Certified homotopy tracking using the Krawczyk method
CoRR(2024)
摘要
We revisit the problem of certifying the correctness of approximate solution
paths computed by numerical homotopy continuation methods. We propose a
conceptually simple approach based on a parametric variant of the Krawczyk
method from interval arithmetic. Unlike most previous methods for certified
path-tracking, our approach is applicable in the general setting of parameter
homotopies commonly used to solve polynomial systems of equations. We also
describe a novel preconditioning strategy and give theoretical correctness and
termination results. Experiments using a preliminary implementation of the
method indicate that our approach is competitive with specialized methods
appearing previously in the literature, in spite of our more general setting.
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