Fitzpatrick Algorithm for Multivariate Rational Interpolation
Peng Xia, Shugong Zhang, Na Lei
TL;DR
This paper adapts the Fitzpatrick algorithm for multivariate rational interpolation and introduces a Neville-like algorithm for efficient pointwise interpolation without full function computation.
Contribution
It extends the Fitzpatrick algorithm to osculatory rational interpolation and develops a Neville-like algorithm for Cauchy interpolation, enabling efficient pointwise evaluation.
Findings
Successfully applied Fitzpatrick algorithm to osculatory rational interpolation
Developed a Neville-like algorithm for Cauchy interpolation
Achieved pointwise interpolation without full rational function computation
Abstract
In this paper, we first apply the Fitzpatrick algorithm to osculatory rational interpolation. Then based on Fitzpatrick algorithm, we present a Neville-like algorithm for Cauchy interpolation. With this algorithm, we can determine the value of the interpolating function at a single point without computing the rational interpolating function.
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Taxonomy
TopicsDigital Filter Design and Implementation · Advanced Numerical Analysis Techniques · Polynomial and algebraic computation