A fast algorithm for rational interpolation via orthogonal polynomials
Authors:
Ömer Eğecioğlu and Çetin K. Koç
Journal:
Math. Comp. 53 (1989), 249264
MSC:
Primary 65D05; Secondary 33A65, 41A05
MathSciNet review:
972369
Fulltext PDF Free Access
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Abstract: A new algorithm for rational interpolation is proposed. Given the data set, the algorithm generates a set of orthogonal polynomials by the classical threeterm recurrence relation and then uses Newton interpolation to find the numerator and the denominator polynomials of the rational interpolating function. The number of arithmetic operations of the algorithm to find a particular rational interpolant is , where is the number of data points. A variant of this algorithm that avoids Newton interpolation can be used to construct all rational interpolants using only arithmetic operations.
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 P. J. Davis, Interpolation and Approximation, Dover, New York, 1975. MR 0380189 (52:1089)
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 G. E. Forsythe, "Generation and use of orthogonal polynomials for data fitting with a digital computer," J. Soc. Indust. Appl. Math., v. 5, 1957, pp. 7478. MR 0092208 (19:1079e)
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 T. J. Rivlin, An Introduction to the Approximation of Functions, Dover, New York, 1969. MR 0249885 (40:3126)
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 G. Szegö, Orthogonal Polynomials, Amer. Math. Soc., Providence, R. I., 1959.
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 W. F. Trench, "An algorithm for the inversion of finite Hankel matrices," J. Soc. Indust. Appl. Math., v. 13, 1965, pp. 11021107. MR 0189232 (32:6659)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909723694
PII:
S 00255718(1989)09723694
Keywords:
Rational interpolation,
orthogonal polynomials,
Hankel matrices
Article copyright:
© Copyright 1989
American Mathematical Society
