Technology Category
Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesKnowledge Representation and Reasoning: Automated Reasoning and Theorem ProvingSearch and Optimization: Non-convex Optimization
Certified surface approximations using the interval Krawczyk test
🤖 AI Summary
This work addresses the problem of constructing certified approximations of high-dimensional surfaces defined by non-square systems, with rigorous guarantees of existence and uniqueness. To this end, we generalize the classical Krawczyk test—originally formulated for square systems—to handle non-square systems and higher-dimensional algebraic varieties. By integrating interval arithmetic with techniques from analytic system solving, we develop a general-purpose algorithm for certified surface approximation. A prototype implementation demonstrates the efficacy of our approach on several complex surface instances, significantly broadening the class of geometric objects amenable to formal certification.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
certified approximation
surface
Krawczyk test
interval arithmetic
non-square systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
interval Krawczyk test
certified approximation
non-square systems
higher-dimensional varieties
interval arithmetic
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