Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914559961333760 |
|---|---|
| author | Huang, Jinzhi Jia, Zhongxiao |
| author_facet | Huang, Jinzhi Jia, Zhongxiao |
| contents | Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition (GSVD) components of a large regular matrix pair. The new methods are called refined cross product-free (RCPF), refined cross product-free harmonic (RCPF-harmonic) and refined inverse-free harmonic (RIF-harmonic) JDGSVD algorithms, abbreviated as RCPF-JDGSVD, RCPF-HJDGSVD and RIF-HJDGSVD, respectively. The new JDGSVD methods are more efficient than the corresponding standard and harmonic extraction-based JDSVD methods proposed previously by the authors, and can overcome the erratic behavior and intrinsic possible non-convergence of the latter ones. Numerical experiments illustrate that RCPF-JDGSVD performs better for the computation of extreme GSVD components while RCPF-HJDGSVD and RIF-HJDGSVD suit better for that of interior GSVD components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair Huang, Jinzhi Jia, Zhongxiao Numerical Analysis 65F15, 15A18, 65F10 Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition (GSVD) components of a large regular matrix pair. The new methods are called refined cross product-free (RCPF), refined cross product-free harmonic (RCPF-harmonic) and refined inverse-free harmonic (RIF-harmonic) JDGSVD algorithms, abbreviated as RCPF-JDGSVD, RCPF-HJDGSVD and RIF-HJDGSVD, respectively. The new JDGSVD methods are more efficient than the corresponding standard and harmonic extraction-based JDSVD methods proposed previously by the authors, and can overcome the erratic behavior and intrinsic possible non-convergence of the latter ones. Numerical experiments illustrate that RCPF-JDGSVD performs better for the computation of extreme GSVD components while RCPF-HJDGSVD and RIF-HJDGSVD suit better for that of interior GSVD components. |
| title | Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair |
| topic | Numerical Analysis 65F15, 15A18, 65F10 |
| url | https://arxiv.org/abs/2309.17266 |