Certifying Zeros of Polynomial Systems Using Interval Arithmetic
ACM Transactions on Mathematical Software2023Vol. 49(1), pp. 1–14
Citations Over TimeTop 10% of 2023 papers
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.
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