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

Abstract

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.

Authors:
 [1];  [2];  [3];  [3];  [2]
+ Show Author Affiliations
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Minnesota, Twin Cities, MN (United States)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1438696
Report Number(s):
LLNL-JRNL-685856
Journal ID: ISSN 1064-8275
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 4; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Lanczos algorithm; polynomial filtering; Thick-Restart; deflation; spectrum slicing; interior eigenvalue problems

Citation Formats

Li, Ruipeng, Xi, Yuanzhe, Vecharynski, Eugene, Yang, Chao, and Saad, Yousef. A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems. United States: N. p., 2016. Web. doi:10.1137/15M1054493.
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Li, Ruipeng, Xi, Yuanzhe, Vecharynski, Eugene, Yang, Chao, & Saad, Yousef. A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems. United States. https://doi.org/10.1137/15M1054493
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Li, Ruipeng, Xi, Yuanzhe, Vecharynski, Eugene, Yang, Chao, and Saad, Yousef. Tue . "A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems". United States. https://doi.org/10.1137/15M1054493. https://www.osti.gov/servlets/purl/1438696.
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@article{osti_1438696,
title = {A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems},
author = {Li, Ruipeng and Xi, Yuanzhe and Vecharynski, Eugene and Yang, Chao and Saad, Yousef},
abstractNote = {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.},
doi = {10.1137/15M1054493},
journal = {SIAM Journal on Scientific Computing},
number = 4,
volume = 38,
place = {United States},
year = {Tue Aug 16 00:00:00 EDT 2016},
month = {Tue Aug 16 00:00:00 EDT 2016}
}
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Publisher's Version of Record
https://doi.org/10.1137/15M1054493
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    Works referencing / citing this record:

    Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems: Domain decomposition contour integration eigensolvers
    journal, February 2018

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    • Numerical Linear Algebra with Applications, Vol. 25, Issue 5
    • DOI: 10.1002/nla.2154
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