二元对角向量值有理插值的算法

首先提出了二元对角向量值有理插值问题,它包括主对角和副对角两种向量值有理插值,并分别给出了主对角线和副对角线上向量值有理插值的两种算法,即直接求系数bi,j的算法和基于Samelson广义逆所定义的特殊初等变换的矩阵算法.然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法.最后给出多个数值例子说明上述算法的有效性.

Algorithms for Bivariate Diagonal Vector Valued Rational Interpolants

This paper proposes the problem of bivariate diagonal vector valued rational interpolation: the bivariate vector valued rational interpolation over leading diagonal and sub-diagonal respectively.Two kinds of algorithms are given for computing them: one is a method for computing bi,jdirectly and another is a kind of matrix method which is given by defining a special elementary operation in the sense of Samelson inverse.In addition this paper constructs a matrix algorithm for computing bivariate diagonal vector valued rational interpolants with preassigned poles.At last,some examples are given to illustrate tha validity of the above algorithms.