非奇异H矩阵的一组细分迭代判定条件∗

摘要

Nonsingular H-matrix is a class of special matrices that often arise in science and engineering;so it is very important to know whether a matrix is a nonsingular H-matrix or not. In this paper, by the method of subdivided regions and selecting iterative coefficients, which subdivided the set of non-diagonally dominant rows, a set of subdivided and iterative criteria for nonsingular H-matrices are offered according to the relations of α-chain diagonally domi-nance matrices and nonsingular H-matrices, which extend and improve some related results. Effectiveness of such criteria is illustrated by numerical examples.%非奇异H矩阵是在科学和工程应用中经常遇到的一类特殊矩阵，研究其判定问题非常重要。本文根据α-链对角占优矩阵与非奇异H矩阵的关系，利用细分区间和构造迭代系数的思想，细分了矩阵的非对角占优行集合，给出了非奇异H矩阵的一组细分迭代判定条件，推广和改进了近期的一些结果。数值算例说明了该判定条件的有效性。