摘要: A popular and classical method for finding the best rank one approximation of a real tensor is the higher order power method (HOPM). It is known in the literature that the iterative sequence generated by HOPMconverges globally, while it can converge locally superlinearly, linearly or sublinearly. In this talk, we examine the local convergence rate of HOPM in solving the best rank one approximation problem of real tensors.We first show that the iterative sequence of HOPM always converges globally and provide an explicit eventual sublinear convergence rate. The sublinear convergence rate estimate is in terms of the dimension and the order of the underlying tensor space. Then, we examine the concept of nondegenerate singular vector tuples and show that, if the sequence of HOPM converges to a nondegenerate singular vector tuple, then the local convergence rate is R-linear. 
报告人简介：胡胜龙，天津大学数学学院副教授，计算数学、运筹学与控制论专业硕士研究生指导教师，研究方向为最优化计算理论与方法。2013年在香港理工大学应用数学系获得应用数学专业博士学位，其后在新加坡国立大学、芝加哥大学从事博士后研究工作。在《SIAM Journal on Matrix Analysis and Applications》等期刊发表论文30余篇，其中5篇ESI高被引用论文；研究工作获得过 《Science China：Mathematics》最佳论文奖和天津市数学会青年研究奖；先后主持国家自然科学基金面上项目、青年项目，天津大学自主创新基金等多个科研项目。