تقرير
Certified homotopy tracking using the Krawczyk method
| العنوان: | Certified homotopy tracking using the Krawczyk method |
|---|---|
| المؤلفون: | Duff, Timothy, Lee, Kisun |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Computer Science - Symbolic Computation, Mathematics - Algebraic Geometry, 65H14 |
| الوصف: | We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach based on a parametric variant of the Krawczyk method from interval arithmetic. Unlike most previous methods for certified path-tracking, our approach is applicable in the general setting of parameter homotopies commonly used to solve polynomial systems of equations. We also describe a novel preconditioning strategy and give theoretical correctness and termination results. Experiments using a preliminary implementation of the method indicate that our approach is competitive with specialized methods appearing previously in the literature, in spite of our more general setting. Comment: 19 pages, 4 figures, 4 tables. Accepted for the Proceedings of ISSAC 2024 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.07053 |
| رقم الأكسشن: | edsarx.2402.07053 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |