Rates of convergence for iterative solutions of equations involving set-valued accretive operators
Optimization and Control
2020-04-27 v2 Functional Analysis
Logic
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.
Keywords
Cite
@article{arxiv.1908.06734,
title = {Rates of convergence for iterative solutions of equations involving set-valued accretive operators},
author = {Ulrich Kohlenbach and Thomas Powell},
journal= {arXiv preprint arXiv:1908.06734},
year = {2020}
}