Mathematics, 2021 An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions.
Marianito R. Rodrigo
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Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps [PDF]
Fixed Point Theory and Applications, 2010 We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators.
Xue Zhiqun, Rhoades BE
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Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings ...
Berinde Vasile, Măruşter Ştefan
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The Equivalence between T-Stabilities of The Krasnoselskij and The Mann Iterations [PDF]
Fixed Point Theory and Applications, 2007 We prove the equivalence between the T-stabilities of the Krasnoselskij and the Mann iterations; a consequence is the equivalence with the T-stability of the Picard-Banach iteration.
Ştefan M. Şoltuz
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Journal of Numerical Analysis and Approximation Theory, 2004 In this note we show that a result previously obtained by us [An equivalence between the convergences of Ishikawa, Mann and Picard iterations, Math. Commun., 8, pp.~15--22, 2003], holds under weaker assumptions.
Ştefan M. Şoltuz
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Remarks of Equivalence among Picard, Mann, and Ishikawa Iterations in Normed Spaces
Fixed Point Theory and Applications, 2007 We show that the convergence of Picard iteration is equivalent to the convergence of Mann iteration schemes for various Zamfirescu operators. Our result extends of Soltuz (2005).
Xue Zhiqun
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The equivalence between T-stabilities of Krasnoselskij and Ishikawa iterations
Journal of Numerical Analysis and Approximation Theory, 2008 We prove the equivalence between the \(T\)-stabilities of Krasnoselskij and Ishikawa iterations; a consequence is the equivalence with the \(T\)-stability of Picard-Banach iteration.
Ştefan M. Şoltuz
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Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
Fixed Point Theory and Applications, 2004 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
Berinde Vasile
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Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2) [PDF]
Geoscientific Model DevelopmentSolving the momentum balance is the computationally expensive part of simulating the evolution of ice sheets. The momentum balance is described by the nonlinear full-Stokes equations, which are solved iteratively. We use the Picard iteration and Newton's
N. Schmidt +4 more
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The Equivalence between
Fixed Point Theory and Applications, 2007 We prove the equivalence between the -stabilities of the Krasnoselskij and the Mann iterations; a consequence is the equivalence with the -stability of the Picard-Banach iteration.
Şoltuz Ştefan M
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