Certifying zeros of polynomial systems using interval arithmetic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913425524785152 |
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| author | Breiding, Paul Rose, Kemal Timme, Sascha |
| author_facet | Breiding, Paul Rose, Kemal Timme, Sascha |
| contents | We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk's method. We demonstrate that it dramatically outperforms earlier approaches to certification. We see this contribution as powerful new tool in numerical algebraic geometry, that can make certification the default and not just an option. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_05000 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Certifying zeros of polynomial systems using interval arithmetic Breiding, Paul Rose, Kemal Timme, Sascha Algebraic Geometry We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk's method. We demonstrate that it dramatically outperforms earlier approaches to certification. We see this contribution as powerful new tool in numerical algebraic geometry, that can make certification the default and not just an option. |
| title | Certifying zeros of polynomial systems using interval arithmetic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2011.05000 |