三元Thiele-Newton型有理插值  

Tri-variate Thiele-Newton′s Rational Interpolants

作　　者：王家正[1] 

机构地区：[1]安徽教育学院数学系,安徽合肥230061

出　　处：《河南科技大学学报（自然科学版）》2006年第6期83-86,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：安徽省教育厅自然科学基金项目(2005KJ211)

摘　　要：将Th iele型插值连分式与二元Newton插值多项式结合起来构造三元有理函数,通过引入三元混合差商和倒差商建立了三元有理插值的递推算法、特征定理,给出了相应的证明,并通过数值例子验证了算法的有效性。三元有理插值在几何造型、图像处理、计算机辅助设计等领域都有直接的应用。Tri-variate rational function is structured by incorporating Thiele's branched continued fraction in bivariate Newton's interpolation polynomials.By defining tri-variate mixed difference and inverse difference,tri-variate rational interpolating algorithm is built,and interpolating characteristical theorem and its proof are given.A numerical example is presented to illustrate the efficiency of this algorithm.Tri-variate rational interpolating has direct application in geometrical modeling,image processing and CAGD,etc.

关 键 词：连分式 有理插值 倒差商 特征定理 

分 类 号：O241[理学—计算数学]