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Communications of the ACM

Table of Contents

From the President of ACM

Editor's note

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 …

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 …

On the compilation of subscripted variables

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 …

An approximating transcendental numbers by continued fractions

Table look-at techniques

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 …

Algorithms 41: Evaluation of determinant

Algorithm 42: invert

Algorithm 43: CROUT with pivoting II

Algorithm 44: Bessel Functions computed recursively

Algorithm 45: interest

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

Algorithm 46: exponential of a complex number

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

Algorithm 48: logarithm of a complex number

ACM Algorithm 49: Spherical Neumann Function

Algorithm 53: Nth roots of a complex number

Algorithm 52: a set of test matrices

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

Algorithm 55: complete elliptic integral of the first kind

Algorithm 54: Gamma function for range 1 to 2

Algorithm 56: complete elliptic integral of the second kind

Algorithm 57: BER or BEI function

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

Certification of algorithm 13: Legendre polynomial

Certification of algorithm 10: Chebyschev polynomial Tn

Remark: on frequently occurring errors in Algol-60 programs

Certification of algorithm 43: CROUT II

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.  …

Certification of algorithm 20: real exponential integral

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

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 …

Division and square root in the quarter-imaginary number system

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 …

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 …

Theory of programmed processes

Theory of abstract machines

Information retrieval