一类二元有理插值函数的存在性及算法  

The Existence of a Class of the Bivariate Rational Interpolation Function and Its Algorithn

作　　者：周金明[1] 朱晓临[1] 陶有田[1] 

机构地区：[1]合肥工业大学理学院,合肥230009

出　　处：《大学数学》2007年第6期96-101,共6页College Mathematics

基　　金：国家自然科学基金资助项目(No.60473114)

摘　　要：文[3]构造了对于矩形网格上基于二元Newton插值公式的一类二元有理插值函数,并给出了其存在性的充分条件.本文进一步证明了这类二元有理插值函数存在性的必要条件,特别地,当m=n时,给出了具有三角形结构的系数矩阵的判别方法,该方法计算简便且具有承袭性,文章最后给出的实例说明了方法的有效性.In the reference [3], it constructs a class of bivariate rational interpolation function （BRIF） on the rectangular grids by the bivariate Newton interpolation formula, and it sets up and prove the sufficient condition of the existence of BRIF. In this paper, we prove the necessary condition of the existence of BRIF; especially, as re=n, we provide a method with a coefficientt matrix of a triangular construction to judge whether it exists. The method is convenient to calculate and has some inheritance. Finally, numerical examples are given to illustrate the result.

关 键 词：二元Newton插值公式 二元有理插值 矩形网格 系数矩阵 

分 类 号：O241.3[理学—计算数学]