Certified surface approximations using the interval Krawczyk test
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.
Fields of Study & Subjects
Polynomial and algebraic computation
Numerical Methods and Algorithms
Mathematical and Computational Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint