Order-constrained uniform approximations to the exponential based on restricted rationals |
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| Authors: | Syvert P Nørsett Stewart R Trickett |
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| Institution: | 1. Department of Num. Math, University of Trondheim-NTH, N-7034, Trondheim NTH, Norway
2. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
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| 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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