Applied Mathematics Seminar-Two harmonic Jacobi–Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair

Details

• Time: 03:00 p.m.-04:00 p.m.
• Date: March 24, 2023
• Venue: MA305
• Speaker: Dr. Jinzhi Huang (Soochow University)
• Topic: Two harmonic Jacobi–Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair

Abstract

In this talk, two harmonic extraction based Jacobi–Davidson (JD) type algorithms are introduced to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair. They are called cross product–free (CPF) and inverse-free (IF) harmonic JDGSVD algorithms, abbreviated as CPF-HJDGSVD and IF-HJDGSVD, respectively. Compared with the standard extraction based JDGSVD algorithm, the harmonic extraction based algorithms converge more regularly and suit better for computing GSVD components corresponding to interior generalized singular values. Thick-restart CPF-HJDGSVD and IF-HJDGSVD algorithms with some deflflation and purgation techniques are developed to compute more than one GSVD components. Numerical experiments confifirm the superiority of CPF-HJDGSVD and IF-HJDGSVD to the standard extraction based JDGSVD algorithm.

Speake

Dr. Huang is currently an assistant professor in Soochow University. She completed her undergraduate study in Tsinghua University and received Ph.D. from Tsinghua University. Her research area is mainly in numerical linear algebra and scientifific computing. She has several publications in the renowned journals like SIAM journal of scientifific computing, Journal of scientifific computing and Numerical Algorithms.