Certified surface approximations using the interval Krawczyk test
Numerical Analysis
2026-02-10 v1 Numerical Analysis
Symbolic Computation
Algebraic Geometry
Abstract
We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the existence and uniqueness of a solution to a square system of analytic equations in a region. By generalizing this test, we extend the reach of this technique to non-square systems and higher-dimensional varieties. We provide a prototype implementation and illustrate its use on several examples.
Cite
@article{arxiv.2602.07718,
title = {Certified surface approximations using the interval Krawczyk test},
author = {Michael Burr and Jonathan D. Hauenstein and Kisun Lee},
journal= {arXiv preprint arXiv:2602.07718},
year = {2026}
}
Comments
15 pages, 5 figures