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arXiv · 1908.06734

Rates of convergence for iterative solutions of equations involving set-valued accretive operators

Ulrich Kohlenbach·Thomas Powell
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Abstract

This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract explicit rates of convergence from these proofs which depend on a modulus of uniform accretivity at zero, a concept first introduced by A. Koutsoukou-Argyraki and the first author in 2015. Our highly modular approach, which is inspired by the logic-based proof mining paradigm, also establishes that a number of seemingly unrelated convergence proofs in the literature are actually instances of a common pattern.

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Ulrich Kohlenbach, Thomas Powell. 2019-08-19. Rates of convergence for iterative solutions of equations involving set-valued accretive operators. https://doi.org/10.1016/j.camwa.2020.04.002

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