A Direct Method for Solving the Complex-Valued Triple Decomposition of Third-Order Tensors

报告摘要：A direct method is proposed first to compute a complex-valued triple decomposition of a third-order tensor. There are three assumptions: (i) The triple rank L of an I*J*K dimensional tensor satisfies L*L≤min(I, J, K); (ii) Two factor tensors of the triple decomposition are generic; (iii) The third factor tensor has linearly independent fibers. If I≈J≈K, the computational cost of the proposed direct method is about O(I^3L^2) flops in total. Further, a sufficient condition for the essential uniqueness of the triple decomposition of a tensor is established under these assumptions. Numerical experiments illustrate that the proposed direct method is at least ten times faster than alternating least squares and optimization-based iterative methods. Finally, we display applications of the proposed direct method with triple tensors in large-scale videos and stochastic partial differential equations.

报告人简介：陈艳男，博士，副教授，华南师范大学数学科学学院数据科学系主任。2013年在南京师范大学获得博士学位，陈博士已发表SCI论文30余篇，代表性论文发表于SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., Math. Comput.等国际刊物，参与撰写了一本专著《Tensor Eigenvalues and Their Applications》在Springer出版，完成国家自然科学基金2项，现主持国家自然科学基金1项，获得2020年度广东省自然科学奖二等奖。