Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

M A Freitag; Alastair Spence

doi:10.1016/j.laa.2007.11.013

Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

M A Freitag
, Alastair Spence

Department of Mathematical Sciences

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

27 Citations (SciVal)

259 Downloads (Pure)

Abstract

We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.

Original language	English
Pages (from-to)	2049-2060
Number of pages	12
Journal	Linear Algebra and its Applications
Volume	428
Issue number	8-9
Early online date	27 Dec 2007
DOIs	https://doi.org/10.1016/j.laa.2007.11.013
Publication status	Published - 15 Apr 2008

Keywords

Inexact Rayleigh quotient iteration
Nonsymmetric eigenproblem
Eigenvalue approximation
Preconditioning
Iterative methods

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10.1016/j.laa.2007.11.013

Spence_LAA_freitagspence_accepted.pdfAccepted author manuscript, 156 KB

Cite this

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abstract = "We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.",

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AU - Spence, Alastair

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N2 - We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.

AB - We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.

KW - Inexact Rayleigh quotient iteration

KW - Nonsymmetric eigenproblem

KW - Eigenvalue approximation

KW - Preconditioning

KW - Iterative methods

UR - https://www.scopus.com/pages/publications/39549120904

UR - http://dx.doi.org/10.1016/j.laa.2007.11.013

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JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 8-9

ER -

Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

Abstract

Keywords

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