# Communications of the ACM

#### 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 …

#### 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 …

#### 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 …

#### 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 …

#### 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 …