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The Solution of Simultaneous Equations

Published online by Cambridge University Press:  01 January 2025

P. S. Dwyer
P. S. Dwyer*
Affiliation:
University of Michigan
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Abstract

This paper is an attempt to integrate the various methods which have been developed for the numerical solution of simultaneous linear equations. It is demonstrated that many of the common methods, including the Doolittle Method, are variations of the method of “single division.” The most useful variation of this method, in case symmetry is present, appears to be the Abbreviated Doolittle method. The method of multiplication and subtraction likewise can be abbreviated in various ways of which the most satisfactory form appears to be the new Compact method. These methods are then applied to such problems as the solution of related equations, the solution of groups of equations, and the evaluation of the inverse of a matrix.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 2 , April 1941 , pp. 101 - 129
Copyright
Copyright © 1941 The Psychometric Society

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