Two simple algorithms for discrete rational approximation

Authors:
I. Barrodale and J. C. Mason

Journal:
Math. Comp. **24** (1970), 877-891

MSC:
Primary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1970-0301894-X

MathSciNet review:
0301894

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Abstract | References | Similar Articles | Additional Information

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 , , and approximation are supplied and discussed.

**[1]**K. Appel, "Rational approximation of decay-type functions,"*Nordtsk Tldskr. Informationsbehandling*, v. 2, 1962, pp. 69-75.**[2]**I. Barrodale, "On computing best approximations,"*Approximation Theory*, edited by A. Talbot, Academic Press, London, 1970, pp. 205-215. MR**0264829 (41:9420)****[3]**I. Barrodale & A. Young, "Algorithms for best and linear approximations on a discrete set,"*Numer. Math.*, v. 8, 1966, pp. 295-306. MR**33**#5096. MR**0196912 (33:5096)****[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.**[6]**J. R. Rice,*The Approximation of Functions*. Vol. 2, Addison-Wesley, Reading, Mass., 1969. MR**0244675 (39:5989)****[7]**J. R. Rice & J. S. White, "Norms for smoothing and estimation,"*SIAM Rev.*, v. 6, 1964, pp. 243-256. MR**29**, #5334. MR**0168069 (29:5334)****[8]**L. Wittmeyer, "Rational approximation of empirical functions,"*Nordisk Tidskr. Informationsbehandling*, v. 2, 1962, pp. 53-60.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0301894-X

Keywords:
Rational approximation,
Loeb,
Appel,
weighted linear approximation,
computational experience

Article copyright:
© Copyright 1970
American Mathematical Society