非奇H -矩阵的一个简捷判据

辽宁石油化工大学学报 ›› 2009, Vol. 29 ›› Issue (2): 78-80.

非奇H -矩阵的一个简捷判据

裴芳芳,宋岱才^* ,田秋菊

辽宁石油化工大学理学院,辽宁抚顺113001

收稿日期:2008-07-12 出版日期:2009-06-25 发布日期:2017-07-05
作者简介:裴芳芳(1964-),女,辽宁抚顺市,讲师
基金资助:
辽宁省教育厅高校科研项目(2004F100

A Simple Criterion for Nonsingular [WTHX]H[WTBZ]-Matrix

PEI Fang-fang, SONG Dai-cai*^*, TIAN Qiu-ju

School of Sciences, Liaoning University of Petroleum & Chemical Technology, Fushun Liaoning 113001,P.R.China

Received:2008-07-12 Published:2009-06-25 Online:2017-07-05

摘要/Abstract

摘要： 设A=(aij)∈Cn×n ,若存在α∈(0,1),使∀i∈N ={1,2,…,n},|aii|≥Rα
i (A )S1-α
i (A ),则称A 为
Ostrowski对角占优矩阵。首先推广Ostrowski对角占优矩阵的概念到广义Ostrowski对角占优矩阵;最后得到了
判别非奇异H -矩阵的一个判定方法。进一步丰富和完善了Ostrowski对角占优矩阵和非奇异H -矩阵的理论,为
计算数学、矩阵论、控制论、经济数学等相关领域的研究奠定了坚实的基础。

关键词: 非奇异H -矩阵 , 严格Ostrowski对角占优矩阵 , 广义严格Ostrowski对角占优矩阵

Abstract: Let [WTHX]A[WTBZ]=([WTBX]aij)∈Cn×n, if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A)  be right for i∈N={1,2,…,n}, then [WTHX]A[WTBZ] is called an Ostrowski diagonally dominant matrix. We extended the concept to generalized Ostrowski diagonally dominant matrix，and obtained a new criteria conditions for a matrix to be a nonsingular [WTHX]H[WTBZ]-matrix. The theory of Ostrowski diagonally dominant matrix and nonsingular [WTHX]H[WTBZ]-matrix was improved and completed. These conclusions provide strong basis for the research of relative fields, such as computational mathematics, matrix theory, control theory, mathematical economics, etc.

Key words: Nonsingular [WTHX]H[WTBZ]-matrix , Strictly Ostrowski diagonally dominant matrix , Generalized strictly Ostrowski diagonally dominant matrix

裴芳芳,宋岱才,田秋菊. 非奇H -矩阵的一个简捷判据[J]. 辽宁石油化工大学学报, 2009, 29(2): 78-80.

PEI Fang-fang, SONG Dai-cai*, TIAN Qiu-ju. A Simple Criterion for Nonsingular [WTHX]H[WTBZ]-Matrix[J]. Journal of Liaoning Petrochemical University, 2009, 29(2): 78-80.

[1]	宋岱才,赵晓颖. α-链严格对角占优矩阵的一个充要条件[J]. 辽宁石油化工大学学报, 2011, 31(3): 81-83.
[2]	王明刚,宋岱才,苗晨. α-链对角占优矩阵与非奇异H -矩阵的判别[J]. 辽宁石油化工大学学报, 2010, 30(2): 74-77.
[3]	崔　琦, 宋岱才＊. 非奇异H -矩阵的几个判别条件[J]. 辽宁石油化工大学学报, 2007, 27(2): 80-83.