Block Krylov-Schur method for large symmetric eigenvalue problems

Yunkai Zhou; Yousef Saad

doi:10.1007/s11075-008-9192-9

Block Krylov-Schur method for large symmetric eigenvalue problems

Yunkai Zhou, Yousef Saad

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	341-359
Number of pages	19
Journal	Numerical Algorithms
Volume	47
Issue number	4
DOIs	https://doi.org/10.1007/s11075-008-9192-9
State	Published - Apr 2008

Bibliographical note

Funding Information:
Work supported by US Department of Energy under contract DE-FG02-03ER25585, by NSF grants ITR-0428774 and CMMI-0727194, and by the Minnesota Supercomputing Institute.

Keywords

Block method
Implicit restart
Krylov-Schur
Lanczos

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title = "Block Krylov-Schur method for large symmetric eigenvalue problems",

abstract = "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.",

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doi = "10.1007/s11075-008-9192-9",

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AU - Saad, Yousef

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N2 - 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.

AB - 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.

KW - Block method

KW - Implicit restart

KW - Krylov-Schur

KW - Lanczos

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Block Krylov-Schur method for large symmetric eigenvalue problems

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