Accession Number : AD0687461

Title :   A CONVERGENT SPLITTING OF MATRICES.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Mangasarian,O. L.

Report Date : JAN 1969

Pagination or Media Count : 10

Abstract : Let A, M, N be n x n real matrices, let A = M - N, let A and M be nonsingular, let M'y = or > 0 imply N'y = or > 0, and let A'y = or > 0 imply N'y = or > (where the prime denotes the transpose). Then the spectral radius rho(M superscript(-1) N) of M superscript (-1) N is less than one, and the iterative process x superscript (i+1) = M superscript (-1) N (x superscript i) + M superscript (-1) b converges to the solution of Ax = b starting from any x superscript zero. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), ITERATIONS, CONVERGENCE, INEQUALITIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE