April 1961 Table of Contents | Communications of the ACM

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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
Pages 167-168

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
Page 169

On the compilation of subscripted variables

R. E. Nather
Pages 169-171

An approximating transcendental numbers by continued fractions

E. Karst
Page 171

Table look-at techniques

P. M. Sherman
Pages 172-173

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
Page 174

Algorithm 42: invert

T. C. Wood
Page 176

Algorithm 43: CROUT with pivoting II

Henry C. Thacher
Pages 176-177

Algorithms 41: Evaluation of determinant

Josef G. Solomon
Page 176

Algorithm 44: Bessel Functions computed recursively

Maria E. Wojcicki
Pages 177-178

Algorithm 45: interest

Peter Z. Ingerman
Page 178

Algorithm 46: exponential of a complex number

John R. Herndon
Page 178

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

John R. Herndon
Pages 178-179

Algorithm 48: logarithm of a complex number

John R. Herndon
Page 179

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

John R. Herndon
Page 179

ACM Algorithm 49: Spherical Neumann Function

J. R. Herndon
Page 179

Algorithm 52: a set of test matrices

John R. Herndon
Page 180

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

John R. Herndon
Page 180

Algorithm 55: complete elliptic integral of the first kind

John R. Herndon
Page 180

Algorithm 54: Gamma function for range 1 to 2

John R. Herndon
Page 180

Algorithm 56: complete elliptic integral of the second kind

John R. Herndon
Pages 180-181

Algorithm 53: Nth roots of a complex number

John R. Herndon
Page 180

Remark: on frequently occurring errors in Algol-60 programs

W. Börsch-Supan
Page 181

Algorithm 57: BER or BEI function

John R. Herndon
Page 181

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

John Herndon
Page 181

Certification of algorithm 10: Chebyschev polynomial Tn

John Herndon
Page 181

Certification of algorithm 13: Legendre polynomial

John Herndon
Page 181

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
Pages 182-183

Certification of algorithm 43: CROUT II

Henry C. Thacher
Page 182

Certification of algorithm 20: real exponential integral

William J. Alexander
Page 182

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

H. E. Kulsrud
Pages 184-187

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
Pages 187-191

Division and square root in the quarter-imaginary number system

Morton Nadler
Pages 192-193

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
Page 194

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
Page 194

Theory of programmed processes

T. N. Hibbard
Page 195

Theory of abstract machines

Seymour Ginsburg
Page 195

Information retrieval

L. B. Doyle
Page 195

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
Page 168