构造矩阵有理插值函数降阶的方法

A reduction method for matrix rational interpolation function

由于用Thiele型构造的二元矩阵有理插值函数是(mn+m+n,2[(mn+m+n)/2])型的有理函数,其次数比较大。文章构造一种可以降低其次数的函数——Lagrange型插值函数,其分母的次数可以根据需要确定;讨论了极点和不可达点的相关问题;在一定的条件下还可以降低其分子的次数,计算简单,便于实际应用。

The binary matrix rational interpolation function constructed by Thiele-type structure is（mn＋m＋n,2[（mn＋m＋n）/2]）-type rational function,and its degree is comparatively large.This paper constructs a Lagrange-type interpolation function to reduce its degree,and the denominator degree can be determined according to the needs.It discusses the poles and unattainable points as well.Under certain conditions,the numerator degree can also be reduced,which is simple in calculation,and convenient in practical application.