α-链严格对角占优矩阵的一个充要条件

A Necessary and Sufficient Condition of α-Chain Strictly Diagonally Dominant Matrices

设A=(aij)∈Cn×n,若存在α∈(0,1),使i∈N,|aii|≥Riα(A)Si1-α(A),则称A为α-链对角占优矩阵。利用这一概念给出了α-链严格对角占优矩阵的一个充要条件,从而间接地得到了判别非奇异H-矩阵的必要条件,改进和推广了已有的结论。最后用数值例子说明了所给结果的优越性。

Abstract .. Let A=（aij）∈C^n×n , if there exists a∈（0,1） which can make Ai∈N,｜AII｜≥Ri^a（A）Si^1-a（A） be right for Ai ∈ N= { 1,2,… n}, then A is called an α- chain diagonally dominant matrix. It gave an equivalent condition for chain strictly diagonally dominant matrices, and obtains a necessary condition for a matrix to be a nonsingular H-- matrix indirectly. The result obtained improves the known corresponding results. At last, some numerical examples are given for illustrating advantages of the result.