Robust parallel Lanczos methods for clustered eigenvalues

  • M. Szularz
  • J. Weston
  • M. Clint
Workshop 09: Parallel Numerical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1300)


In this paper two recently proposed single-vector Lanczos methods based on a simple restarting strategy are analysed and their suitability for the computation of closely clustered eigenvalues is evaluated. Both algorithms adopt an approach which yields a fixed k-step restarting scheme in which one eigenpair at a time is computed using a deflation technique in which each Lanczos vector generated is orthogonalized against all previously converged eigenvectors. In the first algorithm each newly generated Lanczos vector is also orthogonalised with respect to all of its predecessors; in the second, a selective orthogonalisation strategy permits re-orthogonalization between the Lanczos vectors to be almost completely eliminated. ‘Reverse communication’ implementations of the algorithms on an MPP Connection Machine CM-200 with 8K processors are discussed. Advantages of the algorithms include the ease with which they cope with genuinely multiple eigenvalues, their guaranteed convergence and their fixed storage requirements.

Key words

Lanczos restart deflation orthogonalization MPP 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • M. Szularz
    • 1
  • J. Weston
    • 1
  • M. Clint
    • 2
  1. 1.School of Information & Software EngineeringUniversity of UlsterColeraineNorthern Ireland
  2. 2.Department of Computer ScienceThe Queen's University of BelfastBelfastNorthern Ireland

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