報(bào) 告 人：魏益民 教授
報(bào)告題目：Efficient algorithms for Tucker decomposition via approximate matrix multiplication
報(bào)告時(shí)間：2025年5月8日（周四）下午15:30—16:30
報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
魏益民，男，教授，博士生導(dǎo)師。復(fù)旦大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，從事矩陣計(jì)算的理論和應(yīng)用研究二十余年。1997年在復(fù)旦大學(xué)數(shù)學(xué)研究所獲得理學(xué)博士學(xué)位，是上海市應(yīng)用數(shù)學(xué)重點(diǎn)實(shí)驗(yàn)室的研究人員，曾獲得上海市高校優(yōu)秀青年教師和上海市“曙光”學(xué)者稱(chēng)號(hào)；獲得上海市自然科學(xué)二等獎(jiǎng)、三等獎(jiǎng)各一項(xiàng)。在國(guó)際學(xué)術(shù)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(fā)表論文150余篇; 在EDP Science, Elsevier, Springer, World Scientific和科學(xué)出版社等出版英語(yǔ)專(zhuān)著5本。10次入選愛(ài)思唯爾“中國(guó)高被引學(xué)者”榜單。Google學(xué)術(shù)引用12000余次，H 指數(shù) 55。魏益民曾主持國(guó)家自然科學(xué)基金、教育部博士點(diǎn)基金項(xiàng)目和973項(xiàng)目的子課題；目前正主持國(guó)家自然科學(xué)基金項(xiàng)目，擔(dān)任國(guó)際學(xué)術(shù)期刊《Computational and Applied Mathematics》、《Journal of Applied Mathematics and Computing》、《FILOMAT》、《Communications in Mathematical Research》和《高校計(jì)算數(shù)學(xué)學(xué)報(bào)》的編委。
報(bào)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.