一类二元有理插值的存在性问题

Study on Existence for a Class of Bivariate Rational Interpolation

利用二元Lagrange插值公式对一类二元有理插值函数的存在性给出了一个判别方法,并在判别出该二元有理插值函数存在时,给出了它的表现公式。此外,对导致二元有理插值函数不存在的不可达点,本文给出了一种处理方法,使之由不可达点变成可达点。文章的最后还给出若干数值例子说明了本方法的有效性.

This paper gives a method to test the existence for a class of bivariate rational interpolation by making use of bivariate Lagrange interpolation formula , and presents the explicit expression of the bivariate rational interpolant when it exists . In addition , a means for dealing with the unattainable points is also given in this paper . At the end of this paper , some numerical examples are given to illustrate the above methods .