Abstract
Several methods for the numerical solution of stiff ordinary differential equations require approximation of an exponential of a matrix. In the present paper we present a technique for estimating the error incurred in replacing a matrix exponential by a rational approximation. This estimation is done by introducing another approximation, of superior order, whose aposteriori evaluation is cheap. Properties of the new approximation pertaining to both its stability and the behavior of the error for matrices with negative eigenvalues are analyzed.
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Communicated by Richard Varga.
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Iserles, A., Nørsett, S.P. Error control of rational approximations to the exponential function. Constr. Approx 2, 41–57 (1986). https://doi.org/10.1007/BF01893416
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DOI: https://doi.org/10.1007/BF01893416