矩阵展形的一些新的上界

J4 ›› 2012, Vol. 47 ›› Issue (10): 54-58.

矩阵展形的一些新的上界

廖文诗,伍俊良

重庆大学数学与统计学院, 重庆 401331

收稿日期:2011-10-12 出版日期:2012-11-20 发布日期:2012-10-26
作者简介:廖文诗(1987- ), 女, 硕士, 研究方向为数值代数. Email:liaowenshi@gmail.com

Some new upper bounds of the spread of a matrix

LIAO Wen-shi, WU Jun-liang

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2011-10-12 Online:2012-11-20 Published:2012-10-26

摘要/Abstract

摘要：

讨论了关于矩阵的特征值的实部和虚部的特性,并利用这些特性得到矩阵的展形更为精确的上界;其次,证明任意矩阵的所有特征值都能用一个椭圆区域来界定,从另一方面得到矩阵的展形上界;最后,给出数值算例进行比较。

关键词: 特征值;矩阵的展形;Euclidean范数;椭圆区域

Abstract:

Some characteristics about the real and imaginary part of matrix eigenvalues are discussed, and obtains some sharper upper bounds of the spread of a matrix. All the eigenvalues of an arbitrarily given matrix are located in elliptic regions is proved and give another upper bounds of the spread of a matrix. An example illustrates the effectiveness of our results.

Key words: eigenvalue; the spread of a matrix; Euclidean norm; elliptic region

廖文诗,伍俊良. 矩阵展形的一些新的上界[J]. J4, 2012, 47(10): 54-58.

LIAO Wen-shi, WU Jun-liang. Some new upper bounds of the spread of a matrix[J]. J4, 2012, 47(10): 54-58.

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