Minimal residual rational Krylov subspace method for sequences of shifted linear systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917224228323328 |
|---|---|
| author | Daas, Hussam Al Palitta, Davide |
| author_facet | Daas, Hussam Al Palitta, Davide |
| contents | The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a lack of performing solvers. For instance, state-of-the-art procedures struggle to handle nonsymmetric problems where the shifts are complex numbers that do not come as conjugate pairs. We design a novel projection strategy based on the rational Krylov subspace equipped with a minimal residual condition. We also devise a novel pole selection procedure, tailored to our problem, providing poles for the rational Krylov basis construction that yield faster convergence than those computed by available general-purpose schemes. A panel of diverse numerical experiments shows that our novel approach performs better than state-of-the-art techniques, especially on the very challenging problems mentioned above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal residual rational Krylov subspace method for sequences of shifted linear systems Daas, Hussam Al Palitta, Davide Numerical Analysis The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a lack of performing solvers. For instance, state-of-the-art procedures struggle to handle nonsymmetric problems where the shifts are complex numbers that do not come as conjugate pairs. We design a novel projection strategy based on the rational Krylov subspace equipped with a minimal residual condition. We also devise a novel pole selection procedure, tailored to our problem, providing poles for the rational Krylov basis construction that yield faster convergence than those computed by available general-purpose schemes. A panel of diverse numerical experiments shows that our novel approach performs better than state-of-the-art techniques, especially on the very challenging problems mentioned above. |
| title | Minimal residual rational Krylov subspace method for sequences of shifted linear systems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.00267 |