判别有理插值函数存在性的一种新方法

A new criterion for the existence of the rational interpolation functions

有理插值函数的存在性问题是有理插值研究的一个重要内容。现有的关于有理插值函数的存在性的方法都是基于求解齐次线性方程组的方法,其系数矩阵的阶数较高,计算复杂度较大。本文利用牛顿差商的性质和分段组合的方法,给出了一种判别有理插值函数存在的方法。较之其他方法,具有计算复杂度较小、承袭性等优点。

The existence of rational interpolation function is an important field in the study of rational interpolation. Existing methods about the existence of rational interpolation function are based on the method of solving the homogeneous linear equations, which has the high order matrix and the high complexity of computation. In this paper, by use of the properties of Newton difference quotient and the method of piecewise combination, we present a method to judge the existence of rational interpolation function. Compared with other methods, it has the advantages of heredity and low complexity of computation.