A Fast solver for high condition linear systems using randomized stable solutions of its blocks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912623417622528 |
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| author | Kar, Suvendu Venkatapathi, Murugesan |
| author_facet | Kar, Suvendu Venkatapathi, Murugesan |
| contents | We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution based on the current residue and effective orthogonality between blocks. This improved method provides significant gains in solving high-condition number linear systems that are either sparse, or dense least-squares problems that are significantly over/under determined. Considering the poor generalizability of preconditioners for such problems, it can also serve as a pre-solver for other iterative numerical methods when required, and as an inner iteration in certain types of GMRES solvers for linear systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fast solver for high condition linear systems using randomized stable solutions of its blocks Kar, Suvendu Venkatapathi, Murugesan Numerical Analysis We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block updates in the solution, and a dynamic proposal distribution based on the current residue and effective orthogonality between blocks. This improved method provides significant gains in solving high-condition number linear systems that are either sparse, or dense least-squares problems that are significantly over/under determined. Considering the poor generalizability of preconditioners for such problems, it can also serve as a pre-solver for other iterative numerical methods when required, and as an inner iteration in certain types of GMRES solvers for linear systems. |
| title | A Fast solver for high condition linear systems using randomized stable solutions of its blocks |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.02156 |