Implementation of a restarted Krylov subspace method for the evaluation of matrix functions

Martin Afanasjew; Michael Eiermann; Oliver G. Ernst; Stefan Güttel

doi:10.1016/j.laa.2008.06.029

Implementation of a restarted Krylov subspace method for the evaluation of matrix functions

Martin Afanasjew, Michael Eiermann, Oliver G. Ernst, Stefan Güttel

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

Abstract

A new implementation of restarted Krylov subspace methods for evaluating f (A) b for a function f, a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp (A) b. © 2008 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	2293-2314
Number of pages	21
Journal	Linear Algebra and its Applications
Volume	429
Issue number	10
DOIs	https://doi.org/10.1016/j.laa.2008.06.029
Publication status	Published - 1 Nov 2008

Keywords

Krylov subspace approximation
Matrix function
Polynomial interpolation
Rational approximation
Restarted Arnoldi/Lanczos method
Stopping criterion based on error indicator

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10.1016/j.laa.2008.06.029

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title = "Implementation of a restarted Krylov subspace method for the evaluation of matrix functions",

abstract = "A new implementation of restarted Krylov subspace methods for evaluating f (A) b for a function f, a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp (A) b. {\textcopyright} 2008 Elsevier Inc. All rights reserved.",

keywords = "Krylov subspace approximation, Matrix function, Polynomial interpolation, Rational approximation, Restarted Arnoldi/Lanczos method, Stopping criterion based on error indicator",

author = "Martin Afanasjew and Michael Eiermann and Ernst, {Oliver G.} and Stefan G{\"u}ttel",

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AU - Afanasjew, Martin

AU - Eiermann, Michael

AU - Ernst, Oliver G.

AU - Güttel, Stefan

PY - 2008/11/1

Y1 - 2008/11/1

N2 - A new implementation of restarted Krylov subspace methods for evaluating f (A) b for a function f, a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp (A) b. © 2008 Elsevier Inc. All rights reserved.

AB - A new implementation of restarted Krylov subspace methods for evaluating f (A) b for a function f, a matrix A and a vector b is proposed. In contrast to an implementation proposed previously, it requires constant work and constant storage space per restart cycle. The convergence behavior of this scheme is discussed and a new stopping criterion based on an error indicator is given. The performance of the implementation is illustrated for three parabolic initial value problems, requiring the evaluation of exp (A) b. © 2008 Elsevier Inc. All rights reserved.

KW - Krylov subspace approximation

KW - Matrix function

KW - Polynomial interpolation

KW - Rational approximation

KW - Restarted Arnoldi/Lanczos method

KW - Stopping criterion based on error indicator

U2 - 10.1016/j.laa.2008.06.029

DO - 10.1016/j.laa.2008.06.029

M3 - Article

SN - 0024-3795

VL - 429

SP - 2293

EP - 2314

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 10

ER -

Implementation of a restarted Krylov subspace method for the evaluation of matrix functions

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Keywords

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