γ-弱对角占优矩阵与严格γ-对角占优矩阵的放缩关系

A Scaling Relationship between γ-Weakly Diagonally Dominant Matrices and Strictly γ-Diagonally Dominant Matrices

摘要: 本文通过构造正对角矩阵D，证明γ-弱对角占优矩阵可经双边正对角放缩转化为严格γ-对角占优矩阵，从而得到其为非奇异H-矩阵。该结果建立了两类矩阵之间的放缩联系，为进一步研究γ-弱对角占优矩阵的性质提供了工具。进一步比较其与相关矩阵类的关系，并讨论参数γ的端点情形及可行集合。

Abstract: We construct a positive diagonal scaling matrix to show that every γ-weakly diagonally dominant matrix can be transformed by a two-sided diagonal scaling into a strictly γ-diagonally dominant matrix. Consequently, every γ-weakly diagonally dominant matrix is a nonsingular H-matrix. This result establishes a scaling relationship between the two classes of matrices. We also compare this class with related matrix classes and examine the endpoint cases and the admissible set of the parameter γ.