应学院邀请,清华大学贾仲孝教授将来bat365官网作学术报告。
报告题目:The joint bidiagonalization method for large GSVD computationsin finite precision
报告摘要: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 theunderlying JBD process and establish relationships between it andtwo mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on the results of numerical analysis, we investigate the convergence of the approximate generalized singular values and vectors of {A,L}. The results show that, under some mild conditions,the semiorthogonality of Lanczos type vectors suffices to deliver approximate generalized singular values with the same accuracyas the full orthogonality does, meaning that it is only necessary to seek for efficient semiorthogonalization strategies for the JBD process. We establish a sharp bound for the residual norm of an approximate generalized singular value and corresponding approximate right generalized singular vectors, which can reliably estimate the residual norm without explicitly computing the approximate right generalizedsingular vectors before the convergence occurs.
报告时间:2023年10月29日下午2:30
报告地点:致勤楼C101
邀 请 人:缪树鑫 教授
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贾仲孝,清华大学二级教授,博士生导师,1994 年获得德国比勒菲尔德(Bielefeld)大学博士学位,第六届国际青年数值分析家--Leslie Fox奖获得者 (1993),国家“百千万人才工程” 入选者 (1999).现任北京数学会第十三届监事会监事长(2021.12—2026.12),曾任清华大学数学科学系学术委员会副主任 (2009—2021),2010 年度“何梁何利奖”数学力学专业组评委,中国工业与应用数学学会 (CSIAM) 第五、六届常务理事 (2008.9—2016.8),中国计算数学学会第七、八届常务理事(2006.10—2014.10),北京数学会第十一、十二届副理事长(2013.12—2021.12),中国工业与应用数学学会 (CSIAM) 监事会监事(2020.1—2021.10). 主要研究领域为数值线性代数和科学计算,在代数特征值问题、奇异值分解和广义奇异值分解问题、离散不适定问题和反问题的正则化理论和数值解法等领域做出了系统性的、有国际影响的重要研究成果,所提出的精化投影方法被公认为是求解大规模矩阵特征值问题和奇异值分解问题的三类投影方法之一.在Inverse Problems, Mathematics of Computation, Numerische Mathematik, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Optimization, SIAM Journal on Scientific Computing 等国际著名杂志上发表论文 70 余篇,研究工作被 41 个国家和地区的近 1000 名专家与研究人员在 19 部经典著作、专著和教材(国外)及 760 多篇论文中他引 1360多篇次(其中被国际学术界 584 篇论文引用 944篇次,包括被书目引用54篇次).引用的书目包括 Bai、Demmel、Dongarra、Ruhe、van der Vorst等五人编辑的 Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide (2000),Golub & van Loan的经典著作Matrix Computations第三、第四版 (1996,2013),Stewart的经典著作Matrix Algorithms II: Eigensystems (2001),Bjorck的专著 Numerical Methods in Matrix Computations (2015),van der Vorst的专著Computational Methods for Large Eigenvalue Problems(2002),Trefethen & Embree的专著Spectra and Pseudospectra, The Behavior of Nonnormal Matrices and Operators(2005),Meurant & Tebbens的专著 Krylov Methods for Nonsymmetric Linear Systems(2020),Quarteroni、Sacco & Saleri的专著 Numerical Mathematics (2000),Brezinski、Meurant & Revido-Zaglia的著作 A Journey Through the History of Numerical Linear Algebra (2022).
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