Stable iterative refinement algorithms for solving linear systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913907504840704 |
|---|---|
| author | Wu, Chai Wah Squillante, Mark S. Kalantzis, Vasileios Horesh, Lior |
| author_facet | Wu, Chai Wah Squillante, Mark S. Kalantzis, Vasileios Horesh, Lior |
| contents | Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination, interest in IR has been revived because of its suitability for execution on fast low-precision hardware such as analog devices and graphics processing units. IR generally converges when the error associated with the solution method is small, but is known to diverge when this error is large. We propose and analyze a novel enhancement to the IR algorithm by adding a line search optimization step that guarantees the algorithm will not diverge. Numerical experiments verify our theoretical results and illustrate the effectiveness of our proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07865 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable iterative refinement algorithms for solving linear systems Wu, Chai Wah Squillante, Mark S. Kalantzis, Vasileios Horesh, Lior Numerical Analysis 65F10 G.1.3 Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination, interest in IR has been revived because of its suitability for execution on fast low-precision hardware such as analog devices and graphics processing units. IR generally converges when the error associated with the solution method is small, but is known to diverge when this error is large. We propose and analyze a novel enhancement to the IR algorithm by adding a line search optimization step that guarantees the algorithm will not diverge. Numerical experiments verify our theoretical results and illustrate the effectiveness of our proposed scheme. |
| title | Stable iterative refinement algorithms for solving linear systems |
| topic | Numerical Analysis 65F10 G.1.3 |
| url | https://arxiv.org/abs/2309.07865 |