特殊矩阵Hadamard积的谱半径的界

Bounds on the Spectral Radius of Hadamard Products of Special Matrices

【目的】对非负矩阵A和M-矩阵B的逆矩阵的Hadamard积谱半径的上界作进一步的估计。【方法】利用特征值包含域定理和optimally scaled矩阵,通过推导出的两个关于B-1的元素βji和βii间的不等式,使得谱半径上界估计更接近真值。【结果】得到了两个新的估计式,并给出了证明。【结论】数值实验表明新估计式优于现有的估计式。

[Purposes]To further estimate the upper bound of the Hadamard product spectral radius of a non-negative matrix A and the inverse matrix of M-matrix B.[Methods] By using the existence theorem of matrix eigenvalues and optimally scaled matrix,through the derivation of two inequalities between the elements βji and βii of the inverse of the matrix B,the upper bound of the spectral radius is estimated to be closer to the true value.[Findings] Two new estimation formulas are obtained,and proofs are given.[Conclusions]Numerical experiments show that the new estimation formulas is better than the existing estimation formulas.