r-H-循环矩阵的性质及其逆的多项式算法  

Properties for r-H-circulant matrices and polynomial algorithm of their inverse

作　　者：雷林 李笑丽 何承源 LEI Lin;LI Xiao-li;HE Cheng-yuan(School of Science,Xihua University,Chengdu 610039,Sichuan,China)

机构地区：[1]西华大学理学院,四川成都610039

出　　处：《山东大学学报（理学版）》2021年第4期102-110,共9页Journal of Shandong University(Natural Science)

基　　金：四川省应用基础研究计划资助项目(2013JY0178)。

摘　　要：提出了r-H-循环矩阵的概念,并得到r-H-循环矩阵的五个等价条件和两个非奇异性的充要条件。此外,利用r-H循环矩阵与多项式之间的关系以及r-H循环矩阵非奇异性和奇异性的充要条件,给出r-H-循环矩阵逆的多项式算法。最后,根据r-H-循环矩阵的结构特点,给出了一些数值例子。The concept of r-H-circulant matrices is proposed,and five equivalent conditions and two necessary and sufficient conditions for nonsingularity of r-H-circulant matrices are gained.Furthermore,utilizing the relationship between the r-H-circulant matrices and polynomial and the sufficient and necessary conditions for nonsingular and singular of r-H-circulant matrices,a polynomial algorithm for the inverse of the r-H-circulant matrices is given.Finally,a number of examples according to the structural characteristics of r-H-circulant matrices is provided.

关 键 词：r-H-循环矩阵 非奇异性 逆 自反广义逆 多项式算法 

分 类 号：O241.6[理学—计算数学]