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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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A fast algorithm for rational interpolation via orthogonal polynomials
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by Ömer Eğecioğlu and Çetin K. Koç PDF
Math. Comp. 53 (1989), 249-264 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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