Certifying Zeros of Polynomial Systems Using Interval Arithmetic
Autor(en): | Breiding, Paul Rose, Kemal Timme, Sascha |
Stichwörter: | Computer Science; Computer Science, Software Engineering; Datasets; gaze detection; HOMOTOPY CONTINUATION; Mathematics; Mathematics, Applied; neural networks; text tagging | Erscheinungsdatum: | 2023 | Herausgeber: | ASSOC COMPUTING MACHINERY | Journal: | ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | Volumen: | 49 | Ausgabe: | 1 | Zusammenfassung: | 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 a powerful new tool in numerical algebraic geometry, which can make certification the default and not just an option. |
ISSN: | 0098-3500 | DOI: | 10.1145/3580277 |
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