Effective alpha theory certification using interval arithmetic: alpha theory over regions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910438516588544 |
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| author | Lee, Kisun |
| author_facet | Lee, Kisun |
| contents | We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence to an exact solution. We introduce the alpha theory computation using interval arithmetic to avoid costly exact arithmetic. As a straightforward variation of the alpha theory, our work improves computational efficiency compared to software employing the traditional alpha theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective alpha theory certification using interval arithmetic: alpha theory over regions Lee, Kisun Symbolic Computation Numerical Analysis Algebraic Geometry 65H14 We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence to an exact solution. We introduce the alpha theory computation using interval arithmetic to avoid costly exact arithmetic. As a straightforward variation of the alpha theory, our work improves computational efficiency compared to software employing the traditional alpha theory. |
| title | Effective alpha theory certification using interval arithmetic: alpha theory over regions |
| topic | Symbolic Computation Numerical Analysis Algebraic Geometry 65H14 |
| url | https://arxiv.org/abs/2405.04842 |