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math.AG2025
A priori bounds for certified Krawczyk homotopy tracking
Kisun Lee
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 tes…
cs.SC2025
Certified algebraic curve projections by path tracking
Michael Burr, Michael Byrd, Kisun Lee
We present a certified algorithm that takes a smooth algebraic curve in and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}…