Effective metastability for a method of alternating resolvents
Functional Analysis
2021-02-01 v1 Logic
Abstract
A generalized method of alternating resolvents was introduced by Boikanyo and Moro{\c s}anu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two different sets of conditions. As a consequence we obtain effective rates of metastability (in the sense of Terence Tao) and quasi-rates of asymptotic regularity. Furthermore, we bypass the need for sequential weak compactness in the original proofs. Our quantitative results are obtained using proof-theoretical techniques in the context of the proof mining program.
Keywords
Cite
@article{arxiv.2101.12675,
title = {Effective metastability for a method of alternating resolvents},
author = {Bruno Dinis and Pedro Pinto},
journal= {arXiv preprint arXiv:2101.12675},
year = {2021}
}