Certified surface approximations using the interval Krawczyk test
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912887939792896 |
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| author | Burr, Michael Hauenstein, Jonathan D. Lee, Kisun |
| author_facet | Burr, Michael Hauenstein, Jonathan D. Lee, Kisun |
| contents | We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the existence and uniqueness of a solution to a square system of analytic equations in a region. By generalizing this test, we extend the reach of this technique to non-square systems and higher-dimensional varieties. We provide a prototype implementation and illustrate its use on several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07718 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Certified surface approximations using the interval Krawczyk test Burr, Michael Hauenstein, Jonathan D. Lee, Kisun Numerical Analysis Symbolic Computation Algebraic Geometry 65H10, 65H14 We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the existence and uniqueness of a solution to a square system of analytic equations in a region. By generalizing this test, we extend the reach of this technique to non-square systems and higher-dimensional varieties. We provide a prototype implementation and illustrate its use on several examples. |
| title | Certified surface approximations using the interval Krawczyk test |
| topic | Numerical Analysis Symbolic Computation Algebraic Geometry 65H10, 65H14 |
| url | https://arxiv.org/abs/2602.07718 |