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Comparison of software for computing the action of the matrix exponential

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Abstract

The implementation of exponential integrators requires the action of the matrix exponential and related functions of a possibly large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with other codes from the literature. As we are interested in applications to exponential integrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal.

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Notes

  1. We thank S. Güttel for providing us with a Matlab code.

  2. We thank A. Tambue for providing us with a Matlab code.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Marco Caliari

  2. Institut für Mathematik, Universität Innsbruck, Technikerstr. 13, 6020, Innsbruck, Austria

    Peter Kandolf, Alexander Ostermann & Stefan Rainer

Authors
  1. Marco Caliari
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  2. Peter Kandolf
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  3. Alexander Ostermann
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  4. Stefan Rainer
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Corresponding author

Correspondence to Alexander Ostermann.

Additional information

Communicated by Ahmed Salam.

Peter Kandolf acknowledges the financial support by a scholarship of the Vizerektorat für Forschung, University of Innsbruck.

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Caliari, M., Kandolf, P., Ostermann, A. et al. Comparison of software for computing the action of the matrix exponential. Bit Numer Math 54, 113–128 (2014). https://doi.org/10.1007/s10543-013-0446-0

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