Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
By Vasile Berinde. 2004
90 citations recorded by the source corpus.
In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/89066b127fe7aab9fa4ca99819391d74ba0e520c
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In Computational Mechanics
In Computational Theory and Mathematics
- Mujahid Abbas
- Talat Nazir
- Vasile Berinde
- Ovidiu Popescu
- Florin Bojor
- K. Vara Prasad
- G. Babu
- Francesca Vetro
In Geometry and Topology
- Mujahid Abbas
- Vasile Berinde
- Talat Nazir
- Ovidiu Popescu
- Florin Bojor
- Calogero Vetro
- Stojan Radenovic
- K. Vara Prasad
Citations in the corpus
- A new faster iteration process applied to constrained minimization and feasibility problems (2014, background): “The following definitions about the rate of convergence are due to Berinde [4].”
- ON THE CONVERGENCE OF THE ISHIKAWA ITERATION IN THE CLASS OF QUASI CONTRACTIVE OPERATORS (2004, methodology): “In view of our paper [2] and based on the proofs of Theorems 1 and 2, it results that, in the class of Zamfirescu operators, the Mann iteration is always faster than the Ishikawa iteration.”