Numerical Algorithms

, Volume 47, Issue 4, pp 341–359

Block Krylov–Schur method for large symmetric eigenvalue problems


    • Department of MathematicsSouthern Methodist University
  • Yousef Saad
    • Department of Computer Science and EngineeringUniversity of Minnesota
Original Paper

DOI: 10.1007/s11075-008-9192-9

Cite this article as:
Zhou, Y. & Saad, Y. Numer Algor (2008) 47: 341. doi:10.1007/s11075-008-9192-9


Stewart’s Krylov–Schur algorithm offers two advantages over Sorensen’s implicitly restarted Arnoldi (IRA) algorithm. The first is ease of deflation of converged Ritz vectors, the second is the avoidance of the potential forward instability of the QR algorithm. In this paper we develop a block version of the Krylov–Schur algorithm for symmetric eigenproblems. Details of this block algorithm are discussed, including how to handle rank deficient cases and how to use varying block sizes. Numerical results on the efficiency of the block Krylov–Schur method are reported.


Block methodKrylov–SchurLanczosImplicit restart
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Copyright information

© Springer Science+Business Media, LLC. 2008