Analytic Complexity Theory and the Solution of Ax=b,

Abstract

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1981
Accession Number
ADA103479

Entities

People

  • Beresford N. Parlett

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Coefficients
  • Computer Science
  • Eigenvalues
  • Equations
  • Identities
  • Language
  • Mathematics
  • Polynomials
  • Residuals
  • Spectra
  • Standards
  • Translations

Readers

  • Approximation Theory.
  • Educational Psychology
  • Graph Algorithms and Convex Optimization.