非奇异H-矩阵的一组细分迭代实用判定方法

A Set of Subdivision Iteration Practical Criteria for Nonsingular H-Matrix

摘要: 非奇异H-矩阵广泛应用于计算数学、控制理论、弹性力学以及神经网络系统等研究领域，但对非奇异H-矩阵的判定十分困难。本文研究了非奇异H-矩阵判定条件，通过对矩阵指标集按要求细分和构造递进的正对角矩阵元素，得到了非奇异H-矩阵的一组细分迭代实用判定方法，并给出证明，运用数值算例表明新判定条件优于已知结果。

Abstract: Nonsingular H-matrices have been widely used in many fields, such as computational mathematics, control theory, elastic mechanics, neural network system, etc. But it is very difficult to judge nonsingular H-matrix. In this paper, the criteria for nonsingular H-matrices are studied. By subdividing the matrix index set according to the requirements and constructing progressive diagonal matrix elements, a set of new subdividing iterative criteria for nonsingular H-matrices are obtained and proved. Finally, numerical examples show that the new decision condition is superior to the known results.