Verification of a low-degree polynomial vanishing at empirical points

Given a set of distinct empirical points with uniform tolerance, based on the LDP algorithm proposed by Fassino and Torrente, we provide a verification algorithm that computes a polynomial, an admissible perturbed point set with verified error bound, such that the polynomial is guaranteed to vanish at a slightly admissible perturbed point set within computed error bound. The effectiveness of our algorithm is demonstrated in several examples.