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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Numerical Chebyshev approximation by interpolating rationals
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by Jack Williams PDF
Math. Comp. 26 (1972), 199-206 Request permission

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
    K. Appel, “Rational approximation of decay-type functions,” Nordisk Tidskr. Informationsbehandling, v. 2, 1962, pp. 69-75.
  • 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
  • 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
  • Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482
  • John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964. MR 0166520
  • J. Williams, Some Numerical Problems in Theoretical Physics, Doctoral Thesis, University of Oxford, Oxford, 1968.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 199-206
  • MSC: Primary 65D15
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0373230-6
  • MathSciNet review: 0373230