Deflated block Krylov subspace methods for large scale eigenvalue problems

Qiang Niu; Linzhang Lu

doi:10.1016/j.cam.2009.11.058

Deflated block Krylov subspace methods for large scale eigenvalue problems

Qiang Niu^*, Linzhang Lu

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We discuss a class of deflated block Krylov subspace methods for solving large scale matrix eigenvalue problems. The efficiency of an Arnoldi-type method is examined in computing partial or closely clustered eigenvalues of large matrices. As an improvement, we also propose a refined variant of the Arnoldi-type method. Comparisons show that the refined variant can further improve the Arnoldi-type method and both methods exhibit very regular convergence behavior.

Original language	English
Pages (from-to)	636-648
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	234
Issue number	3
DOIs	https://doi.org/10.1016/j.cam.2009.11.058
Publication status	Published - 1 Jun 2010
Externally published	Yes

Keywords

Arnoldi process
Krylov subspace
Refined approximate eigenvector
Ritz value
Ritz vector

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10.1016/j.cam.2009.11.058

Cite this

Niu, Q., & Lu, L. (2010). Deflated block Krylov subspace methods for large scale eigenvalue problems. Journal of Computational and Applied Mathematics, 234(3), 636-648. https://doi.org/10.1016/j.cam.2009.11.058

@article{b7162d339a3247bc80fa6db7ce349b5f,

title = "Deflated block Krylov subspace methods for large scale eigenvalue problems",

abstract = "We discuss a class of deflated block Krylov subspace methods for solving large scale matrix eigenvalue problems. The efficiency of an Arnoldi-type method is examined in computing partial or closely clustered eigenvalues of large matrices. As an improvement, we also propose a refined variant of the Arnoldi-type method. Comparisons show that the refined variant can further improve the Arnoldi-type method and both methods exhibit very regular convergence behavior.",

keywords = "Arnoldi process, Krylov subspace, Refined approximate eigenvector, Ritz value, Ritz vector",

author = "Qiang Niu and Linzhang Lu",

note = "Funding Information: This work is supported by the National Natural Science Foundation of China (No. 10961010). Funding Information: The first author would like to thank Prof. Zhaojun Bai and Prof. Ren-Cang Li for their lectures presented at the LSEC Summer School on Numerical Linear Algebra, and many valuable discussions. In addition, sincere thanks go to Michael Ng and anonymous referees for their valuable comments that considerably improved this work. A part of the first author{\textquoteright}s work was performed during this author{\textquoteright}s visit to INRIA, funded by the China Scholarship Council.",

year = "2010",

month = jun,

day = "1",

doi = "10.1016/j.cam.2009.11.058",

language = "English",

volume = "234",

pages = "636--648",

journal = "Journal of Computational and Applied Mathematics",

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T1 - Deflated block Krylov subspace methods for large scale eigenvalue problems

AU - Niu, Qiang

AU - Lu, Linzhang

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (No. 10961010). Funding Information: The first author would like to thank Prof. Zhaojun Bai and Prof. Ren-Cang Li for their lectures presented at the LSEC Summer School on Numerical Linear Algebra, and many valuable discussions. In addition, sincere thanks go to Michael Ng and anonymous referees for their valuable comments that considerably improved this work. A part of the first author’s work was performed during this author’s visit to INRIA, funded by the China Scholarship Council.

PY - 2010/6/1

Y1 - 2010/6/1

N2 - We discuss a class of deflated block Krylov subspace methods for solving large scale matrix eigenvalue problems. The efficiency of an Arnoldi-type method is examined in computing partial or closely clustered eigenvalues of large matrices. As an improvement, we also propose a refined variant of the Arnoldi-type method. Comparisons show that the refined variant can further improve the Arnoldi-type method and both methods exhibit very regular convergence behavior.

AB - We discuss a class of deflated block Krylov subspace methods for solving large scale matrix eigenvalue problems. The efficiency of an Arnoldi-type method is examined in computing partial or closely clustered eigenvalues of large matrices. As an improvement, we also propose a refined variant of the Arnoldi-type method. Comparisons show that the refined variant can further improve the Arnoldi-type method and both methods exhibit very regular convergence behavior.

KW - Arnoldi process

KW - Krylov subspace

KW - Refined approximate eigenvector

KW - Ritz value

KW - Ritz vector

UR - http://www.scopus.com/inward/record.url?scp=77949487038&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2009.11.058

DO - 10.1016/j.cam.2009.11.058

M3 - Article

AN - SCOPUS:77949487038

SN - 0377-0427

VL - 234

SP - 636

EP - 648

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 3

ER -

Deflated block Krylov subspace methods for large scale eigenvalue problems

Abstract

Keywords

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