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A self-validating numerical method for the matrix exponential

Eine selbstverifizierende numerische Methode fuer die Exponentialfunktion einer Matrix

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Abstract

An algorithm is presented, which produces highly accurate and automatically verified bounds for the matrix exponential function. Our computational approach involves iterative defect correction, interval analysis and advanced computer arithmetic. The algorithm presented is based on the “scaling and squaring” scheme, utilizing Padé approximations and safe error monitoring. A PASCAL-SC program is reported and numerical results are discussed.

Zusammenfassung

Es wird ein Algorithmus vorgestellt, der hochgenaue und automatisch verifizierte Grenzen fuer die Exponentialfunktion einer Matrix liefert. Unser Verfahren benuetzt iterative Defektkorrektur, Intervall-Analysis und eine erweiterte Rechnerarithmetik. Der dargestellte Algorithmus basiert auf dem “scaling and squaring” Schema und benutzt Padé-Approximationen und safe-error-monitoring. Es werden ein PASCAL-SC Programm vorgestellt und numerische Resultate diskutiert.

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Authors and Affiliations

  1. Centre for informatics and computer technology, Bulgarian Academy of Sciences, “Acad. G. Bonchev”, str. Block 25/A, 1113, Sofia, Bulgaria

    Pavel Bochev

  2. Institute of Mathematics with Computing Center, Bulgarian Academy of Sciences, P.O. Box 373, 1090, Sofia, Bulgaria

    Svetoslav Markov

Authors
  1. Pavel Bochev
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  2. Svetoslav Markov
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Additional information

The present research is partially supported by the Committee of Science, Sofia, Bulgaria, according to contract No. 755/87

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Bochev, P., Markov, S. A self-validating numerical method for the matrix exponential. Computing 43, 59–72 (1989). https://doi.org/10.1007/BF02243806

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  • DOI: https://doi.org/10.1007/BF02243806

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