Solving ill-conditioned linear algebraic systems using methods that improve conditioning
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911869997940736 |
|---|---|
| author | Leonov, A. S. |
| author_facet | Leonov, A. S. |
| contents | We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it possible to improve the conditionality of the SLAE matrix and, as a result, obtain an approximate solution that is stable to perturbations of the right hand side with higher accuracy than using other methods. The approach is implemented by an algorithm that uses so-called minimal pseudoinverse matrices. The results of numerical experiments are presented that confirm the theoretical provisions of the article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving ill-conditioned linear algebraic systems using methods that improve conditioning Leonov, A. S. Numerical Analysis 15A09, 15A10, 65F22, 15A29 We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it possible to improve the conditionality of the SLAE matrix and, as a result, obtain an approximate solution that is stable to perturbations of the right hand side with higher accuracy than using other methods. The approach is implemented by an algorithm that uses so-called minimal pseudoinverse matrices. The results of numerical experiments are presented that confirm the theoretical provisions of the article. |
| title | Solving ill-conditioned linear algebraic systems using methods that improve conditioning |
| topic | Numerical Analysis 15A09, 15A10, 65F22, 15A29 |
| url | https://arxiv.org/abs/2405.04399 |