广义张量特征值的包含域

Inclusion sets for the generalized tensor eigenvalue problem

张量特征值问题是张量代数理论研究的主要课题,在许多科学领域中都具有重要应用.通过进一步研究正则张量对{A,B}的特征值{α,β}的一些性质,给出了广义张量特征值的新的包含域,并证明了所得到的区域比已有结果中的区域更小.数值例子说明了结果的有效性.

Tensor eigenvalue problem is not only an important branch of tensor algebra, but also have application in many scientific fields.Some properties of the eigenvalue （α,β） of regular tensor pairs {A ,B} are further discussed, we give some inclusion sets for the generalized tensor eigenvalue problem and prove these inclusion sets are tighter than the known resuhs.A numerical experiment shows the efficiency of our new results.