广义对角占优矩阵的新判据

New Criteria for Generalized Diagonally Dominant Matrices

广义对角占优矩阵在矩阵分析和数值代数的研究中具有重要作用,但在实用中要判别广义对角占优矩阵是十分困难的。本文通过对矩阵行标作划分的方法,给出了判定广义对角占优矩阵的一组新条件,改进了近期的相关结果,相应数值例子说明了结果的有效性。

Generalized diagonally dominant matrices play a very important role in the research of matrix analysis and numerical algebra. But it is difficult to determine a generalized diagonally dominant matrix in practice. In this paper, some sufficient conditions for generalized diagonally dominant matrices were obtained according to the partition of the row indices, some related results were improved. Advantages of results obtained are illustrated by a numerical example.