A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef

doi:10.1137/15M1054493

Title: A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

Journal Article · Tue Aug 16 00:00:00 EDT 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/15M1054493· OSTI ID:1438696

Li, Ruipeng ^[1]; Xi, Yuanzhe ^[2]; Vecharynski, Eugene ^[3]; Yang, Chao ^[3]; Saad, Yousef ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Minnesota, Twin Cities, MN (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from one another.

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Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1438696

Report Number(s):: LLNL-JRNL-685856

Journal Information:: SIAM Journal on Scientific Computing, Vol. 38, Issue 4; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 32 works

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Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems: Domain decomposition contour integration eigensolvers Kalantzis, Vassilis; Kestyn, James; Polizzi, Eric Numerical Linear Algebra with Applications, Vol. 25, Issue 5 https://doi.org/10.1002/nla.2154	journal	February 2018

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97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Lanczos algorithm
polynomial filtering
Thick-Restart
deflation
spectrum slicing
interior eigenvalue problems

Title: A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

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