多元零次有理插值的构造性理论及算法  

CONSTRUCTIVE THEORY OF MULTIVARIATE RATIONAL INTERPOLATION OF DEGREE ZERO WITH ALGORITHM

作　　者：李鹏[1] 董天[1] 雷娜[1] 

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《高等学校计算数学学报》2010年第4期303-314,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金："973"项目(2004CB318000)的资助

摘　　要：有理插值问题是由一组给定数据构造分子、分母均属于同一有限维多项式空间的有理函数R的插值问题.一元有理插值已经多年研究,理论比较成熟.然而,多元有理插值问题比一元情形复杂得多,加之研究工具和方法的制约,至今理论还远非完善.作为一次十分有益的尝试,[5]依据多元多项式插值的构造性代数理论,证明了多元Cauchy型有理插值的存在性并给出了插值函数的一般表达式.Multivariate rational interpolation of degree zero,owing to its outstanding approximation property,has become a special but important class of multivariate rational interpolation.In this paper,with the help of the constructive theory of multivariate nonlacunary Lagrange interpolation,we study the construction of a multivariate rational interpolation function of degree zero on a sampled subset W of a given set of nodes V in R^d.We present both the existence and the expression of the rational interpolation function along with a key algorithm for seeking the nodes of W in V.

关 键 词：有理插值问题 构造性 多元多项式插值 CAUCHY型 算法 多项式空间 一般表达式 数据构造 

分 类 号：O241.3[理学—计算数学]