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.

翻译：本文提出一种通过推广Krawczyk检验来构造曲面认证近似算法的方案。Krawczyk检验基于区间算术，能在给定区域内确认解析方程平方系统解的存在性与唯一性。通过推广该检验方法，我们将该技术的适用范围扩展至非平方系统及高维簇。我们提供了原型实现，并通过若干算例演示了其应用效果。