Block Krylov–Schur method for large symmetric eigenvalue problems | Zendy

Yunkai Zhou | Zendy; Yousef Saad | Zendy

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Block Krylov–Schur method for large symmetric eigenvalue problems

Author(s) -

Yunkai Zhou,

Yousef Saad

Publication year - 2008

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/s11075-008-9192-9

Subject(s) - mathematics , block (permutation group theory) , krylov subspace , eigenvalues and eigenvectors , theory of computation , generalized minimal residual method , rank (graph theory) , algorithm , iterative method , combinatorics , physics , quantum mechanics

Stewart's recent Krylov-Schur algorithm ofiers two advantages over Sorensen's im- plicitly restarted Arnoldi (IRA) algorithm. The flrst is ease of de∞ation 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 the rank deflcient cases and how to use difierent block sizes. Numerical results on the e-ciency of the block Krylov-Schur method are reported.

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