On the conditional equivalence of two starting methods for the second algorithm of Remez
Abstract: In computing best min-max rational approximations by the second algorithm of Remez (which is an iterative procedure), one must provide a starting approximation. A method proposed by Ralston and one by Werner are shown to be equivalent under reasonable conditions.
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-  Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070
-  H. Werner, J. Stoer, and W. Bommas, Handbook Series Methods of Approximation: Rational Chebyshev approximation, Numer. Math. 10 (1967), no. 4, 289–306. MR 1553955, https://doi.org/10.1007/BF02162028
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- E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 #924. MR 0201039 (34:924)
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- H. K. E. Werner, J. Stoer & W. Bommas, "Rational Chebyshev approximation," Numer. Math., v. 10, 1967, pp. 289-306. MR 1553955
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Keywords: Approximation by rational functions, min-max rational approximations, Remez algorithm, starting procedures for min-max rational approximations
Article copyright: © Copyright 1974 American Mathematical Society