The Bulirsch-Stoer algorithm for multivariate rational interpolation
The Bulirsch-Stoer algorithm for multivariate rational interpolation
复制标题
用于多元有理插值的 Bulirsch-Stoer 算法
DOI：
10.1002/mma.5233
复制
发表时间：
2018
影响因子：
2.9
通讯作者：
Na Lei
中科院分区：
文献类型：
--
作者：
Peng Xia;Tian Dong;Shugong Zhang;Na Lei
Neville型算法广泛应用于工程和科学领域。Bulirsch‐Stoer算法是一元有理插值的经典算法，它是Neville算法的一种类似。它可用于计算插值函数在给定点处的值或恢复有理函数。在本文中，我们推广的算法多变量的情况下，两个版本的不同情况。这两种推广都是递归算法。第一种方法适用于计算插值函数的值，第二种方法适用于从精确测量值恢复多元有理函数。一些二元例子表明，如果我们恢复高次有理函数，第二种推广方法比Thiele-Thiele连分式和二元Löwner矩阵方法有上级优势.
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 Löwner matrix methods.