【摘 要】
：
It is known that computing the largest(smallest) Z-eigenvalue of a symmetric ten-sor is equivalent to maximizing(minimizing) a homogeneous polynomial over t
【机 构】
：
BeijingUniversityofTechnology
【出 处】
：
2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
It is known that computing the largest(smallest) Z-eigenvalue of a symmetric ten-sor is equivalent to maximizing(minimizing) a homogeneous polynomial over the unit sphere. Based on such a reformulation, we shall propose a feasible trust-region method for calculating extreme Z-eigenvalues of symmetric tensors. One basic feature of the method is that the true Hessian, which is ready for polynomials, is utilized in the trust-region subproblem so that any cluster point of the iterations can be shown to satisfy the second-order necessary conditions. The other feature is that after a trial step dk is provided by solving the trust-region subproblem at the current point xk, the projection of xk+dk to the unit sphere, instead of the point xk+dk itself, is judged and if suc-cessful, is used for the next point. Global convergence and local quadratic convergence of the feasible trust-region method are established for the tensor Z-eigenvalue problem. The preliminary numerical results over several testing problems show that the feasible trust-region method is quite promising.
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