Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair
Abstract
Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed 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 deflation and purgation techniques are developed to compute more than one GSVD components. Numerical experiments confirm the superiority of CPF-HJDGSVD and IF-HJDGSVD to the standard extraction based JDGSVD algorithm.
Cite
@article{arxiv.2201.02903,
title = {Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair},
author = {Jinzhi Huang and Zhongxiao Jia},
journal= {arXiv preprint arXiv:2201.02903},
year = {2022}
}
Comments
24 pages, 5 figures