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Simultaneous self-verified computation of exp (A) and ∫ 10 exp (As) dsexp (As) ds

Parallele validierende Berechnung von exp (A) und ∫ 10 exp (As) dsexp (As) ds

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Abstract

We propose a method for simultaneous computation of verified bounds for the matrix functions exp (A) and ∫ 10 exp (As) ds where the inclusion of the integral is obtained during the computation of verified bounds for exp (A) at very little additional cost. Highly accurate results of our method are achieved by the use of advanced computer arithmetic and an implementation of dynamic precision by means of staggered correction representation.

Zusammenfassung

Vorgeschlagen wird ein Verfahren zur gleichzeitigen Berechnung von verifizierten Schranken für die Matrixfunktionen exp (A) und ∫ 10 exp (As) ds, bei dem die Einschließung des Integrals während der Berechnung von verifizierten Schranken für exp (A) mit sehr geringem zusätzlichen Rechenaufwand erhalten wird. Eine hohe Ergebnisgenauigkeit wird durch die Anwendung einer besonderen Rechnerarithmetik und durch dynamische Genauigkeit mit der “staggered correction”-Darstellung erzielt.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center Section Mathematical Modeling, Bulgarian Academy of Sciences, P.O. Box. 373, 1090, Sofia, Bulgaria

    P. Bochev

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  1. P. Bochev
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Bochev, P. Simultaneous self-verified computation of exp (A) and ∫ 10 exp (As) dsexp (As) ds. Computing 45, 183–191 (1990). https://doi.org/10.1007/BF02247884

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  • DOI: https://doi.org/10.1007/BF02247884

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