应用数学2025，Vol.38Issue(2)：384-393,10.
求解张量广义特征值的自适应信赖域方法
An Adaptive Trust-region Method for Solving Generalized Eigenvalues of Tensors
摘要
Abstract
Tensor eigenvalue problem is an important branch of matrix theory and has a wide range of applications in many scientific fields.A non-monotonic adaptive trust-region method for solving the generalized eigenvalues of symmetric tensors is proposed in this paper.In order to get the maximum generalized eigenvalue of the symmetric tensor,the algorithm applies the projection method in the iteration step to ensure that the iteration points are feasible.Besides,the algorithm combines the adaptive technique to automatically update the radius of the trust region.Meanwhile,the global convergence of the algorithm is proved and the optimal solution satisfies the second-order necessary condition.Numerical experiments show that the algorithm is feasible and effective.关键词
对称张量/广义特征值/信赖域算法/自适应/全局收敛性Key words
Symmetric tensor/Generalized eigenvalue/Trust-region/Adaptive technology/Global convergence分类
数理科学引用本文复制引用
段复建,张义,李向利..求解张量广义特征值的自适应信赖域方法[J].应用数学,2025,38(2):384-393,10.基金项目
国家自然科学基金(11961010) （11961010）
