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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 43: CROUT with pivoting II


Algorithm 42: invert


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 56: complete elliptic integral of the second kind


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 52: a set of test matrices


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