Abstract
LetR n/m(z∶γ)=P n(z∶γ)/(1−γz)m be a rational approximation to exp (z),z ∈C, of ordern for all real positiveγ. In this paper we show there exists exactly one value ofγ in each of min(n+1,m) interpolation intervals such that the uniform error overR − is at a local minimum.
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S. P. Nørsett, S. R. Trickett (1984):Exponential fitting of restricted rational approximations to the exponential function. In: Rational Approximation and Interpolation (P. R. Graves-Morris, E. B. Saff, R. S. Varga, eds.) Lecture Notes in Math 1105, Berlin: Springer-Verlag, 466–476.
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Communicated by Dieter Gaier.
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Nørsett, S.P., Trickett, S.R. Order-constrained uniform approximations to the exponential based on restricted rationals. Constr. Approx 2, 189–195 (1986). https://doi.org/10.1007/BF01893425
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DOI: https://doi.org/10.1007/BF01893425