非奇异H-矩阵的一组新判定法  

A Set of New Criteria for Nonsingular H-matrices

作　　者：陈茜 庹清[1] CHEN Xi;TUO Qing(College of Mathematics and Statistics,Jishou University,Jishou,Hunan 416000)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《工程数学学报》2020年第3期325-334,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11461027).

摘　　要：非奇异H-矩阵作为矩阵论中一类重要的特殊矩阵,在计算数学、统计学、弹性力学和神经网络等众多学科领域里都有广泛应用,因此对其判定条件的研究具有重大意义.本文探讨非奇异H-矩阵的直接判定问题,通过构造不同的正对角因子及新的参数方法,得到了一组简捷实用的非奇异H-矩阵判定新条件,改进和推广了近期一些相关成果,达到了扩充非奇异H-矩阵判定范围的目的.最后,用三个数值例子说明了新判定条件的优越性.Nonsingular H-matrices,as an essential special matrices in the area of matrix theory,has been widely used in many fields such as computational mathematics,statistics,elastic mechanics and neural networks.Therefore,it is important to study its determination criteria.This paper is focused on the direct criteria for nonsingular H-matrix.A set of simple and novel practical criteria for nonsingular H-matrices are obtained through forming different positive diagonal factors and new parameters.The obtained results improve some recent studies and expand the range of determination criteria for nonsingular H-matrices.Three numerical examples illustrate the advantages of the proposed new conditions.

关 键 词：对角占优矩阵 非奇异H-矩阵 不可约 非零元素链 

分 类 号：O151.21[理学—数学]