Generalized Rayleigh Quotient Shift Strategy in QR Algorithm for Eigenvalue Problems

  • Yifan Liu
  • Zheng Su
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)


QR algorithm for eigenproblems is often applied with single or double shift strategies. To save computation effort, double implicit shift technique is employed. In Watkins and Elsner[1], a higher-order shift strategy, generalized Rayleigh quotient shift strategy, is introduced. In this paper, we give a generalization of the double implicit shift technique for the higher-order strategy, and compare the computation cost for different orders with numerical experiments.


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  1. 1.
    Watkins, D., Elsner, L.: Convergence of Algorithms of Decomposition Type for the Eigenvalue Problem. Linear Algebra Appl. 78, 315–333 (1982)Google Scholar
  2. 2.
    Golub, G., Van Loan, C.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  3. 3.
    Dubrulle, A., Golub, G.: A Multishift QR Iteration without Computation of the Shifts. SCCM technical report, NA-93-04Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yifan Liu
    • 1
  • Zheng Su
    • 1
  1. 1.Stanford UniversityStanfordUSA

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