二元向量值有理插值存在性的一种判别方法
In this paper, a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given. This criterion is an algebraic method, i.e., by solving a system of equations based on the given data, we can directly test whether the relevant interpolant exists or not. By coming up with our method,the problem of how to deal with scalar equations and vector equations in the same system of equations is solved. After testing existence, an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently. In addition, the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants. Compared with the Thiele-type method, the one given in this paper is more direct. Finally, some numerical examples are given to illustrate the result.
作 者： 陶有田 朱晓临 周金明 TAO You Tian ZHU Xiao Lin ZHOU Jin Ming 作者单位： 陶有田,TAO You Tian(Department of Mathematics, Chaohu College, Anhui 238000, China;School of Science, Hefei University of Technology, Anhui 230009, China)朱晓临,周金明,ZHU Xiao Lin,ZHOU Jin Ming(School of Science, Hefei University of Technology, Anhui 230009, China)
刊 名： 数学研究与评论 ISTIC PKU 英文刊名： JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION 年，卷(期)： 2008 28(3) 分类号： O2211.5 关键词： bivariate Newton interpolation formula bivariate vector-valued rational inter-polants existence necessary and sufficient conditions