Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
By Ovidiu Popescu. 2007
184 citations recorded by the source corpus.
The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are conver- gent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.
View Paper: https://www.semanticscholar.org/paper/9f5af57e3ef317c7592f6973c226b20a5cec52d2
How researchers see this paper
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- Mihai Postolache
- B. Thakur
- Dipti Thakur
- Vasile Berinde
- Ovidiu Popescu
- Florin Bojor
- E. Karapınar
- G. Babu
Citations in the corpus
- A new iteration scheme for approximating fixed points of nonexpansive mappings (2016, background): “The following definitions about the rate of convergence are due to Berinde [3].”
- Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces (2019, background): “This result has been at the origin of introducing a notion of rate of convergence for comparing two fixed point iterations in [10], a concept that turn out to be very useful, see also [12] and references therein.”