From the President of ACM

Harry D. Huskey

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Page 165
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Editor's note

R. W. B.

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Page 166
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Topological ordering of a list of randomly-numbered elements of a network

A network of directed line segments free of circular elements is assumed. The lines are identified by their terminal nodes and the nodes are assumed to be numbered by a non-topological system. Given a list of these lines in numeric …

Daniel J. Lasser

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Pages 167-168
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Eigenvalues of a symmetric 3 × 3 matrix

Recently, in order to find the principal moments of inertia of a large number of rigid bodies, it was necessary to compute the eigenvalues of many real, symmetric 3 × 3 matrices. The available eigenvalue subroutines seemed rather …

Oliver K. Smith

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Page 168
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On the compilation of subscripted variables

R. E. Nather

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Pages 169-171
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Bessel functions of integral order and complex argument

The FORTRAN II source language [1, 2] places rather severe restrictions on the form a subscript may take, primarily because of the manner in which indices are incremented in iterative loops. In the process of constructing a compiler …

Marion C. Gray

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Page 169
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An approximating transcendental numbers by continued fractions

E. Karst

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Page 171
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Table look-at techniques

P. M. Sherman

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Pages 172-173
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Programmed error correction on a decimal computer

In a previous paper [1], B. Dimsdale and I reported on the use of programmed Hamming codes for error correction on a 7090. The paper generated much interest, but several readers remarked that they could not use the techniqueA …

G. M. Weinberg

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Page 174
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Algorithms 41: Evaluation of determinant

Josef G. Solomon

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Page 176
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Algorithm 43: CROUT with pivoting II

Henry C. Thacher

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Pages 176-177
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Algorithm 42: invert

T. C. Wood

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Page 176
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Algorithm 44: Bessel Functions computed recursively

Maria E. Wojcicki

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Pages 177-178
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Algorithm 45: interest

Peter Z. Ingerman

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Page 178
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Algorithm 47: associated Legendre functions of the first kind for real or imaginary arguments

John R. Herndon

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Pages 178-179
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Algorithm 46: exponential of a complex number

John R. Herndon

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Page 178
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Algorithm 50:Inverse of a finite segment of the Hilbert matrix

John R. Herndon

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Page 179
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Algorithm 48: logarithm of a complex number

John R. Herndon

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Page 179
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ACM Algorithm 49: Spherical Neumann Function

J. R. Herndon

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Page 179
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Algorithm 52: a set of test matrices

John R. Herndon

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Page 180
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Algorithm 54: Gamma function for range 1 to 2

John R. Herndon

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Page 180
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Algorithm 51: adjust inverse of a matrix when an element is perturbed

John R. Herndon

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Page 180
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Algorithm 55: complete elliptic integral of the first kind

John R. Herndon

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Page 180
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Algorithm 53: Nth roots of a complex number

John R. Herndon

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Page 180
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Algorithm 56: complete elliptic integral of the second kind

John R. Herndon

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Pages 180-181
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Algorithm 57: BER or BEI function

John R. Herndon

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Page 181
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Certification of algorithm 3: solution of polynomial equation by Barstow-Hitchcock

John Herndon

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Page 181
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Certification of algorithm 13: Legendre polynomial

John Herndon

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Page 181
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Certification of algorithm 10: Chebyschev polynomial Tn

John Herndon

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Page 181
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Remark: on frequently occurring errors in Algol-60 programs

W. Börsch-Supan

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Page 181
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Certification of algorithm 43: CROUT II

Henry C. Thacher

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Page 182
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Further survey of punched card codes

The valuable “Survey of Punched Card Codes” prepared by Smith and Williams (Comm. ACM 3, Dec. 1960, 638) unfortunately omits the card codes of European equipment, other than IBM. These are presented in the table on page 181.
…

H. McG. Ross

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Pages 182-183
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Certification of algorithm 20: real exponential integral

William J. Alexander

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Page 182
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A practical technique for the determination of the optimum relaxation factor of the successive over-relaxation method

H. E. Kulsrud

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Pages 184-187
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Some numerical experiments using Newton's method for nonlinear parabolic and elliptic boundary-value problems

Using a generalization of Newton's method, a non-linear parabolic equation of the form ut - uxx = g(u), and a non-linear elliptic equation uxx + uyy = eu, are solved numerically. Comparison of these results with results obtained …

Richard Bellman, Mario L. Juncosa, Robert Kalaba

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Pages 187-191
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Division and square root in the quarter-imaginary number system

Morton Nadler

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Pages 192-193
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Laviathan studies

The Leviathan studies are investigations into how people operate in large social organizations. Examples of such groups are a large military command, a governmental agency like the U. S. Bureau of Internal Revenue, or an industrial …

Sydney C. Rome

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Page 194
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Advanced computers

The objective is to investigate significant developments in advanced computers and to explore the relationship between programming and new concepts of computer organization. Two specific studies are in progress: Data Sequencing …

R. A. Brouse

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Page 194
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Theory of programmed processes

T. N. Hibbard

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Page 195
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Theory of abstract machines

Seymour Ginsburg

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Page 195
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Information retrieval

L. B. Doyle

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Page 195
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