非负矩阵Hadamard积最大特征值上界的估计

Method of Estimating for the Greatest Eigenvalue of the Hadamard Product of Two Nonnegative Matrices

矩阵特征值的估算是矩阵理论的的重要问题之一.通过矩阵特征值在椭圆形区域上估计的方法,研究了两个非负矩阵的Hadamard积最大特征值上界估计问题.在任意给出一组正向量组的前提下,证明了其最大特征值满足的新估计式.通过算例,发现该估计式比现有估计式更为精确.并且这些新估计式的计算只依赖于矩阵的元素和矩阵的F范数,容易计算.

Matrices eigenvalues estimation is one of the important problems of matrices theory.Through the estimation method of matrix eigenvalues on the elliptic region,it is studied that the upper bounds of largest eigenvalue of Hadamard product of two nonnegative matrices.According any of the positive vectors given,it is proved that its largest eigenvalues meet the another form.Through numerical example,it is found that the form is verified for higher accuracy.And the form of calculation only depends on the matrices elements and matrices Fnorm.It is easy to calculate.