﻿ p-范数双严格对角占优矩阵与新的矩阵特征值包含区域 p-Norm DSDD Matrices and New Eigenvalue Localization Region

Vol.06 No.03(2017), Article ID:20792,9 pages
10.12677/AAM.2017.63042

p-Norm DSDD Matrices and New Eigenvalue Localization Region

Qiaojuan Zheng, Yaotang Li*

School of Mathematics and Statistics, Yunnan University, Kunming Yunnan

*通讯作者。

Received: May 6th, 2017; accepted: May 24th, 2017; published: May 27th, 2017

ABSTRACT

A new class of nonsingular matrices, p-norm double strictly diagonally dominant matrices, (shorthand for p-norm DSDD matrices), is presented, and it is used to get a new eigenvalue inclusion region. A numerical example is given to show that the eigenvalue inclusion in this paper, in some cases, is in the famous Brauer-Cassini oval area.

Keywords:p-Norm DSDD Matrix, Nonsingular H-Matrix, Eigenvalue Localization

p-范数双严格对角占优矩阵与新的矩阵特征值包含区域

1. 引言

， (1.1)

(1.2)

2. p-范数DSDD矩阵

。 (2.1)

，(2.2)

。 (2.3)

。(2.4)

。若，记，则。令

,

。 (2.5)

， (2.6)

(2) 当时，为¥-范数DSDD矩阵当且仅当

， (2.7)

(3) 当时，为2-范数DSDD矩阵当且仅当

， (2.8)

(4) 由定理6可知，1-范数DSDD矩阵(即为DSDD矩阵)，¥-范数DSDD矩阵，2-范数DSDD矩阵都为非奇异矩阵。

3. p-范数DSDD矩阵与非奇异H-矩阵的关系

， (3.1)

(3.2)

， (3.3)

。 (3.4)

4. 矩阵的特征值包含集

， (4.1)

。 (4.3)

。 (4.3)

，由知，，故为奇异矩阵。由

,

,

Figure 1. The eigenvalue inclusion region of A for Example 2

5. 数值例子

p-Norm DSDD Matrices and New Eigenvalue Localization Region[J]. 应用数学进展, 2017, 06(03): 367-375. http://dx.doi.org/10.12677/AAM.2017.63042

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