三元混合型有理插值  

Tri-variate Mixed Type 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：《河北工业大学学报》2006年第5期28-31,共4页Journal of Hebei University of Technology

基　　金：安徽省教育厅自然科学基金(2005KJ211)

摘　　要：Newton插值和Thiele型连分式插值在多项式插值和有理插值中具有重要的地位,将Newton插值多项式与Thiele型分叉连分式结合起来构造三元混合型有理函数,通过引入差商和倒差商建立三元有理插值算法、特征定理和相应的证明,并给出数值例子验证算法的有效性.Newton＇s polynomials interpolation and Thiele＇s branched continued fraction interpolation have important position in linear and nonlinear interpolation, respectively. In this paper, Tri-variate mixed type rational function is structured by incorporating Newton＇s interpolation polynomials in Thiele＇s branched continued fraction. By defining the difference and inverse difference, tri-variate mixed type rational interpolating algorithm is built, and interpolating characteristical theorem and its proof are given. The end, anumerical example is presented to illustrate the efficiency of this algorithm.

关 键 词：连分式 有理插值 Thiele型插值 特征定理 

分 类 号：O241.3[理学—计算数学]