Comparison of methods for evaluating functions of a matrix exponential

H. A. Ashi; L. J. Cummings; P. C. Matthews

doi:10.1016/j.apnum.2008.03.039

Comparison of methods for evaluating functions of a matrix exponential

H. A. Ashi, L. J. Cummings, P. C. Matthews

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

25 Scopus citations

Abstract

We compare six different categories of numerical methods for the evaluation of functions of the matrix exponential. These functions are required for exponential integrators, and are not straightforward to evaluate because they are highly susceptible to rounding errors when the matrix has small eigenvalues. The comparison takes into account both accuracy and computational time. A scaling and squaring algorithm and a diagonalisation algorithm are both found to be efficient.

Original language	English (US)
Pages (from-to)	468-486
Number of pages	19
Journal	Applied Numerical Mathematics
Volume	59
Issue number	3-4
DOIs	https://doi.org/10.1016/j.apnum.2008.03.039
State	Published - Mar 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

Keywords

Exponential integrators
Exponential time differencing methods
Matrix exponential
Stiff differential equations

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10.1016/j.apnum.2008.03.039

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abstract = "We compare six different categories of numerical methods for the evaluation of functions of the matrix exponential. These functions are required for exponential integrators, and are not straightforward to evaluate because they are highly susceptible to rounding errors when the matrix has small eigenvalues. The comparison takes into account both accuracy and computational time. A scaling and squaring algorithm and a diagonalisation algorithm are both found to be efficient.",

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AU - Cummings, L. J.

AU - Matthews, P. C.

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AB - We compare six different categories of numerical methods for the evaluation of functions of the matrix exponential. These functions are required for exponential integrators, and are not straightforward to evaluate because they are highly susceptible to rounding errors when the matrix has small eigenvalues. The comparison takes into account both accuracy and computational time. A scaling and squaring algorithm and a diagonalisation algorithm are both found to be efficient.

KW - Exponential integrators

KW - Exponential time differencing methods

KW - Matrix exponential

KW - Stiff differential equations

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ER -

Comparison of methods for evaluating functions of a matrix exponential

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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