计算复对称张量US-特征对的拟牛顿法

US-eigenpairs of complex symmetric tensor has received much attention because of its background of quantum entanglement. The problem of finding US-eigenpairs can be regard as an unconstraint nonlinear optimization problem in complex number field. Optimization methods of this kind of problem often need a first- or second-order derivative of the objective function. However, such methods cannot be applied to real valued functions of complex variables because they are not necessarily analytic in their argument. In this paper, we present a quasi-Newton method for computing US-eigenpairs of a complex symmetric tensor, where we take advantage of Wirtinger Calculus to get the gradient of a real valued function defined on complex domain. The global and super-linear convergence of the method is verified. The numerical examples show the feasibility of the proposed method.