学术报告

魏益民

（复旦大学）

报告时间：15:00-16:00，2021-5-17（星期一）

报告地点：北航沙河校区主楼E404

报告题目：Generalized Tensor Function via the Tensor Singular Value Decomposition based on the Tensor-Tensor Decomposition

报告摘要：In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) based on the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors, from which the projection operators and Moore-Penrose inverse of tensors are obtained. We establish the Cauchy integral formula for tensors by using the partial isometry tensors and apply it into the solution of tensor equations. Then we establish the generalized tensor power and the Taylor expansion of tensors. Explicit generalized tensor functions are listed. We define the tensor bilinear and sesquilinear forms and propose theorems on structures preserved by generalized tensor functions. For complex tensors, we established an isomorphism between complex tensors and real tensors. In the last part of our paper, we find that the block circulant operator establishes an isomorphism between tensors and matrices. This isomorphism is used to prove the F-stochastic structure is invariant under generalized tensor functions. The concept of invariant tensor cones is raised.

报告人简介： 魏益民，复旦大学教授、博士生导师，获上海市自然科学三等奖，为上海市高校优秀青年教师和上海市“曙光”学者称号获得者。主要从事矩阵/张量方面的理论和应用研究，在《SIAM J.Matrix Anal. Appl.》《SIAM J. Numer. Anal.》《SIAM J. Sci. Comput.》《J. Sci. Comput.》等权威学术期刊发表论文一百余篇，出版中英文专著3部，英文版教材1部。多次主持国家自然科学基金面上项目、教育部博士点基金项目和973子课题等项目，为《Comput. Appl.Math.》、《J. Appl. Math. Comput.》和《高校计算数学学报》编委。

邀请人：崔春风