Comparison of Lanczos with Conjugate Gradient Using Element Preconditioning,

Abstract

Consider Ax = b where A arises from two different applications; (i) from structural analysis, (ii) from incomprehensible fluid flow. A will never be assembled but the operation v yields Av will be carried out using the element by element representation bars the use of triangular factorization. Two different types of preconditioning are examined and each is used in a comparison of the conjugate gradient method and the Lanczos algorithm using partial reortogonalization. It appears that these element by element preconditioners are more powerful than diagonal scaling. Moreover, the cost of maintaining semiorthogonality is well worth paying; the number of iterations is greatly reduced and consequently the extra burden of occasional orthogonalizations never dominated the cost of the solution algorithm in our examples.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1987
Accession Number
ADA178098

Entities

People

  • A. Raefsky
  • B. N. Partlett
  • B. Nour-omid

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Flow
  • Fluid Flow
  • Iterations
  • Mathematics
  • Structural Analysis

Readers

  • Linear Algebra
  • Systems Analysis and Design