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

 

Two simple algorithms for discrete rational approximation


Authors: I. Barrodale and J. C. Mason
Journal: Math. Comp. 24 (1970), 877-891
MSC: Primary 65D15
MathSciNet review: 0301894
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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_2}$, and $ {l_\infty }$ approximation are supplied and discussed.


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

  • [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 (41 #9420)
  • [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 (33 #5096)
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  • [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 (39 #5989)
  • [7] John R. Rice and John S. White, Norms for smoothing and estimation, SIAM Rev. 6 (1964), 243–256. 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: http://dx.doi.org/10.1090/S0025-5718-1970-0301894-X
PII: S 0025-5718(1970)0301894-X
Keywords: Rational approximation, Loeb, Appel, weighted linear approximation, computational experience
Article copyright: © Copyright 1970 American Mathematical Society