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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


On the conditional equivalence of two starting methods for the second algorithm of Remez

Author: R. E. Huddleston
Journal: Math. Comp. 28 (1974), 569-572
MSC: Primary 65D15
MathSciNet review: 0341804
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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.

References [Enhancements On Off] (What's this?)

  • [1] R. E. Huddleston, REHRAT--A Program for Best Min-Max Rational Approximation, Report #(SCL-DR-72-370), Sandia Laboratories, Livermore, California, 1972.
  • [2] E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 34 #924. MR 0201039 (34:924)
  • [3] A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, New York, 1965. MR 32 #8479. MR 0191070 (32:8479)
  • [4] 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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Additional Information

PII: S 0025-5718(1974)0341804-6
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