Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	张杨文博士，Department of Mathematical Sciences, Carnegie Mellon University, USA
Inviter:	龚伟副研究员
Title:	An answer to an open question in the incremental SVD
Time & Venue:	2022.10.28 09:00-10:00 腾讯会议：626-335-051
Abstract:	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 paper, 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. Numerical experiments are presented to illustrate the performance of our modification. 点击链接入会，或添加至会议列表： https://meeting.tencent.com/dm/Xxhz4e91HA1Y