一类非奇异H-矩阵的细分迭代判别算法

Subdivision Iterative Discriminant Algorithm for a Class of Nonsingular H-Matrix

摘要: 非奇异H-矩阵是一类应用广泛的特殊矩阵，在许多领域都发挥着重要作用。本文就非奇异H-矩阵的判定问题，利用细分区间和迭代系数构造正对角矩阵因子，得到了一类非奇异H-矩阵的细分迭代判别新条件。在此基础上，又相应给出了一组含参数 的判定非奇异H-矩阵的细分迭代算法，并证明了其收敛性，推广与改进了近期的一些结果。最后，用数值算例说明了该算法的优越性。

Abstract: Nonsingular H-matrices are a kind of special matrices which are widely used in many fields. In this paper, we consider the problem of determining nonsingular H-matrices, construct a positive diago-nal matrix factor by using the subdivision interval and iterative coefficient, and obtain a new condi-tion for determining the subdivision iteration of a class of nonsingular H-matrices. On this basis, a set of subdivision iterative algorithms for determining nonsingular H-matrices with parameters are given, and their convergence is proved. Some recent results are extended and improved. Finally, numerical examples are used to illustrate the superiority of the algorithm.