报告题目： An Efficient Algorithm for Computing the Approximate t-URV and its Applications
报 告 人：魏益民教授 复旦大学
报告时间：2023年6月4日 9:30-10:30
报告地点：数学学院第二学术报告厅
校内联系人：刁怀安 diao @ jlu.edu.cn
报告摘要：This talk is devoted to the definition and computation of the tensor complete orthogonal 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.
报告人简介：魏益民，复旦大学教授、博士生导师。主要从事矩阵/张量方面的理论和应用研究，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。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。
