An improved incremental SVD and its applications
报告题目：An improved incremental SVD and its applications
报告专家：张杨文（卡内基梅隆大学）
报告时间：2022年11月29日 10：00-11：00
报告地点：腾讯会议：527-873-387（无密码）
报告摘要：Incremental singular value decomposition (SVD) was proposed by Brand to efficiently compute the SVD of a matrix. The algorithm needs to compute thousands or millions of orthogonal matrices and to multiply them together. However, the multiplications may corrode the orthogonality. Hence many reorthogonalizations are needed in practice. In [Linear Algebra and its Applications 415 (2006) 20-30], Brand asked ``It is an open question how often this is necessary to guarantee a certain overall level of numerical precision; it does not change the overall complexity.'' In this talk, we answer this question, and the answer is we can avoid computing the large amount of those orthogonal matrices and hence the reorthogonalizations are not necessary by modifying his algorithm. We prove that the modification does not change the outcomes of the algorithm and provide an error analysis of our improved scheme. We have successfully applied this algorithm to snapshot-based POD model order reduction, time fractional PDEs and integro-differential equations to reduce their computational cost.
专家简介：密苏里科技大学博士，卡内基梅隆大学博士后，研究方向是优化控制及其数值计算. 在 SIAM Journal on Numerical Analysis、 Mathematics of Computation、 Numerical Mathematics等知名期刊上发表高水平论文近10篇。
邀请人：陈刚
![[lecture]张杨文-01.png](http://tianyuan.scu.edu.cn/upload/default/20221201/%5Blecture%5D%E5%BC%A0%E6%9D%A8%E6%96%87-01.png "[lecture]张杨文-01.png")