非奇异M-矩阵Hadamard积的最小特征值的改进估计式

Some New Estimations for the Minimum Eigenvalue of Hadamard Product of M-Matrices

根据矩阵的Hadamard积和最小特征值的定义以及M-矩阵的性质特点,对不同情况下最小特征值τ(BA-1)和τ(AA-1)做了进一步研究(A,B为非奇异M-矩阵),给出了最小特征值τ(BA-1)和τ(AA-1)2个改进估计式,并从理论上证明了新估计式在一定条件下改进了现有文献的结果。数值算例结果也验证了新估计式改进了Fiedler和Markham的猜想以及现有文献的结果,提高了现有估计式的估计精确度。

According to the definition of the Hadamard product and the minimum eigenvalue of a matrix,and the properties of M-Matrices,some new lower bounds ofτ(BA-1)andτ(AA-1)are further researched,two improved estimations are given respectively.It is proved that the new estimating formule improve the results of some cases;numerical example show that these formulas are more accurate than those ot several existing results.