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arXiv · 2512.01355

A priori bounds for certified Krawczyk homotopy tracking

Kisun Lee
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Abstract

We establish the first complexity analysis for Krawczyk-based certified homotopy tracking. It consists of explicit a priori stepsize bounds ensuring the success of the Krawczyk test, and an iteration count bound proportional to the weighted length of the solution path. Our a priori bounds reduce the overhead of interval arithmetic, resulting in fewer iterations than previous methods. Experiments using a proof-of-concept implementation validate the results.

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Kisun Lee. 2025-12-01. A priori bounds for certified Krawczyk homotopy tracking. https://arxiv.org/abs/2512.01355

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