A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of Communication-Avoiding Krylov Subspace Methods

Abstract

The behavior of conventional Krylov Subspace Methods (KSMs) infinite precision arithmetic is a well-studied problem. The finite precision Lanczos process, which drives convergence of these methods, can lead to a significant deviation between the recursively computed residual and the true residual, b - Axk, decreasing the maximum attainable accuracy of the solution. Van der Vorst and Ye [24] have advocated the use of a residual replacement strategy for KSMs to prevent the accumulation of this error, in which the computed residual is replaced by the true residual at specific iterations chosen such that the Lanczos process is undisturbed.

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Document Details

Document Type
Technical Report
Publication Date
Apr 20, 2012
Accession Number
ADA561766

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
  • Computers
  • Convergence
  • Electrical Engineering
  • Engineering
  • Equations
  • Error Analysis
  • Errors
  • Iterations
  • Numerical Analysis
  • Polynomials
  • Precision

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Systems Analysis and Design