A Simple Criterion for Nonsingular H -Matrix

Journal of Liaoning Petrochemical University ›› 2007, Vol. 27 ›› Issue (4): 92-94.

School of Science , Liaoning Univ ersity of Petroleum & Chemical Technology , Fushun Liaoning 113001 , P .R .China

Received:2007-06-20 Published:2007-12-20 Online:2017-07-05

非奇H -矩阵的一个简捷判别定理

崔　琦, 宋岱才^＊

辽宁石油化工大学理学院, 辽宁抚顺113001

作者简介:崔琦(1982 -), 女, 辽宁朝阳市, 在读硕士。
基金资助:
辽宁石油化工大学重点学科建设资助项目(K200409)

Abstract

Abstract:

　Let A=(a_{i j})∈ C^{n ×n}, if the reexists α∈(0, 1)which can make a_ii≥αRi(A)+(1 -α)S _i(A)be right for i ∈ N ,then A is called a α-diagonally dominant matrix .Ex tend the concept to generalized α-diagonally dominant matrix , and apply the concepts and proper ties of α-diagonally dominant matrices, irreducible α-diag onally dominant matrices and gene ralized strictly α-diag onally dominant matrices to obtain a simple criterion of a nonsingular H-matrix .These conclusions not only enrich and improve the theory of α-diagonally dominant matrices and nonsing ular H-matrix , but also lay a solid foundation for the research of computational mathematic , matrix theory , control theory , mathematical economics , etc .

Key words: 　Nonsing ular H-ma trix, , Irreducible matrix, , Generalized strictly α-diagonally dominant matrices

摘要： 　设A=(a_{i j})∈ C^n×n, 若存在α∈(0, 1), 使 i ∈ N , a_ii ≥αRi(A)+(1 -α)S _i(A), 则称A 为α-对角占优矩阵。首先推广α-对角占优矩阵的概念到广义α-对角占优矩阵;然后利用α-对角占优矩阵、不可约α-对角占优矩阵、广义严格α-对角占优矩阵等概念及性质, 给出了非奇异H-矩阵的一个简捷判别定理。不仅丰富和完善了α-对角占优矩阵与非奇异H-矩阵的理论, 更为计算数学、矩阵论、控制论、经济数学等相关领域的研究奠定了基础。

关键词: 非奇异H-矩阵, 　不可约矩阵, 　广义严格α-对角占优矩阵

CUI Qi,SONG Dai -cai . A Simple Criterion for Nonsingular H -Matrix[J]. Journal of Liaoning Petrochemical University, 2007, 27(4): 92-94.

崔　琦, 宋岱才. 非奇H -矩阵的一个简捷判别定理[J]. 辽宁石油化工大学学报, 2007, 27(4): 92-94.

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