广义严格α-链对角占优矩阵的细分迭代新判据

A New Criterion for Subdivision Iteration of Generalized Strictly α-Chain Diagonally Dominant Matrices

摘要: 广义严格对角占优矩阵在经济价值模型矩阵和反网络分析的系数矩阵以及最优化的线性互补等诸多领域中有着广泛的实际应用。本文依据α-链对角占优矩阵与广义严格对角占优矩阵的关系，通过不等式放缩技巧以及对矩阵行、列指标集进行细分，引入新的迭代因子，给出了一组判定广义严格α-链对角占优矩阵的细分迭代新判据。该判定条件推广和改进了已有的结果，并用数值算例说明了改进后的有效性。

Abstract: Generalized strictly diagonally dominant matrices are widely used in many fields such as economic value model matrix, inverse network analysis coefficient matrix and optimization of linear comple-mentarity. According to the relationship between α-chain diagonally dominant matrix and general-ized strictly diagonally dominant matrix, this paper presents a set of new criteria for subdivision it-eration of generalized strictly α-chain diagonally dominant matrix by means of inequality scaling and subdivision of matrix index set of row and column, and introduces new iteration factors. The results are generalized and improved by this criterion, and the effectiveness of the improved re-sults is illustrated by numerical examples.