一种二元矩阵值Padé型逼近的递推算法  

Recursive algorithms for bivariate matrix-valued Padétype approximation

作　　者：王冬银 开小山 陶有田 WANG Dongyin;KAI Xiaoshan;TAO Youtian(School of Mathematics and Statistics, Chaohu University, Chaohu 238000, China;School of Mathematics, Hefei University of Technology, Hefei 230601, China;School of Business Administration, Chaohu University, Chaohu 238000, China)

机构地区：[1]巢湖学院数学与统计学院,安徽巢湖238000 [2]合肥工业大学数学学院,安徽合肥230601 [3]巢湖学院工商管理学院,安徽巢湖238000

出　　处：《合肥工业大学学报（自然科学版）》2020年第8期1143-1148,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金面上资助项目(61972126);安徽省高校优秀青年人才支持计划资助项目(gxyqZD2016285,gxyq2018076,gxyq2019082);安徽省高等学校自然科学研究资助项目(KJ2018A0455,KJ2019A0683)。

摘　　要：针对一种二元矩阵值Padé型逼近(bivariate matrix-valued Padétype approximation,BMPTA),文章给出了一种更加简洁的递推算法。根据二元齐次数量值正交多项式,定义了二元张量积形式正交多项式(bivariate tensor product formal orthogonal polynomial,BTPFOP)及二元矩阵值张量积形式正交多项式(bivariate matrix tensor product formal orthogonal polynomials,BMTPFOP),并给出BMTPFOP的三项递推公式及九项递推公式;基于上述2个公式,得到了计算BMPTA的递推算法;最后的数值例子说明了算法的有效性。The goal of this paper is to find a more simple recursive algorithm for a bivariate matrix-valued Padétype approximation(BMPTA).According to the bivariate homogeneous scalar orthogonal polynomial,a bivariate tensor product formal orthogonal polynomial(BTPFOP)is defined.Then it is generalized to matrix valued case to deduce a bivariate matrix tensor product formal orthogonal polynomials(BMTPFOP).In order to calculate their coefficients,three-term and nine-term recursive formulas of BMTPFOP are developed.By means of the two formulas,an algorithm for calculating BMPTA is presented.Finally,a numerical example is given to illustrate the validity of the algorithm.

关 键 词：二元矩阵值Padé型逼近(BMPTA) 张量积形式正交多项式 线性泛函 递推算法 

分 类 号：O241.5[理学—计算数学]