Nekrasov矩阵逆的无穷范数改进的估计式

Improved estimations on the infinity norm of the inverse of Nekrasov matrices

摘要: 研究Nekrasov矩阵A的逆的无穷范数的上界.首先,通过引入参数μ和正对角矩阵Δ,构造了严格对角占优矩阵C(μ),Δ-1C(μ)和M矩阵(|D|-|L|)Δ;其次,利用||C-1(µ)Δ||∞,||(|D|-|L|)Δ-1||∞的上界,得到了||A-1||∞的一些新界,并从理论上证明了这些新界改进了相应文献的结果;最后通过5个例子,进一步分析比较了这些新界的优越性.

Abstract: In this paper,studies the upper bounds of the infinite norm of the inverse of Nekrasov matrices A.Firstly,by introducing the parameter μ and positive diagonal matrix Δ,it is constructed strictly diagonally dominant matrices C(μ),Δ-1C(μ) and M matrix (|D|-|L|)ΔSecondlly,using the upper bounds of ||C-1(µ)Δ||∞,||(|D|-|L|)Δ-1||∞,new bounds of ||A-1||∞ is got.It is proved in theory that these new bounds have improved the results of the corresponding literature.Finally,five examples are given to further analyze the superiority of the new bounds.