广义严格对角占优矩阵与非奇M-矩阵的判定

根据不可约弱对角占优矩阵元素的特点,将复矩阵A的行元素划分为三个部分,并对每一部分元素的模求和得到三个值αi,βi,γi,通过比较由这三个值所构造出的hik和Hjk的大小给出了判断不可约矩阵A是广义严格对角占优矩阵的判别条件,并将其结果应用到非奇M 矩阵的判定上,推广了高益明等的主要结果·

Criteria for Strictly Generalized and Diagonally Dominant Matrices and Nonsingular M-Matrices

Based on the other earlier works as shown in reference and the characteristics of the elements of an irreducibly and weakly diagonally dominant matrix, the row elements of the complex matrix A are divided into three parts, then the module of the elements of each and every part are summed up to obtain the three values αi, βi, and γi. Comparing the magnitudes of the values of hik and Hjk, which are both constructed by αi, βi, and γi, the sufficient conditions are given to judge whether an irreducibly and weakly diagonally dominant matrix is a generalized strictly diagonally dominant matrix or not. Then, the results can be applied to the judgment of a nonsingular M-matrix so as to extend the main conclusions as indicated by other earlier works.