非奇H-矩阵的一个简捷判据

A Simple Criterion for Nonsingular H-Matrix

设A=(aij)∈Cn×n,若存在α∈(0,1),使i∈N={1,2,…,n},|aii|≥Riα(A)Si1-α(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。

Let A=（aij）∈C^n×n, if there exists α∈（0,1） which can make ｜aii≥Ri^α（A）Si^1-α（A） be right for arbitary i∈N={1,2,…,n}, then A 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 H-matrix. The theory of Ostrowski diagonally dominant matrix and nonsingular H-matrix was improved and completed. These conclusions provide strong basis for the research of relative fields, such as computational mathematics, matrix theory, control theory, mathematieal economies, etc.