Deep Centralization for the Circumcentered Reflection Method

Pablo Barros

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arXiv · 2512.05324

Deep Centralization for the Circumcentered Reflection Method

Pablo Barros

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Abstract

We introduce the extended centralized circumcentered reflection method (ecCRM), a framework for two-set convex feasibility that encompasses the classical centralized CRM (cCRM) of Behling, Bello-Cruz, Iusem and Santos as a special case. Our method replaces the fixed centralization step of cCRM with an admissible operator $T$ and a parameter $α$, allowing control over computational cost and step quality. We show that ecCRM retains global convergence, linear rates under mild regularity, and superlinearity for smooth manifolds. Numerical experiments on large-scale matrix completion indicate that deeper operators can dramatically reduce overall runtime, and tests on high-dimensional ellipsoids show that vanishing step sizes can yield significant acceleration, validating the practical utility of both algorithmic components of ecCRM.

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Pablo Barros. 2025-12-05. Deep Centralization for the Circumcentered Reflection Method. https://arxiv.org/abs/2512.05324

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