Numerical determination of partial spectrum of Hermitian matrices using a Lánczos method with selective reorthogonalization

Numerical determination of partial spectrum of Hermitian matrices using a Lánczos method with selective reorthogonalization

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication of eigenpairs in finite-precision arithmetic, but uses a new...

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Veröffentlicht in:Computer physics communications 2013-03, Vol.184 (3), p.689-697
Hauptverfasser: Johnson, Chris, Kennedy, A.D.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Arithmetic
Computer simulation
Eigenvalue
Eigenvalues
Eigenvector
Eigenvectors
Hermitian
Krylov
Lanczos
LANSO
Lattice
Lattices
Mathematical models
Operators
Reproduction
Spectrum
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container_title Computer physics communications
container_volume 184
creator Johnson, Chris
Kennedy, A.D.
description We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication of eigenpairs in finite-precision arithmetic, but uses a new bound to decide when such reorthogonalization is required, and only reorthogonalizes with respect to eigenpairs within the region of interest. We investigate its performance for the Hermitian Wilson–Dirac operator γ5D in lattice quantum chromodynamics, and compare it with previous methods.
doi_str_mv 10.1016/j.cpc.2012.11.003
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subjects Algorithms
Arithmetic
Computer simulation
Eigenvalue
Eigenvalues
Eigenvector
Eigenvectors
Hermitian
Krylov
Lanczos
LANSO
Lattice
Lattices
Mathematical models
Operators
Reproduction
Spectrum
title Numerical determination of partial spectrum of Hermitian matrices using a Lánczos method with selective reorthogonalization
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