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

Chris Johnson; A. D. Kennedy

doi:10.1016/j.cpc.2012.11.003

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

Chris Johnson, A. D. Kennedy

School of Physics and Astronomy

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

Abstract

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 (\gamma_5D) in lattice quantum chromodynamics, and compare it with previous methods.

Original language	English
Pages (from-to)	689–697
Journal	Computer Physics Communications
Volume	184
Issue number	3
DOIs	https://doi.org/10.1016/j.cpc.2012.11.003
Publication status	Published - 6 Nov 2012

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10.1016/j.cpc.2012.11.003

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
Leimkuhler, B. (Principal Investigator)
EPSRC
1/08/09 → 31/07/14
Project: Research
The Standard Model and beyond
Kenway, R. (Principal Investigator), Ball, R. (Co-investigator), Berera, A. (Co-investigator), Binoth, T. (Co-investigator), Boyle, P. (Co-investigator), Del Debbio, L. (Co-investigator), Kennedy, A. (Co-investigator), Pendleton, B. (Co-investigator) & Plehn, T. (Co-investigator)
STFC
1/10/08 → 30/09/11
Project: Research

Cite this

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title = "Numerical determination of partial spectrum of Hermitian matrices using a Lanczos method with selective reorthogonalization",

abstract = "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 (\gamma_5D) in lattice quantum chromodynamics, and compare it with previous methods.",

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Y1 - 2012/11/6

N2 - 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 (\gamma_5D) in lattice quantum chromodynamics, and compare it with previous methods.

AB - 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 (\gamma_5D) in lattice quantum chromodynamics, and compare it with previous methods.

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DO - 10.1016/j.cpc.2012.11.003

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SP - 689

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JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 3

ER -

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

Abstract

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Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform

The Standard Model and beyond

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