主讲人简介：

魏益民，复旦大学数学科学院教授、博士生导师。主要从事矩阵/张量方面的理论和应用研究，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。担任国际学术期刊Computational and Applied Mathematics，Journal of Applied Mathematics and Computing，FILOMAT和Communications in Mathematical Research，《高校计算数学学报》的编委。在国际学术期刊Math. Comput.，SIAM J. Sci. Comput.，SIAM J. Numer Anal.，SIAM J. Matrix Anal. Appl.，J. Sci. Comput.，IEEE Trans. Auto. Control，IEEE Trans. Neural Network Learn. System，Neurocomputing和Neural Computation 等发表论文150余篇；在EDP Science，Elsevier，Springer，World Scientific和科学出版社等出版英语专著5本。5次入选爱思唯尔“中国高被引学者”榜单。Google学术引用8900余次，H指数48。

内容摘要：

This talk is devoted to the definition and computation of the tensor complete orthgonal decomposition of a third-order tensor called t-URV decompositions. We first give the definition for the t-URV decomposition of a third-order tensor and derive a deterministic algorithm for computing the t-URV. We then present a randomized algorithm to approximate t-URV, named compressed randomized t-URV (cort-URV). Note that t-URV and cort-URV are extensions of URV and compressed randomized URV from the matrix case to the tensor case, respectively. We also establish the deterministic and average-case error bounds for this algorithm. Finally, we illustrate the effectiveness of the proposed algorithm via several numerical examples, and we apply cort-URV to compress the data tensors from some image and video databases.

主持人：秦玉明