Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

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 $ {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 $ {L_1}$ 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 $ {L_1}$ and $ {L_\infty }$ 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D15

Retrieve articles in all journals with MSC: 65D15

Additional Information

Keywords: Rational approximation, Loeb, Appel, weighted linear approximation, computational experience
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society