On the invertibility of matrices with a double saddle-point structure
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929407503892480 |
|---|---|
| author | Beik, Fatemeh P. A. Greif, Chen Trummer, Manfred |
| author_facet | Beik, Fatemeh P. A. Greif, Chen Trummer, Manfred |
| contents | We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the nullity of the blocks and intersections of their kernels, an explicit formula for the inverse is derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the invertibility of matrices with a double saddle-point structure Beik, Fatemeh P. A. Greif, Chen Trummer, Manfred Numerical Analysis 15A09, 15A03, 15A06 We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider various scenarios, including the case where all diagonal blocks are allowed to be rank deficient. Under certain conditions related to the nullity of the blocks and intersections of their kernels, an explicit formula for the inverse is derived. |
| title | On the invertibility of matrices with a double saddle-point structure |
| topic | Numerical Analysis 15A09, 15A03, 15A06 |
| url | https://arxiv.org/abs/2404.17168 |