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Numerical Chebyshev approximation by interpolating rationals


Author: Jack Williams
Journal: Math. Comp. 26 (1972), 199-206
MSC: Primary 65D15
DOI: https://doi.org/10.1090/S0025-5718-1972-0373230-6
MathSciNet review: 0373230
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Abstract: The paper is concerned with the Chebyshev approximation of decay-type functions $ f(x)$ by interpolating rationals. The interpolating points are chosen to be the zeros of $ f(x)$. Existence, uniqueness and characterization of best approximations are first shown. An exchange algorithm is then described for computing the best approximation.


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

  • [1] K. Appel, ``Rational approximation of decay-type functions,'' Nordisk Tidskr. Informationsbehandling, v. 2, 1962, pp. 69-75.
  • [2] D. C. Handscomb, Methods of Numerical Approximation, Pergamon Press, London, 1966. MR 0455292 (56:13531)
  • [3] C. Hastings, Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955. MR 16, 963. MR 0068915 (16:963e)
  • [4] G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Springer, Berlin, 1964; English transl., Springer Tracts in Natural Philosophy, vol. 13, Springer-Verlag, New York, 1967. MR 31 #547; MR 36 #571. MR 0217482 (36:571)
  • [5] John R. Rice, The Approximation of Functions. Vol. I: Linear Theory, AddisonWesley, Reading, Mass., 1964. MR 29 #3795. MR 0166520 (29:3795)
  • [6] J. Williams, Some Numerical Problems in Theoretical Physics, Doctoral Thesis, University of Oxford, Oxford, 1968.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0373230-6
Keywords: Chebyshev approximation, exchange algorithm
Article copyright: © Copyright 1972 American Mathematical Society

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