Abstract
A method is developed for finding the “best” rational approximationp(x)/q(x) in the least-squares sense of a functionf(x) known at discrete points of an interval. Especially for functions with a steep tangent the method yields far better results than polynomial approximation. The scheme can easily be extended to functions known at all points of an interval.
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References
Hastings, C.,Approximations for digital computers, Princeton 1955.
Fröberg, C. E.,Approximation med rationella funktioner, Nordiskt Symposium för användning av matematikmaskiner. Karlskrona och Lund 1959.
Maehly, H. J.,Rational approximations for transcendental functions, Mathematics Department, Princeton University, Unesco/NS/ICIP/A. 1.12.
Zoutendijk, G.,Methods of feasible directions, Amsterdam · London · New York · Princeton 1960.
Loeb, H. L.,A Note on Rational Function Approximation. Convair Astronautics Applied Mathematical Series # 27.
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Part of this work was carried out at SAAB, Linköping. The present form was developed at the Department of Numerical Analysis, Lund.
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Wittmeyer, L. Rational approximation of empirical functions. BIT 2, 53–60 (1962). https://doi.org/10.1007/BF02024782
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DOI: https://doi.org/10.1007/BF02024782