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 language | English |
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Pages (from-to) | 490-503 |
Number of pages | 14 |
Journal | Computers & Mathematics with Applications |
Volume | 80 |
Issue number | 3 |
Early online date | 23 Apr 2020 |
DOIs | |
Publication status | Published - 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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Thomas Powell
- Department of Computer Science - Senior Lecturer
- Mathematical Foundations of Computation
Person: Research & Teaching