Accuracy Analysis of Hybrid Rational Interpolation

Hiroshi Kai and Matu-Tarow Noda
Department of Computer Science, Faculty of Engineering,
Ehime University, Japan

{kai, noda}@cs.ehime-u.ac.jp
http://hpc.cs.ehime-u.ac.jp/{Ekai,Enoda}

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Abstract:

Hybrid Rational Function Approximation (HRFA) is one of the most important applications of approximate-GCD algorithms. Classical rational interpolation may not yield useful approximation of continuous function by the presence of poles over the approximation range. In HRFA, the poles are removed by computing approximate-GCD of the numerator and the denominator polynomials of the interpolated rational function. In this paper, a method of how to estimate the numerical error of rational approximation obtained by HRFA is proposed by using the approximate-GCD proposed by Hribernig and Stetter. A theorem for the error estimation is established.