Numerical Instability of Algebraic Rootfinding Methods
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916348194455552 |
|---|---|
| author | Graf, Emil Townsend, Alex |
| author_facet | Graf, Emil Townsend, Alex |
| contents | We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are constructed at intermediate steps. In particular, we give multidimensional polynomial systems for which the conditioning of a subproblem can be worse than the conditioning of the original problem by a factor that grows exponentially with the number of variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Instability of Algebraic Rootfinding Methods Graf, Emil Townsend, Alex Numerical Analysis Algebraic Geometry 65H04 (Primary) 65F35, 13P15 (Secondary) G.1 We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are constructed at intermediate steps. In particular, we give multidimensional polynomial systems for which the conditioning of a subproblem can be worse than the conditioning of the original problem by a factor that grows exponentially with the number of variables. |
| title | Numerical Instability of Algebraic Rootfinding Methods |
| topic | Numerical Analysis Algebraic Geometry 65H04 (Primary) 65F35, 13P15 (Secondary) G.1 |
| url | https://arxiv.org/abs/2408.02805 |