Accession Number : AD0657448

Title :   THE LINEAR EQUATIONS PROBLEM.

Descriptive Note : Technical rept.,

Corporate Author : APPLIED MATHEMATICS AND STATISTICS LABS STANFORD UNIV CALIF

Personal Author(s) : Givens,Wallace

Report Date : 01 DEC 1959

Pagination or Media Count : 29

Abstract : The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned.

Descriptors :   (*EQUATIONS, NUMERICAL ANALYSIS), MATRICES(MATHEMATICS), LINEAR SYSTEMS, DETERMINANTS(MATHEMATICS), ALGORITHMS, MATHEMATICS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE