Accession Number : ADA140097

Title :   Banded Preconditioning for the Solution of Symmetric Positive Definite Linear Systems,

Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS

Personal Author(s) : Nour-Omid,B ; Simon,H D

PDF Url : ADA140097

Report Date : Oct 1983

Pagination or Media Count : 18

Abstract : The preconditioned conjugate gradient algorithm has been successfully applied to solving symmetric linear systems of equations arising from finite difference and finite element discitizations of a variety of problems. In this paper the authors consider a matrix splitting A = M + R, where M is a part of A chosen such that its factorization has little or no fill-in. They develop a simple criterion to check for the positive definiteness of M. It turns out that a large class of matrices, including matrices arising from finite element discretization of elliptic boundary value problems, satisfy this criterion. Presented are some numerical tests where M is used as a preconditioning matrix for the conjugate gradient algorithm. Examples include problems arising from structural engineering. A comparison with the preconditioning based on an incomplete Choleski factorization is encouraging.

Descriptors :   *Linear systems, *Linear differential equations, *Problem solving, *Algorithms, Symmetry, Finite element analysis, Finite difference theory, Boundary value problems, Matrices(Mathematics), Splitting, Factor analysis

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE