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arXiv · 2101.12675

Effective metastability for a method of alternating resolvents

Bruno Dinis·Pedro Pinto
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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.

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Bruno Dinis, Pedro Pinto. 2021-01-29. Effective metastability for a method of alternating resolvents. https://arxiv.org/abs/2101.12675

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