A CONVERGENT SPLITTING OF MATRICES.

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)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1969
Accession Number
AD0687461

Entities

People

  • Olvi L. Mangasarian

Organizations

  • University of Wisconsin–Madison

Tags

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Technical Research and Report Writing.