A fast algorithm for rational interpolation via orthogonal polynomials

Authors:
Ömer Eğecioğlu and Çetin K. Koç

Journal:
Math. Comp. **53** (1989), 249-264

MSC:
Primary 65D05; Secondary 33A65, 41A05

DOI:
https://doi.org/10.1090/S0025-5718-1989-0972369-4

MathSciNet review:
972369

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Abstract | References | Similar Articles | Additional Information

Abstract: A new algorithm for rational interpolation is proposed. Given the data set, the algorithm generates a set of orthogonal polynomials by the classical three-term 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 $O({N^2})$, where $N + 1$ 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 $O({N^2})$ arithmetic operations.

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*An*$O(N\log N)$

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Additional Information

Keywords:
Rational interpolation,
orthogonal polynomials,
Hankel matrices

Article copyright:
© Copyright 1989
American Mathematical Society