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Communications of the ACM

Table of Contents

Programming systems, whither?

Communications between independently translated blocks

Solution of Eigenvalue problems with approximately known Eigenvectors

It is often desired to solve eigenvalue problems of the type (A - &lgr;1)C = 0 or (A - &lgr;B)C = 0 repeatedly for similar values of the matrix elements Aij, where A and B are Hermitean or real symmetric matrices. Among the various methods …

A modified inversion procedure for product form of the inverse linear programming codes

This paper describes a new algorithm for the selection of the pivot row in matrix inversion when using the product form of the inverse. This algorithm has been developed for linear programming codes; however, it would be valuable …

Simulation of a computer timing device

On translation of Boolean expressions

A program which translates an algorithmic language such as ALGOL into the machine language of an electronic computer performs the following functions: Analysis. From the program in algorithmic language are determined the operations …

Algorithm 104: Reduction to Jacobi

Algorithm 105: Newton Maehly

Algorithm 109: Definite exponential integrals B

Algorithm 108: Definite exponential integrals A

Algorithm 106: Complex number to a real power

Algorithm 107: Gauss's method

Algorithm 110: Quantum mechanical integrals of Slater-type orbitals

Algorithm 111: Molecular-orbital calculation of molecular interactions

Remark on Algorithm 48: Logarithm of a complex number

Remark on Algorithm 34: Gamma function

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

Certification of Algorithm 75: Factors

Certification of Algorithm 84: Simpson's integration

Certification of Algorithm 57: Ber or bei function

Certification of Algorithm 70: Interpolation by Aitken

Certification of Algorithm 110: Quantum mechanical integrals of Slater-type orbitals

Certification of Algorithm 108: Definite exponential integrals A

Certification of Algorithm 109: Definite exponential integrals B

A machine program for theorem-proving

The programming of a proof procedure is discussed in connection with trial runs and possible improvements.

Nonlinear regression and the solution of simultaneous equations

If one has a set of observables (z1, ··· , zm) which are bound in a relation with certain parameters (a1, ··· , an) by an equation &zgr;(z1, ··· , a1, ···) = 0, one frequently has the problem of determining a set of values of the …

Triangular walk pattern for the down-hill method of solving a transcendental equation

The down-hill method by Ward is a numerical method for determining a complex root of ƒ(z) = 0 and suitable for machine computation [1]. It is based on a theorem that W(z) = |Re(ƒ)| + |Im(ƒ)| (1) has minimum value, actually zero …

Logic of English grammar

The logic of English grammar is being investigated by a process of approximative logical synthesis. Beginning with a kernel language which is an alphabetically spelled form of symbolic logic with English-like vocabulary, English …

Quick calculation of Jacobian elliptic functions

Digital synthesis of correlated stationary noise

In this note we propose a method of generating stationary noise with a prescribed auto-covariance function by digital methods. The need for such a technique often arises in testing the performance of data processing and engineering …

On the computation of rational approximations to continuous functions

Person-matching by electronic methods

Record linkage in the updating of files is accomplished in many establishments through the use of a preassigned number, such as payroll number, customer number, or social security number. In vital and health records, however, …

A computer method for radiation treatment planning

Automatic computation methods were first developed and applied to the problem of radiation therapy treatment planning by the Physics staff at Memorial Hospital and Sloan-Kettering Institute in 1954 and reported in 1955 [1]. The …

Regression and coded patterns in data editing

FORTRAN for business data processing