English

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}
}