A complete solution to Saad’s open problem

报告摘要：In 2009, von Neumann prize-winner Yousef Saad proposed the open problem on characterizing the convergence rate of the classical alternating polar decomposition method for low rank orthogonal tensor approximation problem. Actually, this problem was initiated by Gene Golub in 2001 for the rank one case, and received considerable study in the past twenty years. In 2015, Wolfgang Hackbusch presented concrete examples showing that the convergence rate may be sublinear, linear and superlinear. In this talk, we show that for a generic tensor, the algorithm converges linearly without any further assumption.

报告人简介：杭州电子科技大学理学院教授，博士研究生导师。先后毕业于天津大学和香港理工大学。中国青年科技工作者协会成员、中国运筹学会理事、浙江省数学会理事。研究方向为张量计算的理论与算法及其应用。先后解决了Gene Golub和Yousef Saad等提出的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率等公开问题。部分研究成果发表在Math Prog、Num Math、SIMAX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。先后主持国家自然科学基金和浙江省自然科学基金多项。