矩形网格上二元矩阵切触有理插值的新方法  

New method of bivariate matrix osculatory rational interpolation on rectangular grids

作　　者：经慧芹[1] 张桂芳[2] 廖永宜[1] 

机构地区：[1]昆明理工大学成人教育学院,昆明650051 [2]昆明理工大学冶金与能源工程学院,昆明650093

出　　处：《计算机工程与应用》2013年第17期58-62,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.51066003);云南省自然科学基金(No.2011FZ025)

摘　　要：熟知的矩阵切触有理插值的方法都与连分式有关,不仅计算繁琐,而且难以避免出现"极点、不可达点"。用网格点构造有理插值基函数,用型值点构造具有承袭性的各阶矩阵插值算子,通过插值基函数与插值算子作线性运算,构造出二元矩阵各阶切触有理插值函数,有效避免了有理插值的"极点、不可达点"问题。若选择适当的参数,还可以任意降低插值函数的次数,数值例子表明了该方法简单、有效、实用性强。The well-known algorithms of the matrix osculatory rational interpolations are all related to continued fractions, con-tinued fraction method not only needs a high computation but also is difficult to avoid ＂poles and inaccessible points＂. In this paper, the grid points are applied to construct the rational interpolation base functions, the type value points are applied to construct each order matrix interpolation operators of inheritedness, by interpolation basis functions and interpolation operators do linearity operation, bivariate matrix each order osculatory rational interpolation functions are produced to effectively avoid ＂poles and inac-cessible points＂ problem of rational interpolation. If the appropriate parameters are selected, it can reduce degree of the interpola-tion functions arbitrarily, a numerical example shows the method is simple and effective oractical.

关 键 词：矩形网格 二元矩阵 切触有理插值 

分 类 号：O241.3[理学—计算数学]