报告题目：Quantifying low rank approximations of third order symmetric tensors

报告人：胡胜龙

报告时间：2024年9月9日11:00-12:00

地点：数学与统计学院245会议室

报告摘要：In this talk, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approximation is attained if a control parameter is zero or quantified quasi-optimal low rank approximation is obtained if the control parameter is positive. This is based on a primal-dual method for computing a low rank approximation for a given tensor. The certification is derived from the global optimality of the primal and dual problems, and is characterized by easily checkable relations between the primal and the dual solutions together with another rank condition. The theory is verified theoretically for orthogonally decomposable tensors as well as numerically through examples in the general case.

个人简介：胡胜龙，国防科技大学教授，研究方向为张量计算的理论与算法及其应用。证明了张量最佳秩一逼近经典幂法和张量正交低秩逼近经典交替极分解法的线性收敛性，解决了Yousef Saad等提出的公开问题。部分研究成果发表在Math Program、Num Math、SIMAX、SIIMS、J Symb Comput等期刊。获得天津市数学会青年研究奖、Sci China-Math优秀论文奖、浙江省数学会研究成果奖等。主持国家自然科学基金和浙江省自然科学基金多项。