Two simple algorithms for discrete rational approximation

Author:

Barrodale I.,Mason J. C.

Abstract

This paper reports on computational experience with algorithms due to Loeb and Appel for rational approximation on discrete point sets. Following a brief review of the linear discrete approximation problem, the two rational algorithms are stated in a general setting. Finally, several numerical examples of applications to l 1 {l_1} , l 2 {l_2} , and l {l_\infty } approximation are supplied and discussed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference8 articles.

1. K. Appel, "Rational approximation of decay-type functions," Nordtsk Tldskr. Informationsbehandling, v. 2, 1962, pp. 69–75.

2. On computing best 𝐿₁ approximations;Barrodale, I.,1970

3. Algorithms for best 𝐿₁ and 𝐿_{∞} linear approximations on a discrete set;Barrodale, Ian;Numer. Math.,1966

4. H. L. Loeb, On Rational Fraction Approximations at Discrete Points, Convair Astronautics, Math. Preprint #9, 1957.

5. J. C. Mason, Some New Approximations for the Solution of Differential Equations, Doctoral Thesis, Oxford, 1965.

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