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sloisel/MPE-Formal

Sébastien Loisel

Palomar Registrypalomar/PALOMAR-2026-08-20-000009Aug 20, 2026math.NAscore 0

Machine-checked proofs of three probabilistic convergence theorems for restarted Minimal Polynomial Extrapolation (MPE) applied to nonlinear fixed-point iterations. Dithered restarts keep the error below the doubly exponential schedule delta^(theta^m), for any theta in (1,2), from every starting point -- the breakdown set included -- with an explicit failure-probability exponent over the dither; in the root sense the convergence order is at least theta. Under simple spectrum, the error follows a quadratically shrinking dither schedule (root order at least 2) with failure probability linear…

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