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Numerische Mathematik

, Volume 66, Issue 1, pp 97–122 | Cite as

On the global and cubic convergence of a quasi-cyclic Jacobi method

  • Noah H. Rhee
  • Vjeran Hari
Article

Summary

In this paper we consider the global and the cubic convergence of a quasi-cyclic Jacobi method for the symmetric eigenvalue, problem. The method belongs to a class of quasi-cyclic methods recently proposed by W. Mascarenhas. Mascarenhas showed that the methods from his class asymptotically converge cubically per quasi-sweep (one quasi-sweep is equivalent to 1.25 cyclic sweeps) provided the eigenvalues are simple. Here we prove the global convergence of our method and derive very sharp asymptotic convergence bounds in the general case of multiple eigenvalues. We discuss the ultimate cubic convergence of the method and present several numerical examples which all well comply with the theory.

Mathematics Subject Classifications (1991)

65F15 

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Noah H. Rhee
    • 1
  • Vjeran Hari
    • 2
  1. 1.Department of MathematicsUniversity of Missouri-Kansas CityKansas CityUSA
  2. 2.Department of MathematicsUniversity of ZagrebZagrebCroatia

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