報 告 人：魏益民 教授
報告題目：Efficient algorithms for Tucker decomposition via approximate matrix multiplication
報告時間：2025年5月8日（周四）下午15:30—16:30
報告地點：靜遠樓1506學術報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
魏益民，男，教授，博士生導師。復旦大學數學科學學院教授，從事矩陣計算的理論和應用研究二十余年。1997年在復旦大學數學研究所獲得理學博士學位，是上海市應用數學重點實驗室的研究人員，曾獲得上海市高校優秀青年教師和上海市“曙光”學者稱號；獲得上海市自然科學二等獎、三等獎各一項。在國際學術期刊《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》 等發表論文150余篇; 在EDP Science, Elsevier, Springer, World Scientific和科學出版社等出版英語專著5本。10次入選愛思唯爾“中國高被引學者”榜單。Google學術引用12000余次，H 指數 55。魏益民曾主持國家自然科學基金、教育部博士點基金項目和973項目的子課題；目前正主持國家自然科學基金項目，擔任國際學術期刊《Computational and Applied Mathematics》、《Journal of Applied Mathematics and Computing》、《FILOMAT》、《Communications in Mathematical Research》和《高校計算數學學報》的編委。
報告摘要：
This talk develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated high-order singular value decomposition (T-HOSVD) and the sequentially T-HOSVD (ST-HOSVD), which are two common algorithms for approximating Tucker decomposition. To reduce the complexities of these two algorithms, fast and efficient algorithms are designed by combining two algorithms and approximate matrix multiplication. The theoretical results are also achieved based on the bounds of singular values of standard Gaussian matrices and the theoretical results for approximate matrix multiplication. Finally, the efficiency of these algorithms are illustrated via some test tensors from synthetic and real datasets.