Sylvester-Kac矩阵的奇异值所在区间估计
The interval estimate on the singular values of Sylvester-Kac matrix
白明月 1秦建国1
作者信息
- 1. 郑州商学院通识教育中心,河南巩义 451200
- 折叠
摘要
利用n+1阶置换矩阵,将Sylvester-Kac矩阵化为一个主对角线上2个零块,斜对角线上2个非零块的四分块矩阵,再利用矩阵A的奇异值分解问题等价于矩阵AA*的特征值分解问题的关系,以及矩阵的Gerschgorin圆盘定理、Hermite矩阵、半正定矩阵的性质,获得了这个三对角矩阵的m个奇异值的区间估计,还获得了这个矩阵的谱半径的区间估计.
Abstract
Using n+1 order permutation matrix,the Sylvester-Kac matrix is transformed into a four blocks matrix with two zero blocks on the main diagonal and two non-zero blocks on the diagonal.Then,by utilizing the equivalent relationship between the eigenvalue decomposition problem of matrix A and the singular value decomposition problem of matrice AA*,as well as the Gerschgorin disk theorem of matrices,Hermite matrices,and properties of positive semidefinite matrices,interval estimates of m singular values of tridiagonal matrices are obtained.We also obtained an interval estimate of the spectral radi-us of this matrix.
关键词
Sylvester-Kac矩阵/奇异值/Gerschgorin圆盘/区间估计Key words
Sylvester-Kac matrix/Singular value/Gerschgorin disk/Interval estimate引用本文复制引用
出版年
2024
NETL
NSTL
维普
万方数据