Computing

, Volume 43, Issue 1, pp 59–72 | Cite as

A self-validating numerical method for the matrix exponential

  • Pavel Bochev
  • Svetoslav Markov
Article

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.

AMS Subject Classification

65G10 65L05 65F30 41A21 

Key words

matrix exponential Padé approximations iterative defect correction 

Eine selbstverifizierende numerische Methode fuer die Exponentialfunktion einer Matrix

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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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Pavel Bochev
    • 1
  • Svetoslav Markov
    • 2
  1. 1.Centre for informatics and computer technologyBulgarian Academy of Sciences, “Acad. G. Bonchev”SofiaBulgaria
  2. 2.Institute of Mathematics with Computing CenterBulgarian Academy of SciencesSofiaBulgaria

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