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Error analysis of two algorithms for the computation of the matrix exponential

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Abstract

We analyze two algorithms for the computation of the matrix exponential: the Taylor Series and the Scaling and Squaring methods. We give new upper bounds on the roundoff and truncation errors introduced, and we present some numerical experiments, comparing the actual outcomes to the theoretical error bounds.

We analyze, in detail, the reasons why the Taylor Series method can compete with Scaling and Squaring method if the norm of the original matrix is less than one.

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Authors and Affiliations

  1. Istituto di Elaborazione dell'Informazione del CNR, Via S. Maria, 46, 56125, Pisa, Italia

    B. Codenotti

  2. Dipartimento di Informatica, Corso Italia, 40, 56100, Pisa, Italia

    C. Fassino

Authors
  1. B. Codenotti
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  2. C. Fassino
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Codenotti, B., Fassino, C. Error analysis of two algorithms for the computation of the matrix exponential. Calcolo 29, 1–31 (1992). https://doi.org/10.1007/BF02576760

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