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Attainable order of rational approximations to the exponential function with only real poles

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Abstract

Rational approximations of the form Σ m i=0 a i q i/Π n i=1 (1+γ i q) to exp(−q),qεC, are studied with respect to order and error constant. It is shown that the maximum obtainable order ism+1 and that the approximation of orderm+1 with least absolute value of the error constant has γ1=γ2=...=γ n . As an application it is shown that the order of av-stage semi-implicit Runge-Kutta method cannot exceedv+1.

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Authors and Affiliations

  1. Institutt for Numerisk Matematikk, Universitetet I Trondheim — Nth, N-7034, Trondheim, Norway

    Syvert P. Nørsett & Arne Wolfbrandt

  2. Dept. of Computer Sciences, Chalmers University of Technology, S-402 20, Göteborg 5, Sweden

    Syvert P. Nørsett & Arne Wolfbrandt

Authors
  1. Syvert P. Nørsett
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  2. Arne Wolfbrandt
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Nørsett, S.P., Wolfbrandt, A. Attainable order of rational approximations to the exponential function with only real poles. BIT 17, 200–208 (1977). https://doi.org/10.1007/BF01932291

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  • DOI: https://doi.org/10.1007/BF01932291

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