Ostrowski对角占优矩阵与非奇H-矩阵的简捷判定

摘要

Ostrowski strictly diagonally dominant matrices play an important role in numerical analysis and matrix theory. Let A=(aij)∈Cn×n, if there exists a∈(0,l) which can make |all|≥R1a(A)S11-a(A)be right for (V)I∈N={l, 2, …, n) , then A is called a Ostrowski diagonally dominant matrix. In this paper, we give an equivalent condition for Ostrowski strictly diagonally dominant matrices and obtain a necessary condition for a matrix to be a nonsingular H-matrix indirectly. The result obtained improve the known corresponding results. At last some numerical examples are given for illustrating the advantages of the result.%Ostrowski对角占优矩阵在数值分析和矩阵理论的研究中非常重要.设A=(aij)∈Cn×n,若存在α∈(0,1),使(V)i∈N,|ai|≥Riα(AS1i-α(A),则称A为Ostrowski对角占优矩阵.本文利用这一概念给出了Ostrowski对角占优矩阵的一个充要条件,从而间接地得到了判别非奇异H-矩阵的必要条件,改进和推广了已有的结论.最后用数值例子说明了所给结果的优越性.