Shifting Strategies for the Parallel QR Algorithm

  • D. S. Watkins
Chapter
Part of the NATO ASI Series book series (NSSE, volume 232)

Abstract

Consider the problem of finding all eigenvalues of a real square matrix A that has no special structure to exploit. The QR algorithm has been the method of choice for solving such problems for the past 30 years. However, in recent years it has been suggested that the days of the QR algorithm may be numbered, for the QR algorithm has proven difficult to parallelize. Such predictions are at best premature. A simple modification of the shifting strategy promises to improve the parallel performance of the QR algorithm significantly and keep the competition at bay for years to come.

Keywords

QR algorithm parallel implementation shifts 
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References

  1. [1]
    A. A. Dubrulle. The multishift QR algorithm—is it worth the trouble? Manuscript, 1991.Google Scholar
  2. [2]
    R. A. van de Geijn. Deferred shifting schemes for parallel QR methods. SIAM J. Matrix Anal. Appl., to appear.Google Scholar
  3. [3]
    D.S. Watkins. Shifting strategies for the parallel QR algorithm. Manuscript submitted for publication, 1992.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • D. S. Watkins
    • 1
  1. 1.Department of Pure and Applied MathematicsWashington State UniversityPullmanUSA

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