Two deterministic algorithms for finding the first zero-crossing point of a multiextremal function

In this paper, we propose a deterministic approach for finding the first zero-crossing point of a differentiable, possibly multiextremal univariate function, that combines a Branch-and-Bound framework with piece-wise linear under- and overestimators derived from Lipschitz intervals. Two algorithms are presented: a baseline algorithm and a version enhanced with interval reduction techniques. Theoretical guarantees of correctness and finite termination of the introduced methods are established. Extensive numerical experiments on 27 benchmark problems demonstrate that the proposed methods outperform the existing interval Branch-and-Bound approach both in terms of running time and accuracy.