二元切触有理插值函数的构造方法  

Method of constructing bivariate osculatory rational interpolation function

作　　者：荆科[1] 康宁[1] 王茂华[1] 

机构地区：[1]阜阳师范学院数学与计算科学学院,安徽阜阳236041

出　　处：《计算机工程与应用》2012年第32期56-59,207,共5页Computer Engineering and Applications

基　　金：国家特色专业(数学与应用数学)(No.TS11496);安徽省高等学校省级教学质量与教学改革工程重点项目(No.20101984);阜阳师范学院科研项目(No.2012FSKJ07)

摘　　要：二元切触有理插值函数的构造方法大都是基于连分式进行的,其算法可行性是有条件的,且计算量较大,有理函数的次数较高。利用分段组合方法,构造出一种二元切触有理插值函数并将其推广到向量值切触有理插值情形,既解决了切触有理插值函数的存在性问题,又降低了切触有理插值函数的次数。相比于其他方法,其构造过程公式化,算法的可行性是无条件的,有理插值函数次数较低,且计算量较小,便于实际应用。The methods of constructing bivariate osculatory rational interpolation function are mostly based on the continued fraction. But feasibility of the algorithm is conditional, the computation is large, and the degree of it is high. It constructs the bivariate osculatory rational interpolation function and extends it to vector-valued case, by means of the method of piecewise combination. It not only solves the existence problem of osculatory rational inter- polation function, but also reduces the degree of rational function. Compared to other methods, the course of con- structing function is formulary, the degree of rational interpolation function is lower, the feasibility of algorithm is unconditional, and the algorithm needs less computation and facilitates the practical application.

关 键 词：二元切触有理插值 分段组合 插值公式 二元埃米特插值 

分 类 号：O241.3[理学—计算数学]