Analysis of the Finite Precision s-Step Biconjugate Gradient Method

Abstract

We analyze the s-step biconjugate gradient algorithm in nite precision arithmetic and derive a bound for the residual norm in terms of a minimum polynomial of a perturbed matrix multiplied by an ampli cation factor. Our bound enables comparison of s-step and classical biconjugate gradient in terms of ampli cation factors. Our results show that for s-step biconjugate gradient the ampli cation factor depends heavily on the quality of s-step polynomial bases generated in each outer loop.

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Document Details

Document Type
Technical Report
Publication Date
Mar 13, 2014
Accession Number
ADA604544

Entities

People

  • Erin Carson
  • James Demmel

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Arithmetic
  • Computational Fluid Dynamics
  • Computations
  • Computer Science
  • Convergence
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Equations
  • Errors
  • Iterations
  • Linear Systems
  • Polynomials
  • Precision
  • Residuals

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