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

Ulrich Kohlenbach, Thomas Powell

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)490-503
Number of pages14
JournalComputers & Mathematics with Applications
Volume80
Issue number3
Early online date23 Apr 2020
DOIs
Publication statusPublished - 1 Aug 2020

Keywords

  • Accretive operators
  • Ishikawa iterations
  • Proof mining
  • Rates of convergence
  • Uniform accretivity
  • Uniformly smooth Banach spaces

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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