--594
H. L. Gray and
T. A. Atchison The Generalized ${G}$-Transform . . . . 595--605
V. L. N. Sarma Eberlein Measure and Mechanical
Quadrature Formulae. I: Basic Theory . . 607--616
John W. Wrench, Jr. Concerning Two Series for the Gamma
Function . . . . . . . . . . . . . . . . 617--626
Yudell L. Luke Approximations for Elliptic Integrals 627--634
Oscar L. Fleckner A Method for the Computation of the
Fresnel Integrals and Related Functions 635--640
W. J. Cody and
Henry C. Thacher, Jr. Rational Chebyshev Approximations for
the Exponential Integral ${E}_1 (x)$ . . 641--649
M. M. Chawla Error Estimates for the Clenshaw--Curtis
Quadrature . . . . . . . . . . . . . . . 651--656
Franz Stetter Error Bounds for Gauss--Chebyshev
Quadrature (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 657--659
Franz Stetter On a Generalization of the Midpoint Rule
(in Technical Notes and Short Papers) 661--663
Yonathan Bard On a Numerical Instability of
Davidon-Like Methods (in Technical Notes
and Short Papers) . . . . . . . . . . . 665--666
Gilbert C. Best Powers of a Matrix of Special Type (in
Technical Notes and Short Papers) . . . 667--668
Edward L. Spitznagel, Jr. and
Stephen A. Szygenda A Computer Study of the Orders of Finite
Simple Groups (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 669--671
A. M. Chak Polynomial System Satisfying a Special
Functional Equation (in Technical Notes
and Short Papers) . . . . . . . . . . . 673--676
Paul Bratley and
John McKay More Amicable Numbers (in Technical
Notes and Short Papers) . . . . . . . . 677--678
Mohan Lal and
James Dawe Solutions of the Diophantine Equation
$x^2 - Dy^4 = k$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 679--682
Anonymous Corrigenda . . . . . . . . . . . . . . . 699--699
Heinz-Otto Kreiss Stability Theory for Difference
Approximations of Mixed Initial Boundary
Value Problems. I . . . . . . . . . . . 703--714
A. R. Gourlay and
J. Ll. Morris A Multistep Formulation of the Optimized
Lax--Wendroff Method for Nonlinear
Hyperbolic Systems in Two Space
Variables . . . . . . . . . . . . . . . 715--719
Pierre Jamet Numerical Methods and Existence Theorems
for Parabolic Differential Equations
whose Coefficients are Singular on the
Boundary . . . . . . . . . . . . . . . . 721--743
Alexandre Joel Chorin Numerical Solution of the Navier--Stokes
Equations . . . . . . . . . . . . . . . 745--762
Theodore Katsanis Numerical Solution of Symmetric Positive
Differential Equations . . . . . . . . . 763--783
J. M. Varah The Calculation of the Eigenvectors of a
General Complex Matrix by Inverse
Iteration . . . . . . . . . . . . . . . 785--791
J. M. Varah Rigorous Machine Bounds for the
Eigensystem of a General Complex Matrix 793--801
Beresford N. Parlett Global Convergence of the Basic QR
Algorithm on Hessenberg Matrices . . . . 803--817
Choong Yun Cho On the Triangular Decomposition of
Cauchy Matrices . . . . . . . . . . . . 819--825
Harold Willis Milnes A Note Concerning the Properties of a
Certain Class of Test Matrices . . . . . 827--832
G. Dahlquist and
B. Sjoberg and
P. Svensson Comparison of the Method of Averages
with the Method of Least Squares . . . . 833--845
T. N. L. Patterson The Optimum Addition of Points to
Quadrature Formulae . . . . . . . . . . 847--856
I. J. Good and
R. F. Churchhouse The Riemann Hypothesis and Pseudorandom
Features of the Möbius Sequence . . . . . 857--861
Eugene R. Rodemich and
Howard Rumsey, Jr. Primitive Trinomials of High Degree (in
Technical Notes and Short Papers) . . . 863--865
V. J. Law and
R. H. Fariss On the Relations between Eigenvalues and
Eigenvectors for Matrices Resulting from
Pre and Post Multiplication by the
Transpose (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 867--868
T. L. Markham An Iterative Procedure for Computing the
Maximal Root of a Positive Matrix (in
Technical Notes and Short Papers) . . . 869--871
Lee Johnson Unicity in Approximation of a Function
and Its Derivatives (in Technical Notes
and Short Papers) . . . . . . . . . . . 873--875
T. N. L. Patterson On Some Gauss and Lobatto Based
Integration Formulae (in Technical Notes
and Short Papers) . . . . . . . . . . . 877--881
Van E. Wood Efficient Calculation of Clausen's
Integral (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 883--884
D. C. Galant and
P. F. Byrd High Accuracy Gamma Function Values for
Some Rational Arguments (in Technical
Notes and Short Papers) . . . . . . . . 885--887
M. M. Chawla Error Bounds for the Gauss--Chebyshev
Quadrature Formula of the Closed Type
(in Technical Notes and Short Papers) 889--891
W. G. Book Review: Donald Greenspan, editor,
\booktitleNumerical Solutions of
Nonlinear Differential Equations, John
Wiley & Sons, Inc., New York, 1966, x +
347 pp. . . . . . . . . . . . . . . . . 896--898
Anonymous Corrigenda . . . . . . . . . . . . . . . 911--911
Gilbert Stengle Uniform Asymptotic Solution of Second
Order Linear Differential Equations
without Turning Varieties . . . . . . . 1--22
R. B. Kellogg A Nonlinear Alternating Direction Method 23--27
David W. Kammler Numerical Solution of the Dirichlet
Problem for Systems of Circular
Conductors between Parallel Ground Lines 29--36
Blair Swartz and
Burton Wendroff Generalized Finite-Difference Schemes 37--49
J. Boersma Expansions for Coulomb Wave Functions 51--59
H. Van de Vel On the Series Expansion Method for
Computing Incomplete Elliptic Integrals
of the First and Second Kinds . . . . . 61--69
B. W. Ninham and
J. N. Lyness Further Asymptotic Expansions for the
Error Functional . . . . . . . . . . . . 71--83
H. L. Gray and
R. W. Thompson and
G. V. McWilliams A New Approximation for the Chi-Square
Integral . . . . . . . . . . . . . . . . 85--89
James W. Daniel Summation of Series of Positive Terms by
Condensation Transformations . . . . . . 91--96
G. Blanch and
D. S. Clemm The Double Points of Mathieu's
Differential Equation . . . . . . . . . 97--108
Walter Gautschi On the Condition of a Matrix Arising in
the Numerical Inversion of the Laplace
Transform . . . . . . . . . . . . . . . 109--118
C. W. Gear A Simple Set of Test Matrices for
Eigenvalue Programs . . . . . . . . . . 119--125
Victor Lovass-Nagy and
David L. Powers Reduction of Functions of Some
Partitioned Matrices . . . . . . . . . . 127--133
Rodney James and
John Cannon Computation of Isomorphism Classes of
$p$-Groups . . . . . . . . . . . . . . . 135--140
W. G. Spohn On the Lattice Constant for $|x^3 + y^3
+ z^3| \leq 1$ . . . . . . . . . . . . . 141--149
Daniel Shanks On Gauss's Class Number Problems . . . . 151--163
Seymour Haber and
Charles F. Osgood On a Theorem of Piatetsky-Shapiro and
Approximation of Multiple Integrals (in
Technical Notes and Short Papers) . . . 165--168
Z. A. Melzak On the Solid-Packing Constant for
Circles (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 169--172
A. C. R. Newbery Some Extensions of Legendre Quadrature
(in Technical Notes and Short Papers) 173--176
Fred W. Dorr Remarks on the Iterative Solution of the
Neumann Problem on a Rectangle by
Successive Line Over-Relaxation (in
Technical Notes and Short Papers) . . . 177--179
Mohan Lal Iterates of a Number-Theoretic Function
(in Technical Notes and Short Papers) 181--183
P. S. Chiang Computer Investigation of Landau's
Theorem (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 185--188
D. Kershaw The Explicit Inverses of Two Commonly
Occurring Matrices (in Technical Notes
and Short Papers) . . . . . . . . . . . 189--191
Peter A. Businger Extremal Properties of Balanced
Tri-Diagonal Matrices (in Technical
Notes and Short Papers) . . . . . . . . 193--195
George E. Collins Computing Multiplicative Inverses in
$\mathrm{GF}(p)$ (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 197--200
C. H. Yang On Designs of Maximal $(+1,
-1)$-Matrices of Order $n \equiv 2
(\operatorname{mod} 4)$. II (in
Technical Notes and Short Papers) . . . 201--205
Anonymous Corrigenda . . . . . . . . . . . . . . . 219--219
Gene H. Golub and
John H. Welsch Calculation of Gauss Quadrature Rules 221--230
W. E. Smith and
J. N. Lyness Applications of Hilbert Transform Theory
to Numerical Quadrature . . . . . . . . 231--252
M. Wayne Wilson A General Algorithm for Nonnegative
Quadrature Formulas . . . . . . . . . . 253--258
Richard L. Lewis On Finite Integrals Involving
Trigonometric, Bessel, and Legendre
Functions . . . . . . . . . . . . . . . 259--273
Jonas T. Holdeman, Jr. A Method for the Approximation of
Functions Defined by Formal Series
Expansions in Orthogonal Polynomials . . 275--287
W. J. Cody and
Henry C. Thacher, Jr. Chebyshev Approximations for the
Exponential Integral $\mathrm{Ei}(x)$ 289--303
H. M. Srivastava An Extension of the Hille--Hardy Formula 305--311
P. H. Sterbenz and
C. T. Fike Optimal Starting Approximations for
Newton's Method . . . . . . . . . . . . 313--318
D. E. Amos and
W. G. Bulgren On the Computation of a Bivariate
$t$-Distribution . . . . . . . . . . . . 319--333
Stanley Osher Stability of Difference Approximations
of Dissipative Type for Mixed
Initial-Boundary Value Problems . . . . 335--340
Alexandre Joel Chorin On the Convergence of Discrete
Approximations to the Navier--Stokes
Equations . . . . . . . . . . . . . . . 341--353
P. L. Richman Compressible Fluid Flow and the
Approximation of Iterated Integrals of a
Singular Function . . . . . . . . . . . 355--372
V. Thuraisamy Approximate Solutions for Mixed Boundary
Value Problems by Finite-Difference
Methods . . . . . . . . . . . . . . . . 373--386
V. Thuraisamy Monotone Type Discrete Analogue for the
Mixed Boundary Value Problem . . . . . . 387--394
Neil M. Wigley On a Method to Subtract off a
Singularity at a Corner for the
Dirichlet or Neumann Problem . . . . . . 395--401
I. Gargantini On the Computation of the Eigenvalues of
a Tridiagonal Matrix (in Technical Notes
and Short Papers) . . . . . . . . . . . 403--405
Graeme Fairweather A Note on a Generalisation of a Method
of Douglas (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 407--409
T. N. L. Patterson Integration Formulae Involving
Derivatives (in Technical Notes and
Short Papers) . . . . . . . . . . . . . 411--412
Hans Riesel Some Factors of the Numbers ${G}_n =
6^{2^n} + 1$ and ${H}_n = 10^{2^n} + 1$
(in Technical Notes and Short Papers) 413--415
J. van de Lune and
E. Wattel On the Numerical Solution of a
Differential-Difference Equation Arising
in Analytic Number Theory (in Technical
Notes and Short Papers) . . . . . . . . 417--421
M. Lal and
W. Russell and
W. J. Blundon A Note on Sums of Four Cubes (in
Technical Notes and Short Papers) . . . 423--424
E. J. Cockayne Computation of Galois Group Elements of
a Polynomial Equation (in Technical
Notes and Short Papers) . . . . . . . . 425--428
Evelyn Frank Computer Use in Continued Fraction
Expansions (in Technical Notes and Short
Papers) . . . . . . . . . . . . . . . . 429--435
R. E. Barnhill and
J. E. Dennis, Jr. and
G. M. Nielson A New Type of Chebyshev Quadrature (in
Technical Notes and Short Papers) . . . 437--441
Anonymous Corrigenda . . . . . . . . . . . . . . . 473--473
Harvey Cohn Some Computer-Assisted Topological
Models of Hilbert Fundamental Domains 475--487
Robert Spira Calculation of Dirichlet ${L}$-Functions 489--497
Harold Brown An Algorithm for the Determination of
Space Groups . . . . . . . . . . . . . . 499--514
H. Zassenhaus and
J. Liang On a Problem of Hasse . . . . . . . . . 515--519
E. J. Cockayne Computation of minimal length full
Steiner trees on the vertices of a
convex polygon . . . . . . . . . . . . . 521--531
Tauno Metsankyla Calculation of the First Factor of the
Class Number of the Cyclotomic Field . . 533--537
Peter Hagis, Jr. On Relatively Prime Odd Amicable Numbers 539--543
Elvin Lee On Divisibility by Nine of the Sums of
Even Amicable Pairs . . . . . . . . . . 545--548
S. Abarbanel and
G. Zwas An Iterative Finite-Difference Method
for Hyperbolic Systems . . . . . . . . . 549--565
Stanley Osher On Systems of Difference Equations with
Wrong Boundary Conditions . . . . . . . 567--572
James W. Daniel On the Approximate Minimization of
Functionals . . . . . . . . . . . . . . 573--581
J. B. Diaz and
H. W. McLaughlin Simultaneous Approximation of a Set of
Bounded Real Functions . . . . . . . . . 583--593
Peter Linz A Method for Solving Nonlinear Volterra
Integral Equations of the Second Kind 595--599
J. N. Lyness Quadrature Methods Based on Complex
Function Values . . . . . . . . . . . . 601--619
S. W. Kahng Osculatory Interpolation . . . . . . . . 621--629
W. J. Cody Rational Chebyshev Approximations for
the Error Function . . . . . . . . . . . 631--637
Edward W. Ng and
C. J. Devine and
R. F. Tooper Chebyshev Polynomial Expansion of
Bose--Einstein Functions of Orders $1$
to $10$ . . . . . . . . . . . . . . . . 639--643
Alex Reichel The Integral of the $n$th Power of the
Voigt Function . . . . . . . . . . . . . 645--649
Chi Fu Den Summation of a Slowly Convergent Series
Arising in Antenna Study . . . . . . . . 651--654
D. E. Amos On Computation of the Bivariate Normal
Distribution . . . . . . . . . . . . . . 655--659
N. M. Steen and
G. D. Byrne and
E. M. Gelbard Gaussian Quadratures for the Integrals
$\int^\infty_0 \exp(-x^2)f(x)dx$ and
$\int^b_0 \exp(-x^2)f(x)dx$ . . . . . . 661--671
Milton R. Pine Notes on the Tables for Gaussian
Quadrature of N. M. Steen, G. D. Byrne
and E. M. Gelbard . . . . . . . . . . . 673--673
David Galant Gauss Quadrature Rules for the
Evaluation of $2\pi^{-1/2} \int^\infty_0
\exp (-x^2)f(x)dx$ . . . . . . . . . . . 674
Anonymous Corrigendum . . . . . . . . . . . . . . 693--693
J. H. Bramble and
B. E. Hubbard and
Vidar Thomee Convergence Estimates for Essentially
Positive Type Discrete Dirichlet
Problems . . . . . . . . . . . . . . . . 695--709
Carl E. Pearson Asymptotic Behavior of Solutions to the
Finite-Difference Wave Equation . . . . 711--715
Alfred Carasso Finite-Difference Methods and the
Eigenvalue Problem for Nonselfadjoint
Sturm--Liouville Operators . . . . . . . 717--729
L. F. Shampine and
H. A. Watts Block Implicit One-Step Methods . . . . 731--740
James Case A Note on the Stability of
Predictor-Corrector Techniques . . . . . 741--749
Seymour Haber Stochastic Quadrature Formulas . . . . . 751--764
Philip Rabinowitz and
Nira Richter Perfectly Symmetric Two-Dimensional
Integration Formulas with Minimal
Numbers of Points . . . . . . . . . . . 765--779
V. L. N. Sarma and
A. H. Stroud Eberlein Measure and Mechanical
Quadrature Formulae. II. Numerical
Results . . . . . . . . . . . . . . . . 781--784
Michael Goldberg Stability Configurations of Electrons on
a Sphere . . . . . . . . . . . . . . . . 785--786
Richard J. Hanson and
Charles L. Lawson Extensions and Applications of the
Householder Algorithm for Solving Linear
Least Squares Problems . . . . . . . . . 787--812
Marcel Meicler A Steepest Ascent Method for the
Chebyshev Problem . . . . . . . . . . . 813--817
P. A. Businger Reducing a Matrix to Hessenberg Form . . 819--821
Robert J. Herbold A Generalization of a Class of Test
Matrices . . . . . . . . . . . . . . . . 823--826
Jerry A. Walters Nonnegative Matrix Equations Having
Positive Solutions . . . . . . . . . . . 827--827
G. W. Stewart, III On Lehmer's Method for Finding the Zeros
of a Polynomial . . . . . . . . . . . . 829--835, s24--s30
R. E. Scraton The Solution of Integral Equations in
Chebyshev Series . . . . . . . . . . . . 837--844
E. O. Schulz-DuBois Integral Relations Among Bessel
Functions . . . . . . . . . . . . . . . 845--847
H. L. Gray and
W. R. Schucany Some Limiting Cases of the
${G}$-Transformation . . . . . . . . . . 849--859
Robert J. McEliece Factorization of Polynomials Over Finite
Fields . . . . . . . . . . . . . . . . . 861--867
Hans Riesel Lucasian Criteria for the Primality of
$\mathcal{N} = h \cdot 2^n - 1$ . . . . 869--875
Simcha Brudno Some New Results on Equal Sums of Like
Powers . . . . . . . . . . . . . . . . . 877--880
Anonymous Corrigenda . . . . . . . . . . . . . . . 893--893
G. W. Stewart, III Corrigendum: ``On Lehmer's Method for
Finding the Zeros of a Polynomial'' . . 203--203
Jet Wimp Corrigendum: \booktitlePolynomial
expansions of Bessel functions and some
associated functions (Math. Comp. \bf 16
(1962), 446--458) . . . . . . . . . . . 309--309