2022/08/02 by Kisun Lee, Lee, Kisun
Computer Science · Mathematics · #65H14 #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Numerical methods for differential equations #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2208.01784
openalex publication_date 2022/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The package NumericalCertification implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's α-theory and Krawczyk method. For a singular solution, we implement soft verification using the iterative deflation method. We demonstrate the functionalities of the package focusing on interaction with current numerical solvers in Macaulay2.