Last update: Tue Sep 17 11:02:32 MDT 2024
Volume 4, Number 29, January, 1950R. C. Gibbs Note of Appreciation . . . . . . . . . . 1--1 Albert A. Bennett Raymond Clare Archibald . . . . . . . . 1--2 J. C. P. Miller Checking by Differences---I . . . . . . 3--11 George W. Reitwiesner An ENIAC Determination of $\pi$ and $e$ to more than 2000 Decimal Places . . . . 11--15 Arnold A. Cohen Technical Developments: Magnetic Drum Storage for Digital Information Processing Systems (in Automatic Computing Machinery) . . . . . . . . . . 31--39 Anonymous Notes on Modern Numerical Analysis---I (in Automatic Computing Machinery; Discussions) . . . . . . . . . . . . . . 39--39 John Todd Solution of Differential Equations by Recurrence Relations (in Automatic Computing Machinery; Discussions) . . . 39--44 G. A. Montgomerie Addition and Subtraction on a Logarithmic Slide Rule (in Other Aids to Computation) . . . . . . . . . . . . . . 53--53 Anonymous Corrigenda . . . . . . . . . . . . . . . 59--59
M. V. Wilkes and W. Renwick The EDSAC (Electronic Delay Storage Automatic Calculator) . . . . . . . . . 61--65 Stanley P. Frankel Convergence Rates of Iterative Treatments of Partial Differential Equations . . . . . . . . . . . . . . . 65--75 R. H. Ritchie On a Definite Integral . . . . . . . . . 75--77 H. D. Huskey Technical Developments: Characteristics of the Institute for Numerical Analysis Computer (in Automatic Computing Machinery) . . . . . . . . . . . . . . . 103--108 N. C. Metropolis and G. Reitwiesner and J. von Neumann Statistical treatment of values of first $2,000$ decimal digits of $e$ and of $\pi$ calculated on the ENIAC . . . . . 109--111 Olga Taussky Notes on Numerical Analysis. II. Note on the Condition of Matrices . . . . . . . 111--112 Anonymous Corrigenda . . . . . . . . . . . . . . . 125--125
George E. Forsythe and Richard A. Leibler Matrix Inversion by a Monte Carlo Method 127--129 D. H. Sadler Maximum-Interval Tables . . . . . . . . 129--132 F. J. M. Planning and Error Considerations for the Numerical Solution of a System of Differential Equations on a Sequence Calculator . . . . . . . . . . . . . . . 133--144 MDL Staff Technical Developments: The Incorporation of Subroutines into a Complete Problem on the NBS Eastern Automatic Computer (in Automatic Computing Machinery) . . . . . . . . . . 164--168 G. R. Stibitz A Note on ``Is'' and ``Might Be'' in Computers (in Automatic Computing Machinery; Discussions) . . . . . . . . 168--169 Anonymous Corrigenda . . . . . . . . . . . . . . . 180--180
A. Reiz On a Special Case of a Quadrature Formula of Christoffel . . . . . . . . . 181--185 R. C. Archibald New Information Concerning Isaac Wolfram's Life and Calculations . . . . 185--200 L. Couffignal Technical Developments: Report on the Machine of the Institut Blaise Pascal (in Automatic Computing Machinery) . . . 225--229 Electronic Laboratory Staff at N. B. S. The Operating Characteristics of the SEAC (in Automatic Computing Machinery) 229--230 J. O. Harrison, Jr. Binary--Decimal Conversion on a Desk Calculator (in Automatic Computing Machinery; Discussions) . . . . . . . . 231--234 Anonymous Bibliography Z --- XIII . . . . . . . . 234--238 Anonymous News . . . . . . . . . . . . . . . . . . 238--239 Anonymous Bibliography Z--XIII . . . . . . . . . . 239--244 Fred Gruenberger Tests of random digits . . . . . . . . . 244--245 Anonymous Corrigenda . . . . . . . . . . . . . . . 246--246
D. F. Votaw, Jr. and J. A. Rafferty High Speed Sampling . . . . . . . . . . 1--8 H. E. Salzer Radix Table for Trigonometric Functions and their Inverses to High Accuracy . . 9--11 Goran Kjellberg and Gosta Neovius Technical Developments: The BARK, A Swedish General Relay Computer (in Automatic Computing Machinery) . . . . . 29--34 C. W. Clenshaw and F. W. J. Olver Notes on Numerical Analysis---3: Solution of Differential Equations by Recurrence Relations (in Automatic Computing Machinery; Discussions) . . . 34--39 Anonymous Corrigenda . . . . . . . . . . . . . . . 55--55
Paul L. Morton The California Digital Computer . . . . 57--61 Samuel Herrick Step-by-Step Integration of $\ddot x = f(x, y, z, t)$ without a ``Corrector'' 61--67 H. E. Salzer Formulas for Calculating the Error Function of a Complex Variable . . . . . 67--70 Anonymous Technical Developments (in Automatic Computing Machinery) . . . . . . . . . . 86--86 Donald B. MacMillan and Richard H. Stark ``Floating Decimal'' Calculation on the IBM Card Programmed Electronic Calculator (in Automatic Computing Machinery; Discussions) . . . . . . . . 86--92 L. Fox Notes on Numerical Analysis---4: Relaxation and Step-by-Step Methods (in Automatic Computing Machinery; Discussions) . . . . . . . . . . . . . . 92--95 C. P. Atkinson and A. S. Levens A New Differentiating Machine (in Other Aids to Computation) . . . . . . . . . . 99--102 Anonymous Bibliography Z--XV . . . . . . . . . . . 102--108 Fred Gruenberger and A. M. Mark The $d^2$ test of random digits . . . . 109--110 Anonymous Corrigenda . . . . . . . . . . . . . . . 113--113
Ascher Opler Monte Carlo Matrix Calculation with Punched Card Machines . . . . . . . . . 115--120 Wilton R. Abbott Computing Logical Truth with the California Digital Computer . . . . . . 120--128 Max Lotkin On the Accuracy of Runge--Kutta's Method 128--133 L. Fox and J. C. P. Miller Notes on Numerical Analysis---5: Table-Making for Large Arguments. The Exponential Integral (in Automatic Computing Machinery) . . . . . . . . . . 163--166 J. T. Editorial Note (in Automatic Computing Machinery) . . . . . . . . . . . . . . . 167--167 Anonymous Corrigenda . . . . . . . . . . . . . . . 184--184
G. Blanch and E. C. Yowell A Guide to Tables on Punched Cards . . . 185--212 H. E. Salzer Formulas for Finding the Argument for which a Function has a Given Derivative 213--215 P. Stein Technical Developments: Provision for Expansion in the SEAC (in Automatic Computing Machinery) . . . . . . . . . . 232--240 John E. Maxfield and Frederick V. Waugh A Graphic Solution of Simultaneous Linear Equations (in Other Aids to Computation) . . . . . . . . . . . . . . 246--248 Anonymous Corrigenda . . . . . . . . . . . . . . . 259--259
Granino A. Korn The Difference Analyzer: a Simple Differential Equation Solver . . . . . . 1--8 George E. Forsythe and Theodore S. Motzkin An Extension of Gauss' Transformation for Improving the Condition of Systems of Linear Equations . . . . . . . . . . 9--17 R. E. Sprague Technical Developments: Fundamental Concepts of the Digital Differential Analyzer Method of Computation (in Automatic Computing Machinery) . . . . . 41--49 Anonymous Corrigenda . . . . . . . . . . . . . . . 61--61
P. Brock and F. J. Murray The Use of Exponential Sums in Step by Step Integration . . . . . . . . . . . . 63--78 W. R. Wasow A Note on the Inversion of Matrices by Random Walks . . . . . . . . . . . . . . 78--81 John F. Donan Technical Developments: The Serial-Memory Digital Differential Analyzer (in Automatic Computing Machinery) . . . . . . . . . . . . . . . 102--112 R. A. Brooker and S. Gill and D. J. Wheeler The Adventures of a Blunder (in Automatic Computing Machinery; Discussions) . . . . . . . . . . . . . . 112--113 Anonymous Corrigenda . . . . . . . . . . . . . . . 126--126
D. Teichroew Use of Continued Fractions in High Speed Computing . . . . . . . . . . . . . . . 127--133 B. A. Griffith and K. W. Smillie On a Punched-Card Method of Solving Certain Integral Equations . . . . . . . 133--138 P. Brock and F. J. Murray The Use of Exponential Sums in Step by Step Integration---II . . . . . . . . . 138--150 T. Pearcey Technical Developments: An Automatic Computer in Australia (in Automatic Computing Machinery) . . . . . . . . . . 167--172 David P. Perry Minimum Access Programming (in Automatic Computing Machinery; Discussions) . . . 172--182 Landis Gephart Linear Algebraic Systems and the REAC (in Other Aids to Computation) . . . . . 190--203
J. Jay Wolf The Office of Naval Research Relay Computer . . . . . . . . . . . . . . . . 207--212 A. M. Ostrowski On the Rounding Off of Difference Tables for Linear Interpolation . . . . . . . . 212--214 Yudell L. Luke Mechanical Quadrature Near a Singularity 215--219 Gertrude Blanch On the Numerical Solution of Equations Involving Differential Operators With Constant Coefficients . . . . . . . . . 219--223 S. Lubkin Asynchronous Signals in Digital Computers (in Automatic Computing Machinery; Discussions) . . . . . . . . 238--241 Anonymous Corrigenda . . . . . . . . . . . . . . . 257--257
Gertrude Blanch and Everett C. Yowell Addendum to a Guide to Tables on Punched Cards . . . . . . . . . . . . . . . . . 1--6 D. H. L. The Sieve Problem for All-Purpose Computers . . . . . . . . . . . . . . . 6--14 L. Fox The Use of Large Intervals in Finite-Difference Equations . . . . . . 14--18 H. P. Edmundson Monte Carlo Matrix Inversion and Recurrent Events . . . . . . . . . . . . 18--21 J. J. Stone Technical Developments: The USAF--Fairchild Specialized Computer (in Automatic Computing Machinery) . . . . . 34--37 R. A. Brooker and D. J. Wheeler Floating Operations on the EDSAC (in Automatic Computing Machinery; Discussions) . . . . . . . . . . . . . . 37--47 Max G. Scherberg and John F. Riordan Analogue Calculation of Polynomial and Trigonometric Expansions (in Other Aids to Computation) . . . . . . . . . . . . 61--65 Anonymous Corrigenda . . . . . . . . . . . . . . . 72--72 D. H. Lehmer Two New Mersenne Primes . . . . . . . . 72--72
H. J. Gray, Jr. and M. Rubinoff and H. Sohon A Technique for Real Time Simulation of a Rigid Body Problem . . . . . . . . . . 73--77 Gabriel G. Bejarano and Bruce R. Rosenblatt A Solution of Simultaneous Linear Equations and Matrix Inversion With High Speed Computing Devices . . . . . . . . 77--81 A. de la Garza Error Bounds of Approximate Solutions to Systems of Linear Algebraic Equations 81--84 Gerald Estrin Technical Developments: The Electronic Computer at the Institute for Advanced Study (in Automatic Computing Machinery) 108--114
J. von Neumann and H. H. Goldstine A numerical study of a conjecture of Kummer . . . . . . . . . . . . . . . . . 133--134
Anonymous Corrigenda . . . . . . . . . . . . . . . 134--134
E. C. Du Fort and S. P. Frankel Stability Conditions in the Numerical Treatment of Parabolic Differential Equations . . . . . . . . . . . . . . . 135--152 A. Ostrowski On Over and Under Relaxation in the Theory of the Cyclic Single Step Iteration . . . . . . . . . . . . . . . 152--159 Theodore E. Sterne The Accuracy of Numerical Solutions of Ordinary Differential Equations . . . . 159--164 K. E. Iverson The Zeros of the Partial Sums of $e^z$ 165--168 J. P. Walker, Jr. Technical Developments: a Special Purpose Digital Computer (in Automatic Computing Machinery) . . . . . . . . . . 190--195 Anonymous Corrigenda . . . . . . . . . . . . . . . 213--213
Robert T. Gregory Computing Eigenvalues and Eigenvectors of a Symmetric Matrix on the ILLIAC . . 215--220 George E. Forsythe A Numerical Analyst's Fifteen-Foot Shelf 221--228 Edward Saibel and W. J. Berger On Finding the Characteristic Equation of a Square Matrix . . . . . . . . . . . 228--236 Anonymous Recent Mathematical Tables . . . . . . . 236--246 Anonymous Mathematical Tables --- Errata . . . . . 246--247 Anonymous Unpublished Mathematical Tables . . . . 247--249 John Greig Technical Developments: The Circle Computer (in Automatic Computing Machinery) . . . . . . . . . . . . . . . 249--255 Anonymous Bibliography of Coding Procedure . . . . 256--256 Anonymous Bibliography Z . . . . . . . . . . . . . 256--266 Anonymous News . . . . . . . . . . . . . . . . . . 266--268 Anonymous Bibliography Z . . . . . . . . . . . . . 268--272 W. F. Cahill and Philip Davis Note: On a computation of the capacity of a cube . . . . . . . . . . . . . . . 272--273 Walter Soden Note: a Method of Radix Conversion . . . 273--274 J. L. Selfridge Note: Factors of Fermat numbers . . . . 274--275 Anonymous Corrigenda . . . . . . . . . . . . . . . 275--275 Anonymous Volume Information . . . . . . . . . . . 276--289 Anonymous Back Matter . . . . . . . . . . . . . . ??
Gertrude Blanch On Modified Divided Differences I . . . 1--11 G. C. Best A Minimum Problem Solved by Mesh Methods 11--13 M. C. K. Tweedie A Modification of the Aitken--Neville Linear Iterative Procedures for Polynomial Interpolation . . . . . . . . 13--16 J. N. P. Hume Technical Developments: Input and Organization of Sub-Routines for Ferut (in Automatic Computing Machinery) . . . 30--36 W. F. Cahill Programs for Computing the Hypergeometric Series (in Automatic Computing Machinery; Discussions) . . . 36--37 Anonymous Corrigendum . . . . . . . . . . . . . . 51--51
Arthur W. Burks and Don W. Warren and Jesse B. Wright An Analysis of a Logical Machine Using Parenthesis-Free Notation . . . . . . . 53--57 Oliver Gross Polynomial-Like Approximation . . . . . 58--60 Daniel Shanks A Logarithm Algorithm . . . . . . . . . 60--64 George B. Dantzig and Wm. Orchard-Hays The Product Form for the Inverse in the Simplex Method . . . . . . . . . . . . . 64--67 Gertrude Blanch On Modified Divided Differences II . . . 67--75 Andrew D. Booth Technical Developments: The Development of A.P.E.(X).C. (in Automatic Computing Machinery) . . . . . . . . . . . . . . . 98--105 Anonymous Corrigendum . . . . . . . . . . . . . . 124--124
James D. Riley Iteration Procedures for the Dirichlet Difference Problem . . . . . . . . . . . 125--131 Robert L. LaFara A Method for Calculating Inverse Trigonometric Functions . . . . . . . . 132--139 Harvey M. Wagner A Partitioning Method of Inverting Symmetric Definite Matrices on a Card-Programmed Calculator . . . . . . . 139--143 C. W. Clenshaw Polynomial Approximations to Elementary Functions . . . . . . . . . . . . . . . 143--147 Jan V. Garwick Technical Developments: a Punched Card Machine Especially Equipped for Scientific Computations (in Automatic Computing Machinery) . . . . . . . . . . 167--170 Anonymous Corrigenda . . . . . . . . . . . . . . . 188--188
J. H. Curtiss A Generalization of the Method of Conjugate Gradients for Solving Systems of Linear Algebraic Equations . . . . . 189--193 P. Davis and P. Rabinowitz On the Estimation of Quadrature Errors for Analytic Functions . . . . . . . . . 193--203 A. Dalgarno Integrals Occurring in Problems of Molecular Structure . . . . . . . . . . 203--212 Robert L. Bivins and N. Metropolis and Paul R. Stein and Mark B. Wells Characters of the Symmetric Groups of Degree $15$ and $16$ . . . . . . . . . . 212--216 Anonymous Recent Mathematical Tables . . . . . . . 216--226 Anonymous Mathematical Tables---Errata . . . . . . 227--228 Lorraine Schwartz Review of P. C. Mahalanobis, \em Tables of random samples from a normal population . . . . . . . . . . . . . . . 228--230 Anonymous Bibliography of Coding Procedure . . . . 230--231 Anonymous Bibliography Z . . . . . . . . . . . . . 231--233 J. E. Maxfield A Useful Technique in Programming for Analog Computers (in Other Aids to Computation) . . . . . . . . . . . . . . 233--234 Anonymous Corrigenda . . . . . . . . . . . . . . . 245--245
Robert E. Greenwood Coupon Collector's Test for Random Digits . . . . . . . . . . . . . . . . . 1--5 J. A. Postley A Method for the Evaluation of a System of Boolean Algebraic Equations . . . . . 5--8 Stefan Bergman Tables for the Determination of Fundamental Solutions of Equations in the Theory of Compressible Fluids . . . 8--14 Eugene H. Herbst and N. Metropolis and Mark B. Wells Analysis of Problem Codes on the MANIAC 14--20 A. D. Booth A note on approximating polynomials for trigonometric functions . . . . . . . . 21--23 R. C. Archibald and A. D. Booth and John von Neumann and Bryant Tuckerman and B. Zondek and R. L. La Fara Technical Notes and Short Papers . . . . 21--25 John von Neumann and Bryant Tuckerman Continued Fraction Expansion of $2^{1/3}$ . . . . . . . . . . . . . . . 23--25 Anonymous Corrigenda . . . . . . . . . . . . . . . 45--45
J. Greenstadt A Method for Finding Roots of Arbitrary Matrices . . . . . . . . . . . . . . . . 47--52 Kuo-Chu Ho Double Interpolation Formulae and Partial Derivatives in Terms of Finite Differences . . . . . . . . . . . . . . 52--62 R. C. Archibald and Luigi Jacchia and A. M. Ostrowski and Preston C. Hammer and S. Lipton Technical Notes and Short Papers . . . . 62--70
Henry E. Fettis Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula . . . . . . . . . . . 85--92 Preston C. Hammer and Jack W. Hollingsworth Trapezoidal Methods of Approximating Solutions of Differential Equations . . 92--96 James D. Riley Solving Systems of Linear Equations With a Positive Definite, Symmetric, but Possibly Ill-Conditioned Matrix . . . . 96--101 John W. Sheldon On the Numerical Solution of Elliptic Difference Equations . . . . . . . . . . 101--112 Beatrice H. Worsley Solutions of a Nonlinear Differential Equation Arising in the Theory of Diffusion Flames . . . . . . . . . . . . 112--116 C. W. Clenshaw A note on the summation of Chebyshev series . . . . . . . . . . . . . . . . . 118--120 I. J. Good Conjectures concerning the Mersenne numbers . . . . . . . . . . . . . . . . 120--120 J. L. Brenner and G. W. Reitwiesner and C. W. Clenshaw and I. J. Good Technical Notes and Short Papers . . . . 117--121 Anonymous Reviews and Descriptions of Tables and Books . . . . . . . . . . . . . . . . . 126--136 Anonymous Corrigenda . . . . . . . . . . . . . . . 137--137
Cyril Atkinson Polynomial Root Solving on the Electronic Differential Analyser (A Technique for Finding the Real and Complex Roots of a Polynomial Using an Electronic Differential Analyser) . . . 139--143 Stig Comét Notations for Partitions . . . . . . . . 143--146 Marshall Hall, Jr. and J. D. Swift Determination of Steiner Triple Systems of Order $15$ . . . . . . . . . . . . . 146--152 Mark Lotkin A Set of Test Matrices . . . . . . . . . 153--161 S. C. Nicholson and J. Jeenel Some Comments on a NORC Computation of $\pi$ . . . . . . . . . . . . . . . . . 162--164 Herbert E. Salzer Orthogonal Polynomials Arising in the Numerical Evaluation of Inverse Laplace Transforms . . . . . . . . . . . . . . . 164--177 James N. Snyder On the Improvement of the Solutions to a Set of Simultaneous Linear Equations Using the ILLIAC . . . . . . . . . . . . 177--184 J. H. Wilkinson The Use of Iterative Methods for Finding the Latent Roots and Vectors of Matrices 184--191 M. Dank and S. W. Barber and N. Macon Technical Notes and Short Papers . . . . 191--195 Anonymous Corrigenda . . . . . . . . . . . . . . . 229--229
P. Davis and P. Rabinowitz Some Monte Carlo Experiments in Computing Multiple Integrals . . . . . . 1--8 D. L. Johnson Generating and Testing Pseudo Random Numbers on the IBM Type 701 . . . . . . 8--13 Yudell L. Luke Evaluation of an Integral Arising in Numerical Integration Near a Logarithmic Singularity . . . . . . . . . . . . . . 14--21 R. J. Porter On Irregular Negative Determinants of Exponent $9n$ . . . . . . . . . . . . . 22--25 George E. Forsythe and Morio Onoe and Z. Pawlak and R. A. Rubenstein and Marjorie Huse and Stefan Machlup and Hugh E. Stelson Technical Notes and Short Papers . . . . 25--34 C. B. Tompkins Review of \em A Million Random Digits With 100,000 Normal Deviates . . . . . . 39--43 Anonymous Corrigenda . . . . . . . . . . . . . . . 55--55
A. Ashour and A. Sabri Tabulation of the Function $\psi(\theta) = \sum_{n=1}^\infty \frac{\sin n\theta}{n^2}$ . . . . . . . . . . . . . 57--65 G. A. Chisnall A Modified Chebyshev--Everett Interpolation Formula . . . . . . . . . 66--73 D. P. Flemming Iterative Procedure for Evaluating a Transient Response Through its Power Series . . . . . . . . . . . . . . . . . 73--81 T. R. Goodman and G. N. Lance The Numerical Integration of Two-Point Boundary Value Problems . . . . . . . . 82--86 K. S. Kunz High Accuracy Quadrature Formulas From Divided Differences With Repeated Arguments . . . . . . . . . . . . . . . 87--90 P. Wynn On a Device for Computing the $e_m({S}_n)$ Transformation . . . . . . 91--96 E. T. Goodwin and P. Wynn Technical Notes and Short Papers . . . . 96--100
Harvey Cohn Stability Configurations of Electrons on a Sphere . . . . . . . . . . . . . . . . 117--120 D. P. Flemming An Iterative Method for Taylor Expansion of Rational Functions, and Applications 120--130 P. C. Hammer and O. J. Marlowe and A. H. Stroud Numerical Integration Over Simplexes and Cones . . . . . . . . . . . . . . . . . 130--137 Preston C. Hammer and Arthur H. Stroud Numerical Integration Over Simplexes . . 137--139 H. Hurwitz, Jr. and P. F. Zweifel Numerical Quadrature of Fourier Transform Integrals . . . . . . . . . . 140--149 Herbert E. Salzer Formulas for the Partial Summation of Series . . . . . . . . . . . . . . . . . 149--156 R. B. Horgan and E. E. Allen and D. D. Wall Technical Notes and Short Papers . . . . 156--168 Olga Taussky Alan Mathison Turing 1912--1954 . . . . 180--181 Anonymous Corrigenda . . . . . . . . . . . . . . . 182--182
P. R. Garabedian Estimation of the Relaxation Factor for Small Mesh Size . . . . . . . . . . . . 183--185 Marshall Hall, Jr. and J. Dean Swift and Robert J. Walker Uniqueness of the Projective Plane of Order Eight . . . . . . . . . . . . . . 186--194 Emma Lehmer On the Location of Gauss Sums . . . . . 194--202 D. R. Morrison A Method for Computing Certain Inverse Functions . . . . . . . . . . . . . . . 202--208 David E. Muller A Method for Solving Algebraic Equations Using an Automatic Computer . . . . . . 208--215 Thomas H. Southard Everett's Formula for Bivariate Interpolation and Throwback of Fourth Differences . . . . . . . . . . . . . . 216--223 K. W. Morton and H. Nagler and Hans Riesel Technical Notes and Short Papers . . . . 223--227 Anonymous Corrigenda . . . . . . . . . . . . . . . 262--263
Herbert Fishman Numerical Integration Constants . . . . 1--9 Frank E. Harris Tables of the Exponential Integral $ {\rm Ei}(x) $ . . . . . . . . . . . . . 9--16 Yudell L. Luke On the Computation of $\log {Z}$ and $\operatorname{arc} \tan {Z}$ . . . . . 16--18 LL. G. Chambers and Raphael M. Robinson Technical Notes and Short Papers . . . . 19--22 Anonymous Corrigenda . . . . . . . . . . . . . . . 54--54
Thomas C. Doyle Inversion of Symmetric Coefficient Matrix of Positive-Definite Quadratic Form . . . . . . . . . . . . . . . . . . 55--58 Preston C. Hammer and A. Wayne Wymore Numerical Evaluation of Multiple Integrals I . . . . . . . . . . . . . . 59--67 R. V. Viswanathan Solution of Poisson's Equation by Relaxation Method---Normal Gradient Specified on Curved Boundaries . . . . . 67--78 G. Belford and L. Jackson Laslett and J. N. Snyder Table Pertaining to Solutions of a Hill Equation . . . . . . . . . . . . . . . . 79--81 J. M. Cook Rational Formulae for the Production of a Spherically Symmetric Probability Distribution . . . . . . . . . . . . . . 81--82 I. J. Good On the Numerical Solution of Integral Equations . . . . . . . . . . . . . . . 82--83 M. J. R. Healy A Rotation Method for Computing Canonical Correlations . . . . . . . . . 83--86 A. J. M. Hitchcock Polynomial Approximations to Bessel Functions of Order Zero and One and to Related Functions . . . . . . . . . . . 86--88 N. S. Mendelsohn An Iterative Method for the Solution of Linear Equations Based on the Power Method for Proper Vectors . . . . . . . 88--91 N. S. Mendelsohn The Computation of Complex Proper Values and Vectors of a Real Matrix with Application to Polynomials . . . . . . . 91--94 H. I. Meyer and B. J. Hollingsworth A Method of Inverting Large Matrices of Special Form . . . . . . . . . . . . . . 94--97 J. C. P. Miller Note on the General Solution of the Confluent Hypergeometric Equation . . . 97--99 Thomas H. Southard Approximation and Table of the Weierstrass $\wp$ Function in the Equianharmonic Case for Real Argument 99--100 Harvey M. Wagner A Lemma for Automatic Optimum Programming on the IBM 650 . . . . . . . 101--104 C. B. T. Book Review: A. V. Lebedev and R. M. Fedorova, \booktitleSpravochnik po Matematicheskim Tablitsam (Guide to Mathematical Tables), Moscow, 1956, xlvi + 549 p., 26 cm. Price 29.20 rubles . . 104--106 Morris Newman Comment: D. H. Lehmer, \booktitleOn the diophantine equation $x^3 + y^3 + z^3 = 1$, London Math. Soc., Jn., v. 31, 1956, p. 275--280 . . . . . . . . . . . . . . 106--107 Harvey Cohn Comment: J. Godwin, \booktitleReal quartic fields with small discriminant, London Math. Soc., Jn., v. 31, 1956, p. 478--485 . . . . . . . . . . . . . . . . 107--107 Morris Newman Comment: D. H. Lehmer, \booktitleOn the roots of the Riemann zeta-function, Acta Mathematica, v. 95, 1956, p. 291--298 107--108 W. L. Wilson, Jr. Comment: W. L. Wilson, Jr., \booktitleTables of Inverses to Laplacian Operators over Triangular Grids, two typewritten leaves $81 \times 11$ inches and one transparency $27 \times 48$ inches deposited in UMT File 108--108 C. B. T. Comment: NBS Applied Mathematics Series, No. 35, \booktitleTables of Lagrangian Coefficients for Sexagesimal Interpolation, U. S. Govt. Printing Office, Wash- ington, D. C., 1954, ix + 157 p., 26 cm. Price \$2.00} . . . . . . 108--108 J. T. Comment: E. Salzer, \booktitleCoefficients for complex osculatory interpolation over a Cartesian grid, J. Math. Phys., v. 35, 1956, p. 152--163 . . . . . . . . . . . 109--109 Morris Newman Comment: O. Emersleben, \booktitleAnwendungen zahlentheoretischer Abschatzungen bei numerischen Rechnungen, Z. angew. Math. Mech., v. 33, 1953, p. 1-3. O. Emersleben, \booktitleÜber Summen Epsteinscher Zetafunktionen regelmassig Verteilter unterer' Parameter, Math. Nachr., v. 13, 1955, p. 59-72. O. Emersleben, \booktitleÜber Zwei Epsteinsche Zetafunktionen 4. und 8. Ordnung, Ber. Math. Tagung, 1953, p. 233-250. O. Emersleben, \booktitleÜber eine doppelperiodische Parallelströmung zäher Flüssigkeiten, Z. angew. Math. Mech., v. 35, 1955, p. 156--160 . . . . 109--110 C. B. T. Comment: T. H. Southard, \booktitleApproximation and table of the Weierstrass $\wp$ function in the equianharmonic case for real argument. [MTAC, this issue, p. 99--100] . . . . . 110--110 C. B. T Comment: F. H. Hollander and C. B. Tompkins, \booktitleWhat you should know about digital computers, Chem. Eng. Prog., v. 52, 1956, p. 451--454 . . . . 110--110 F. H. Hollander Comment: G. Belford, L. Jackson Laslett, and J. N. Snyder, \booktitleTable Pertaining to Solutions of a Hill Equation, 1956, 420 p., two $8\frac{1}{2} \times 11$ multilithed copies in notebook binders deposited in the UMT file. . . . . . . . . . . . . . 110--110 Peter Henrici Comment: D. Bierens de Haan, \booktitleNouvelles Tables d'Intégrales Définies, Hafner Publishing Co., New York, 1957 (edition of 1867-corrected), xiv + 716 p., 24 cm. Price \$12.50} . . 111--111 J. T. Comment: Ernst Glowatzki, \booktitleSechsstellige Tafel der Cauer-Parameter, Abh. Bayer. Akad. Wiss. Math.-Nat. Kl. (N.F.), v. 67, 1955, 37 p. . . . . . . . . . . . . . . . . . . . 111--111 C. T. Tomizuka Comment: T. Sasaki, \booktitleThe Effect of Earth and Sea on the Propagation of Radio Waves, Numerical Computation Bureau, Report No. 6, Tokyo, 1952. 14 mimeographed pages of theory, 25 cm., and 6 tables of functions, $25 \times 34$ cm. . . . . . . . . . . . . . . . . 111--112 Harold Davis Comment: J. Halcomb Laning, Jr., and Richard H. Battin, \booktitleRandom Processes in Automatic Control, McGraw-Hill Series in Control Systems Engineering, McGraw-Hill Book Co., Inc., New York, 1956, ix + 434 p., 23 cm. Price \$10.00} . . . . . . . . . . . . . 112--112 M. A. Melkanoff Comment: J. L. Wolfson and H. S. Gellman, \booktitleFive Figure Tables for the Conversion of Electron Momentum to Electron Kinetic Energy from 100 to 20000 Gauss-Cm, Atomic Energy of Canada, Ltd., Chalk River, Ontario, 1954 (reprinted July, 1956), A.E.C.L. Report No. 327, i + 43 p., 27 cm. Price \$1.00} 112--113 P. P. Ewald Comment: O. Emersleben, \booktitleDer Wert der Madelung Konstanten des Steinsalzgitters, Wissenschaftliche Zeitschrift der Universitat Greifswald, v. 3, 1953--54, Math. naturw. Reihe, p. 607--617 . . . . . . . . . . . . . . . . 113--114 P. P. Ewald Comment: O. Emersleben, \booktitleMit welcher Genauigkeit benötigt man die Madelung-konstante eines Kristalls beispielweise vom Steinsalzgitter? Z. fur Physik. Chemie, v. 204, 1955, p. 43--55 . . . . . . . . . . . . . . . . . 114--114 A. F. Comment: A. Erd'elyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, \booktitleHigher Transcendental Functions. Based, in part, on notes left by H. Bateman. McGraw-Hill, New York, Toronto, London, v. 1, 1953, xxvi + 302 p., 23 cm. Price \$6.50; V. 2,1953, xvii + 396 p., 23 cm. Price \$7,50; v. 3, 1955, xvii + 292 p., 23 cm. Price \$6.50} . . . . . . . . . . . . . . . . 114--116 E. T. Goodwin Comment: NBS Applied Mathematics Series, No. 15, \booktitleProblems for the Numerical Analysis of the Future, U. S. Gov. Printing Office, Washington, D. C., 1951, iv + 21 p., 26.0 cm. Price \$0.20.} . . . . . . . . . . . . . . . . 116--117 Peter Henrici Comment: Albert A. Bennett, William E. Milne, and Harry Bateman, \booktitleNumerical Integration of Differential Equations, Dover Publications, Inc., New York, 1956, 108 p., 20 cm. Price \$1.35} . . . . . . . . 117--118 Robert T. Gregory Comment: L. Couffignal, \booktitleRésolution Numérique des Syst\`emes d'Équations Linéaires, Gauthier-Villars, Paris, v. 2, 1956, iii + 180 p., 21 cm. Price \$5.86} . . . . . 118--119 A. H. T. Comment: J. Crank, \booktitleThe Mathematics of Diffusion, Oxford University Press, New York, 1956, vi + 347 p., 23.5 cm. Price \$8.00} . . . . . 119--120 A. H. T. Comment: Marcel van Laethem, \booktitleUne Méthode Nouvelle et Générale de Calcul des Intégrales Géneralisiées, Publications Universitaires de Louvain, Louvain (Belgique), 1956, viii + 180 p., 23 cm. Price 250 Fr.b. (\$5.00)} . . . . 120--121 Gerald Estrin Comment: \booktitleThe Proceedings of the Institution of Electrical Engineers, v. 103, Part B, Supplement No. 1--3, 1956 (Convention on Digital Computer Techniques), British Institution of Electrical Engineers, London. Price one pound. . . . . . . . . . . . . . . . . . 121--124 Ida Rhodes Comment: S. A. Lebedev, Elektronnye Vyclislitel'nye Mashiny i Obrabotka Informatksi (Electronic Computing Machines and Information Processes), Akad. Nauk SSSR, Moscow, 1956, 47 p., 20 cm. Price 65 kopeks . . . . . . . . . . 124--125 Anonymous Table Errata: A. A. Abramov, \booktitleTablitsy $\ln \Gamma[z]$ v Komplekno\uì Oblasti (Tables of $\ln \Gamma[z]$ in a Complex Region), Akad. Nauk SSSR, Moscow, 1953. . . . . . . . . 125--125 Anonymous Table Errata: Akademiia Nauk SSSR. Institut Tohnol mekhaniky i vychislitel'no\uì tekhniki. Matematicheskie Tablitsy. \booktitleDesiatiéna Tablitsy logarifmov kompleksnykh chisel i perekhoda ot dekartovykh koordinat k poliarnym. Tablitsy funktsi\uì [Ten place tables of logarithms of complex numbers and of the transformation from cartesian to polar coordinates. Tables of functions] $\ln x$, $\arctg x$, $2 \ln (1 + x^2)$, $(1 + x^2)^{1/2}$. Moscow, 1952. [See RMT 1206, MTAC, v. 8, 1954, p. 149] . . . . 125--126 Anonymous Table Errata: Akademiia Nauk SSSR. [Institut Tochnol\uì mekhanik\uì i vychislitel'no\uì tekhniki]. Matematicheskie Tablitsy. \booktitleTablitsy Integralov Frenelia (Tables of Fresnel Integrals), Moscow, 1953. [See Rev. 40, MTAC, v. 9, 1955, p. 75--76] . . . . . . . . . . . . . . . . 126--126 Diamond Ordnance Fuze Laboratories Table Errata: Isabelle Arsham, \booktitleChebyshev Coefficients for Chebyshev Polynomials of Orders 12 and 24 under the General Linear Transformation (U), Report No. TR-326, Diamond Ordnance Fuze Laboratories, Ordnance Corps, Department of the Army, Washington, D. C., 1956 [Review 72, MTAC, v. 10, 1956, p. 231]. . . . . . . 126--127 Anonymous Notes: John von Neumann 1903--1957 [obituary] . . . . . . . . . . . . . . . 127--127 Anonymous Corrigenda: Harvard University, Computation Laboratory, Annals, \booktitleTables of the Function $\arcsin z$, MTAC, v. 10, 1956, Review 66, p. 229, line 3; Mark Lotkin, \booktitleA set of test matrices, MTAC, v. 9, 1955, p. 161; M. Schuler \and H. Gebelein, (a) \booktitleAcht- und neunstellige Tabellen zu den elliptischen Funktionen (Eight and Nine Place Tables of Elliptical Functions), (b) \booktitleFünfstellige Tabellen zu den elliptischen Funktionen (Five Place Tables of Elliptical Functions), MTAC, v. 10, 1956, Review 102, p. 247 . . . . 129--130
C. C. Farrington and R. T. Gregory and A. H. Taub On the Numerical Solution of Sturm--Liouville Differential Equations 131--150 Donald Greenspan On the Numerical Evaluation of the Stokes' Stream Function . . . . . . . . 150--160 Chih-Bing Ling Tables of Values of $16$ Integrals of Algebraic-Hyperbolic Type . . . . . . . 160--166 I. M. Longman Tables for the Rapid and Accurate Numerical Evaluation of Certain Infinite Integrals Involving Bessel Functions . . 166--180 J. W. Sheldon and B. Zondek and M. Friedman On the Time-Step to be Used for the Computation of Orbits by Numerical Integration . . . . . . . . . . . . . . 181--189 Henry C. Thacher, Jr. Optimum Quadrature Formulas In $s$ Dimensions . . . . . . . . . . . . . . . 189--194 E. W. Dijkstra A Method to Investigate Primality (in Technical Notes and Short Papers) . . . 195--196 Herbert E. Salzer Equally-Weighted Quadrature Formulas for Inversion Integrals (in Technical Notes and Short Papers) . . . . . . . . . . . 197--200 Herbert S. Wilf An Open Formula for the Numerical Integration of First Order Differential Equations (in Technical Notes and Short Papers) . . . . . . . . . . . . . . . . 201--203 M. V. Wilkes and D. J. Wheeler Note on ``A Method for Computing Certain Inverse Functions'' (in Technical Notes and Short Papers) . . . . . . . . . . . 204--204 Anonymous Corrigenda . . . . . . . . . . . . . . . 228--228
Edwin S. Campbell A Method for Integrating a Set of Ordinary Differential Equations Subject to a Type of Numerical Indeterminacy . . 229--233 John C. Holladay A Smoothest Curve Approximation . . . . 233--243 William H. Peirce Numerical Integration Over the Spherical Shell . . . . . . . . . . . . . . . . . 244--249 Herschel F. Smith On a Generalization of the Prime Pair Problem . . . . . . . . . . . . . . . . 249--254 Irene A. Stegun and Milton Abramowitz Generation of Bessel Functions on High Speed Computers . . . . . . . . . . . . 255--257 A. H. Stroud Remarks on the Disposition of Points in Numerical Integration Formulas . . . . . 257--261 Bruno A. Boley Technical Notes and Short Papers: a Method for the Numerical Evaluation of Certain Infinite Integrals . . . . . . . 261--264 Roger G. Hart A Formula for the Approximation of Definite Integrals of the Normal Distribution Function . . . . . . . . . 265--265 Raphael M. Robinson Some Factorizations of Numbers of the Form $2^n \pm 1$ . . . . . . . . . . . . 265--268 F. J. Warner On the Solution of ``Jury'' Problems With Many Degrees of Freedom . . . . . . 268--271 Anonymous Corrigenda . . . . . . . . . . . . . . . 314--314
Edwin S. Campbell and E. M. Fishbach and J. O. Hirschfelder Coefficients and Roots of the Polynomials Which Define the Derivatives of the Exponential of $(- \epsilon/{T})$ 1--17 M. Goldstein and R. M. Thaler Bessel Functions for Large Arguments . . 18--26 U. W. Hochstrasser Numerical Experiments in Potential Theory Using the Nehari Estimates . . . 26--33 P. A. P. Moran Approximate Relations Between Series and Integrals . . . . . . . . . . . . . . . 34--37 E. T. Parker and Paul J. Nikolai A Search for Analogues of the Mathieu Group . . . . . . . . . . . . . . . . . 38--43 Wolfgang Wasow On the Accuracy of Implicit Difference Approximations to the Equation of Heat Flow . . . . . . . . . . . . . . . . . . 43--55 Herbert S. Wilf An Open Formula for the Numerical Integration of First Order Differential Equations (II) . . . . . . . . . . . . . 55--58 D. J. Hofsommer and Hans Riesel Technical Notes and Short Papers . . . . 58--60
Pentti Laasonen On the Iterative Solution of the Matrix Equation ${AX}^2 - {I} = 0$ . . . . . . 109--116 Alexander M. Ostrowski On Gauss' Speeding Up Device in the Theory of Single Step Iteration . . . . 116--132 Herbert E. Salzer and Genevieve M. Kimbro Extension of Lindow's Tables for Numerical Differentiation Using Newton--Stirling and Newton--Bessel Differences . . . . . . . . . . . . . . 133--140 Herbert E. Salzer and Norman Levine Technical Notes and Short Papers . . . . 141--144 John Leech Groups of Primes Having Maximum Density 144--145 Anonymous Corrigenda . . . . . . . . . . . . . . . 166--166
Mervin E. Muller An Inverse Method for The Generation of Random Normal Deviates on Large-Scale Computers . . . . . . . . . . . . . . . 167--174 J. W. Sheldon Algebraic Approximations for Laplace's Equation in the Neighborhood of Interfaces . . . . . . . . . . . . . . . 174--186 James Miller and R. P. Hurst Simplified Calculation of the Exponential Integral . . . . . . . . . . 187--193 Daniel C. Fielder A Note on Summation Formulas of Powers of Roots . . . . . . . . . . . . . . . . 194--198 S. D. Conte and R. T. Dames An Alternating Direction Method for Solving the Biharmonic Equation . . . . 198--205 I. M. Longman On the Numerical Evaluation of Cauchy Principal Values of Integrals (in Technical Notes and Short Papers) . . . 205--207 Hans Riesel Mersenne Numbers (in Technical Notes and Short Papers) . . . . . . . . . . . . . 207--213 Harvey Cohn A Computation of Some Bi-Quadratic Class Numbers (in Technical Notes and Short Papers) . . . . . . . . . . . . . . . . 213--217 D. D. Wall Multiplication Time on the IBM 709 (in Technical Notes and Short Papers) . . . 217--218 Carl-Erik Froberg Diagonalization of Hermitian Matrices (in Technical Notes and Short Papers) 219--220
L. Stoller and D. Morrison A Method for the Numerical Integration of Ordinary Differential Equations . . . 269--272 Preston C. Hammer and Arthur H. Stroud Numerical Evaluation of Multiple Integrals II . . . . . . . . . . . . . . 272--280 Carl-Erik Froberg Technical Notes and Short Papers: Some Computations of Wilson and Fermat Remainders . . . . . . . . . . . . . . . 281--281
John R. Pasta and S. Ulam Heuristic Numerical Work in Some Problems of Hydrodynamics . . . . . . . 1--12 P. Laasonen On the Simultaneous Determination of Several Eigensolutions of a Self-Adjoint System of Differential Equations . . . . 13--20 John R. Isbell On the Enumeration of Majority Games . . 21--28 John I. Derr A Unified Process for the Evaluation of the Zeros of Polynomials over the Complex Number Field . . . . . . . . . . 29--36 R. E. Greenwood and P. D. M. Carnahan and J. W. Nolley Numerical Integration Formulas for use with Weight Functions $x^2$ and $x/\surd{\overline{1 - x^2}}$ . . . . . 37--40 Richard B. Smith Two Theorems on Inverses of Finite Segments of the Generalized Hilbert Matrix . . . . . . . . . . . . . . . . . 41--43 O. Gross and S. M. Johnson Sequential Minimax Search for a Zero of a Convex Function . . . . . . . . . . . 44--51 B. Zondek and J. W. Sheldon On the Error Propagation in Adams' Extrapolation Method . . . . . . . . . . 52--55
Samuel Schechter On the Inversion of Certain Matrices . . 73--77 Daniel Shanks A Sieve Method for Factoring Numbers of the Form $n^2 + 1$ . . . . . . . . . . . 78--86 H. Hurwitz, Jr. and R. A. Pfeiffer and P. F. Zweifel Numerical Quadrature of Fourier Transform Integrals II . . . . . . . . . 87--90 Walter Gautschi Note on Bivariate Linear Interpolation for Analytic Functions . . . . . . . . . 91--96 J. A. Riley and C. Billings Gaussian Quadrature of Some Integrals Involving Airy Functions . . . . . . . . 97--101 M. Goldstein and R. M. Thaler Recurrence Techniques for the Calculation of Bessel Functions . . . . 102--108 Harry Polachek Calculation of Transient Excitation of Ship Hulls by Finite Difference Methods 109--116 Irwin Roman Skip-Term Summation of Sequences (in Technical Notes and Short Papers) . . . 117--121 R. B. Killgrove and K. E. Ralston On a Conjecture Concerning the Primes (in Technical Notes and Short Papers) 121--122 D. S. Stoller and L. C. Stoller Calculating the Coefficients of Certain Linear Predictors (in Technical Notes and Short Papers) . . . . . . . . . . . 122--124 Anonymous Corrigenda . . . . . . . . . . . . . . . 143--143
A. Blair and N. Metropolis and J. von Neumann and A. H. Taub and M. Tsingou A Study of a Numerical Solution to a Two-Dimensional Hydrodynamical Problem 145--184 F. D. Murnaghan and J. W. Wrench, Jr. The Determination of the Chebyshev Approximating Polynomial for a Differentiable Function . . . . . . . . 185--193 Lucien Neustadt A Method of Computing Eigenvectors and Eigenvalues on an Analog Computer . . . 194--201 T. Mirsepassi Graphical Evaluation of a Convolution Integral . . . . . . . . . . . . . . . . 202--212 Gerard Salton The Use of the Central Limit Theorem for Interpolating in Tables of Probability Distribution Functions . . . . . . . . . 213--216
Marshall Hall, Jr. and J. Dean Swift and Raymond Killgrove On Projective Planes of Order Nine . . . 233--246 Richard Bellman and Stuart Dreyfus Functional Approximations and Dynamic Programming . . . . . . . . . . . . . . 247--251 A. R. Mitchell The Influence of Critical Boundary Conditions on Finite Difference Solutions of Two Point Boundary Value Problems . . . . . . . . . . . . . . . . 252--260 Yudell L. Luke Expansion of the Confluent Hypergeometric Function in Series of Bessel Functions . . . . . . . . . . . . 261--271 Daniel Shanks Quadratic Residues and the Distribution of Primes . . . . . . . . . . . . . . . 272--284 Philip Rabinowitz and George Weiss Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the Form $\int^\infty_0 e^{-x}x^nf(x) dx$ 285--294 Gerald E. Bartholomew Numerical Integration Over the Triangle 295--298 Sherwood Skillman Efficient Method for Solving Atomic Schrödinger's Equation (in Technical Notes and Short Papers) . . . . . . . . 299--302 Dietrich Suschowk Explicit Formulae for $25$ of the Associated Legendre Functions of the Second Kind (in Technical Notes and Short Papers) . . . . . . . . . . . . . 303--305 I. M. Longman A Short Table of $\int^\infty_x {J}_0(t)t^{-n} dt$ and $\int^\infty_x {J}_1(t) t^{-n} dt$ (in Technical Notes and Short Papers) . . . . . . . . . . . 306--311 Gerard P. Weeg Numerical Integration of $\int^\infty_0 e^{-x} {J}_0\Bigg(\frac{\eta x}{\xi} \Bigg) {J}_1 \Bigg(\frac{x}{\xi}\Bigg) x^{-n} dx$ (in Technical Notes and Short Papers) . . . . . . . . . . . . . . . . 312--313 M. E. Sherry and S. Fulda Calculation of Gamma Functions to High Accuracy (in Technical Notes and Short Papers) . . . . . . . . . . . . . . . . 314--315 Peter Henrici Book Review: \booktitleThe Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, by L. Fox . . . . . . . . . . . . . . . . . 322--323 Anonymous Corrigenda . . . . . . . . . . . . . . . 335--335