报告人：贾仲孝 教授（清华大学）

报告时间：2021年11月24日，10:00-11:00

报告地点：腾讯会议 ID：141 770 164

摘要： The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair (A,L). We make a numerical analysis of the underlying JBD process and establish relationships between the JBD process and two mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on the results of numerical analysis, we investigate the convergence and accuracy of the approximate generalized singular values and vectors of (A,L). The results show that the semiorthogonality of Lanczos type vectors suffices to deliver approximate generalized singular values with the same accuracy as the full orthogonality does, meaning that it is only necessary to seek for efficient semiorthogonalization strategies for the JBD process. We also establish a sharp bound for the residual norm of an approximate generalized singular value and corresponding approximate generalized singular vectors, which can reliably estimate the residual norm without explicitly computing the approximate right generalized singular vectors before the convergence occurs.

报告人简介：贾仲孝（清华大学二级教授）博士毕业于德国Bielefeld大学，主要研究方向为数值线性代数，科学计算；特别是在大规模矩阵（广义）特征值问题和(广义)奇异值分解问题中，提出了精化Rayleigh-Ritz方法，成果获得英国数学及其应用学会(IMA)颁发的“第六届国际青年数值分析家奖--Leslie Fox奖”，两篇论文被美国科学信息所（ISI）授予高影响力论文（High Impact Papers）的“经典引文(Citation Classic Award)”。入选 “国家百千万人工程”，清华大学“百人计划”特聘教授等。曾任中国工业与应用数学学会(CSIAM)常务理事，中国计算数学学会常务理事，北京数学会副理事长，清华大学数学科学系学术委员会副主任等。

邀请人：张雷洪、黄金枝