Year: 2026
Type: preprint
Abstract: We present a root isolation algorithm for an analytic function. The method combines interval subdivision with a heuristic test based on local cubic Hermite interpolation. Whenever the function is sufficiently close to its cubic Hermite interpolant at a few sample points, we assume that the critical points of the cubic interpolant give a valid root isolation for the original function. Such an algorithm cannot, in general, provide a rigorous certification of the computed intervals. Nevertheless, extensive numerical experiments show that it is highly efficient and almost always produces the correct results. We hope that a probabilistic or exact algorithm can be derived from this work.
Source: arXiv (Cornell University)
Author: Raffalli, Christophe
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220337578