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 𝐿₁ approximations*, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 205–215. MR**0264829****[3]**Ian Barrodale and Andrew Young,*Algorithms for best 𝐿₁ and 𝐿_{∞} linear approximations on a discrete set*, Numer. Math.**8**(1966), 295–306. MR**0196912**, https://doi.org/10.1007/BF02162565**[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]**John R. Rice,*The approximation of functions. Vol. 2: Nonlinear and multivariate theory*, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR**0244675****[7]**John R. Rice and John S. White,*Norms for smoothing and estimation*, SIAM Rev.**6**(1964), 243–256. MR**0168069**, https://doi.org/10.1137/1006061**[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