广义α-双对角占优矩阵的判定

Criteria of Generalized α-doubly Diagonally Dominant Matrix

设A=(aij)∈Cn×n,若存在α∈(0,1),使i≠j(i,j∈N={1,2,…,n}),有aiiajj>[αRi(A)+(1-α)Si(A)]×[αRj(A)+(1-α)Sj(A)],则称A为严格α-双对角占优矩阵。首先推广严格α-双对角占优矩阵的概念到广义α-双对角占优矩阵;然后得到了判别广义α-双对角占优矩阵的一个充分必要条件,改进和推广了已有的结论,进一步丰富和完善了α-双对角占优矩阵的理论。最后举例说明了所给结果的优越性。

Let A=（aij）∈C^n×n,if there exists α∈（0,1）,which can make aiiajj[αRi（A）＋（1-α）Si×（A）][αRj（A）＋（1-α）Sj（A）]be right for i≠j（i,j∈N={1,2,…,n}）,then A is called a α-doubly diagonal strictly dominant matrix.First,the concept is extend to generalized α-doubly diagonally strictly dominant matrix,and obtain a new necessary and sufficient condition for A=（aij）∈Cn×n to be generalized α-doubly diagonally dominant matrix,improving and generalizing the related results.This result enriches and improves the theory of α-doubly diagonally dominant matrix.Finally,two numerical examples are given for illustrating advantage of results.