Seminars on Numerical Algebra, Optimization and Data Sciences：Nonlinear power-like iteration by polar decomposition and its application to tensor approximation

：董波（大连理工大学）
：2022-11-25 15:00
：腾讯会议ID：950-144-778（无密码）

报告人：董波（大连理工大学）

时  间：11月25日下午15:00-16:30

地  点：腾讯会议ID：950-144-778（无密码）

内容摘要:

Low rank tensor approximation is an important subject with a wide range of appli- cations. Most prevailing techniques for computing the low rank approximation in the Tucker format often first assemble relevant factors into matrices and then update by turns one factor matrix at a time. In order to improve two factor matrices simultaneously, a special system of nonlinear matrix equations over a certain product Stiefel manifold must be resolved at every update. The solution to the system consists of orbit varieties invariant under the orthogonal group action, which thus imposes challenges on its analysis. In this talk, we will propose a scheme similar to the power method for subspace iterations except that the polar decomposition is used as the normalization process and that the iteration can be applied to both the orbits and the cross-sections. The notion of quotient manifold is employed to factor out the effect of orbital solutions. The dynamics of the iteration is completely characterized. An isometric isomorphism between the tangent spaces of two properly identified Riemannian manifolds is established to lend a hand to the proof of convergence.

个人简介：

董波，大连理工大学数学科学学院教授、博士生导师。主要的研究工作包括非线性方程组全部解问题、矩阵特征值问题、张量分析等，在SINUM、SIMAX、Math. Comput.、Numer. Math、J. Sci. Comput. 等计算数学著名期刊上发表论文20余篇。

 

联系人：白正简