二元混合有理插值新方法  

A novel bivariate blending rational interpolation with high-accuracy

作　　者：张玉武[1,2] 赵前进[1] 唐如忠[1] 

机构地区：[1]安徽理工大学理学院,安徽淮南232001 [2]六安职业技术学院基础部,安徽六安237158

出　　处：《合肥工业大学学报（自然科学版）》2010年第12期1908-1911,共4页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(60973050;30570431;60873144);安徽省教育厅自然科学基金资助项目(KJ2009A50;KJ2007B173);安徽省优秀人才基金资助项目;教育部新世纪优秀人才支持计划资助项目(NCET-06-0555);国家863高技术研究发展计划基金资助项目(2006AA01Z104)

摘　　要：用基于连分式的二元混合有理插值逼近二元连续函数有许多缺点,如无法避免极点也无法控制极点的位置、可能出现不可达点及偏逆差商可能不存在等。重心有理插值比传统的连分式有理插值具有很多优点,如计算量小、数值稳定性好、没有极点以及可以避免不可达点等。文章基于多项式插值和重心有理插值构造了一种二元混合有理插值函数,同时给出了误差分析;数值实例表明了新方法的有效性。To approximate a bivariate continued function by a bivariate blending rational interpolation based on continued fractions has some disadvantages.For instance it is hard to avoid poles and unattainable points and to control the location of poles,and the partial inverse differences may not exist,and so on.Compared with the traditional rational interpolation based on continued fractions,the barycentric rational interpolation has many advantages such as small calculation quantity,good numerical stability,no poles and unattainable points,etc.Based on polynomial interpolation and barycentric rational interpolation,a bivariate blending rational interpolation function is constructed in this paper and the error estimation is also given.Numerical examples show the effectiveness of this new method.

关 键 词：重心有理插值 二元混合有理插值 误差 

分 类 号：O241.3[理学—计算数学]