不可约M-矩阵的一种判别法

An Algorithm for Identifying Irreducible M-matrices

M-矩阵是一类很重要的特殊矩阵,在实际中有着广泛的应用.如何判别一个给定的矩阵是否为M-矩阵则是一个重要的问题.虽然至今已有不少文献提出了各种不同的判别法,但是大多并不实用,更难以在计算机上实现.为此,提出了一个判定不可约M-矩阵的算法,相比之前的方法更加实用简洁,而且可以很容易地在计算机上实现.并且给出了相应的理论分析,最后数值算例也展示了该算法的有效性和优越性.

M-matrices are a very important class of special matrices and have many applications in numerical analysis. In practice, how to determine whether a given matrix is an M-matrix is an important issue. Although a variety of discriminate methods have been proposed,most of them are not practical and hardly can be implemented on the computer. In this paper,we present an algorithm for determining whether or not an irreducible matrix to be an M-matrix. Some theoretical analyses for the algorithm are given, and numerical examples are offered to show that the algorithm is indeed effective and efficient.