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Numerical Chebyshev approximation by interpolating rationals

Author: Jack Williams
Journal: Math. Comp. 26 (1972), 199-206
MSC: Primary 65D15
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 (ed.), Methods of numerical approximation, Pergamon Press, Oxford-New York-Toronto, Ont., 1966. Lectures delivered at a Summer School held at Oxford University, Oxford, September, 1965. MR 0455292
  • [3] Cecil Hastings Jr., Approximations for digital computers, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR 0068915
  • [4] Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition. Translated by Larry L. Schumaker. Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. MR 0217482
  • [5] John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
  • [6] J. Williams, Some Numerical Problems in Theoretical Physics, Doctoral Thesis, University of Oxford, Oxford, 1968.

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Keywords: Chebyshev approximation, exchange algorithm
Article copyright: © Copyright 1972 American Mathematical Society

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