Root isolation for analytic functions using cubic hermite interpolation

Christophe Raffalli

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arXiv · 2610.02934

Root isolation for analytic functions using cubic hermite interpolation

Christophe Raffalli

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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.

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Christophe Raffalli. 2026-10-02. Root isolation for analytic functions using cubic hermite interpolation. https://arxiv.org/abs/2610.02934

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