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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.
- ISSN
- 0098-3500
- eISSN
- 1557-7295
- DOI
- 10.1145/3580277
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery
Published: Mar 21, 2023
Keywords: Datasets