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

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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1983
Accession Number
ADA140097

Entities

People

  • B. Nour-omid
  • H. D. Simon

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • California
  • Classification
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Linear Systems
  • Mathematics
  • Partial Differential Equations
  • Security
  • Splitting
  • Structural Engineering
  • Universities

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Systems Analysis and Design