Ostrowski对角占优矩阵与非奇H-矩阵的简捷判定

Simple Criteria for Ostrowski Diagonally Dominant Matrices and Nonsingular H-matrix

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i∈N,|aii|≥Riα(A)S1i-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。

Ostrowski strictly diagonally dominant matrices play an important role in numerical analysis and matrix theory.Let A=（aij）∈Cn×n,if there exists α∈（0,1） which can make ｜aii｜≥Riα（A）S1i-α（A） be right for i∈N={1,2,…,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 indi-rectly.The result obtained improve the known corresponding results.At last some numerical examples are given for il-lustrating the advantages of the result.