非奇异H -矩阵的简洁判据

辽宁石油化工大学学报 ›› 2005, Vol. 25 ›› Issue (3): 90-93.

非奇异H -矩阵的简洁判据

李　阳

辽宁石油化工大学理学院, 辽宁抚顺113001

收稿日期:2005-03-11 出版日期:2005-03-25 发布日期:2005-03-25
作者简介:李阳(1970 -), 男, 辽宁抚顺市, 讲师, 硕士

Simple Cri teria for Nonsingular H -Matrices

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

Received:2005-03-11 Published:2005-03-25 Online:2005-03-25

摘要/Abstract

摘要： 　利用矩阵的不可约、α-对角占优、α-双对角占优等概念, 一方面, 通过G -函数及矩阵有向图的方法给出非奇异H-矩阵的判别准则及相关性质;另一方面, 从若干角度分析了在不可约且对角占优条件下, 矩阵的特征值和奇异性问题。进一步丰富和完善了α-双对角占优与非奇异H -矩阵的理论, 为相关领域如数值分析、矩阵论、控制论、经济数学等提供了理论基础。

关键词: 　G -函数, 　不可约矩阵, 　α-双对角占优, 　H -矩阵

Abstract:

　 Some criterions and proper ties were presented for a matrix to be a no nsingular H -matrix using matrix' s concepts of irreducibility , α-diagonally dominance and α-doubly diagonally dominance and the method of G -function and matrix' s directed graph.In the meantime , the matrix' seigenwert and nonsingular problem was analyzed under the condition of irreducibility and diagonally dominance .The theory of α-doubly diagonally dominance and H -matrix was improved and enriched, which provided the theory' s base for relative fields, such as in numerical analysis, matrix theory , control theory and mathematical economics .

Key words: G -Function , 　Irreducible matrix , , α-Doubly diagonally dominance , 　H -Matrix ;

李　阳. 非奇异H -矩阵的简洁判据[J]. 辽宁石油化工大学学报, 2005, 25(3): 90-93.

LI Yang. Simple Cri teria for Nonsingular H -Matrices[J]. Journal of Liaoning Petrochemical University, 2005, 25(3): 90-93.

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