Title of Paper:The Bulirsch-Stoer algorithm for multivariate rational interpolation

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Date of Publication:2018-11-30

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals:SCIE

Volume:41

Issue:17

Page Number:7698-7710

ISSN No.:0170-4214

Key Words:Bulirsch-Stoer algorithm; multivariate rational interpolation

Abstract:The Neville-type algorithms are widely used in engineering and sciences. As an analog of Neville's algorithm that deals with univariate polynomial interpolation, Bulirsch-Stoer algorithm is a classical one for univariate rational interpolations. It can be applied to calculating the value of the interpolating function at the given point or recovering rational functions. In this paper, we generalize the algorithm to multivariate cases with two versions for different situations. These two generalizations are recursive algorithms. The first one is suitable to calculate the value of the interpolating function and the other one can be applied to recovering multivariate rational functions from accurate measurements. Some two-variable examples illustrate that, if we recover the rational functions with higher degrees, the second generalization is superior to Thiele-Thiele continued fraction and two-variable Lowner matrix methods.