具不变主对角线元矩阵新的特征值包含集  

A new eigenvalue inclusion set of matrices with invariant main diagonal elements

作　　者：李静 李耀堂[1] Li Jing;Li Yaotang(College of Mathematics and Statistics,Yunnan University,Kunming 650500,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《纯粹数学与应用数学》2018年第2期195-204,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11361074)

摘　　要：利用S-SDD矩阵的非奇异性给出具不变主对角线元矩阵非奇异的一个充分条件,并由此得到了具不变主对角线元矩阵的一个新的特征值包含集,改进了相关文献的结果.最后把该结果应用到Toeplitz矩阵,得到Toeplitz矩阵的一个新的特征值包含集.文中数值例子表明在某些情况下该结果也改进了几个已有结果.A sufficient condition for the nonsingularity of matrices with invariant main diagonal elements is given by using the theory of nonsingularity of S-SDD matrices, a new eigenvalue inclusion set of matrices with invariant main diagonal elements is obtained, which improves the results of relevant literature. Finally, the result is applied to Toeplitz matrices and a new eigenvalue inclusion set of Toeplitz matrices is obtained. The numerical examples in this paper show that the result also improves several existing results in some cases.

关 键 词：S-SDD矩阵 具不变主对角线元矩阵 TOEPLITZ矩阵 非奇异 特征值包含集 

分 类 号：O151.21[理学—数学]