Explicit, nearly optimal, linear rational approximation with preassigned poles
Author:
Frank Stenger
Journal:
Math. Comp. 47 (1986), 225252
MSC:
Primary 41A20; Secondary 41A25, 65D15
MathSciNet review:
842132
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Abstract: This paper gives explicit rational functions for interpolating and approximating functions on the intervals , , and . The rational functions are linear in the functions to be approximated, and they have preassigned poles. The error of approximation of these rationals is nearly as small as the error of best rational approximation with numerator and denominator polynomials of the same degrees. Regions of analyticity are described, which make it possible to tell a priori the accuracy which we can expect from this type of rational approximation.
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 J. E. Andersson, "Optimal quadrature functions," Math. Z., v. 172, 1980, pp. 5562. MR 576296 (83m:41023)
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 P. Borwein, "Approximations with negative roots or poles," J. Approx. Theory, v. 35, 1982, pp. 132141. MR 662161 (83j:41020)
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 W. Gautschi, "Computational methods in special functionsA survey," in Theory and Applications of Special Functions, Academic Press, New York, 1975, pp. 198. MR 0391476 (52:12297)
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 J. R. Lund, Numerical Evaluation of Integral Transforms, Ph.D. Thesis, University of Utah, 1978.
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 National Bureau of Standards, Handbook of Mathematical Functions, N.B.S. Applied Math. Series, vol. 55, 1964.
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 H. Padé, "Sur la représentation approchée d'une fonction par des fractions rationelles," Ann. Fac. Sci. École Norm. Sup., v. 9, 1892, pp. 193.
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 E. B. Saff & R. S. Varga, Eds., Padé and Rational Approximation, Academic Press, New York, 1977. MR 0458010 (56:16213)
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 J. Szabados, Uniform Approximation of Continuous Functions by Rational Functions, Ph.D. Thesis, Hungarian Academy of Sciences, 1968. (Hungarian)
 [29]
 T. N. Thiele, "Differences reciproques," Overs, danske Vids, Selsk. Forhadl. (Sitzber., Akad. Kopenhagen), 1906.
 [30]
 R. S. Varga, Topics in Polynomial and Rational Interpolation and Approximation, Les Presses de l'Université de Montréal, no. 55, 1982. MR 654329 (83h:30041)
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 P. Wynn, "On a device for computing the transformation," Math. Comp., v. 10, 1965, pp. 9196. MR 0084056 (18:801e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608421320
PII:
S 00255718(1986)08421320
Article copyright:
© Copyright 1986
American Mathematical Society
