Results 11 to 20 of about 505,478 (275)
Errors estimation for implicit Mann iteration [PDF]
Journal of Numerical Analysis and Approximation Theory, 2006 We study the errors estimation for the implicit Mann iteration..
Ştefan M. Şoltuz
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On the equivalence of Mann and Ishikawa iteration methods
International Journal of Mathematics and Mathematical Sciences, 2003 We show that certain Mann and Ishikawa iteration schemes are equivalent for various classes of functions.
B. E. Rhoades, Stefan M. Soltuz
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Local convergence of generalized Mann iteration [PDF]
Numerical Algorithms, 2017 The article deals with generalized Mann iterations \[ x_{n+1} = (I - D_n)x_n + D_nT(x_n), \qquad n = 0,1,2,\ldots,\eqno(1) \] for the approximative construction of fixed points of a nonlinear operator \(T:\;C \to H\), where \(H\) is a real Hilbert space, \(C\) an open subset of \(H\), \(\{D_n\} \subset L(H)\) is a generalized control sequence.
Stefan Maruster, Laura Maruster
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International Journal of Mathematics and Mathematical Sciences, 2004 We show that the Ishikawa iteration and the corresponding Mann iteration are equivalent when applied to ψ-uniformly pseudocontractive or ψ-uniformly accretive maps.
B. E. Rhoades, Ştefan M. Şoltuz
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Journal of Mathematics, 2022 Mann iteration is weakly convergent in infinite dimensional spaces. We, in this paper, use the nearest point projection to force the strong convergence of a Mann-based iteration for nonexpansive and monotone operators.
Songtao Lv
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On the boundedness of the associated sequence of Mann iteration for several operator classes with applications [PDF]
Journal of Numerical Analysis and Approximation Theory, 2005 We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is ...
Ştefan M. Şoltuz
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Local convergence radius for the Mann-type iteration
Annals of the West University of Timisoara: Mathematics and Computer Science, 2015 A procedure to estimate the local convergence radius for a Mann-type iteration is given in the setting of a finite dimensional space. In particular we obtain the estimation of radius for classical Newton method.
Măruşter Ştefan
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Rates of asymptotic regularity for the alternating Halpern–Mann iteration
Optimization Letters, 2023 In this paper we extend to $UCW$-hyperbolic spaces the quantitative asymptotic regularity results for the alternating Halpern-Mann iteration obtained by Dinis and the second author for CAT(0) spaces. These results are new even for uniformly convex normed spaces. Furthermore, for a particular choice of the parameter sequences, we compute linear rates of
Laurentiu Leustean, Pedro Pinto 0003
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On Modified Halpern and Tikhonov–Mann Iterations [PDF]
Journal of Optimization Theory and Applications, 2023 AbstractWe show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Panyanak and the Tikhonov–Mann iteration introduced by H. Cheval and L. Leuştean as a generalization of an iteration due to Y. Yao et al.
Horatiu Cheval +2 more
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On the Mann and Ishikawa iteration processes [PDF]
Abstract and Applied Analysis, 1996 It is shown that a result of Chidume, involving the strong convergence of the Mann iteration process for continuous strongly accretive operators, is actually a corollary to a result by Nevanlinna and Reich. It is then shown that the Nevanlinna and Reich result can be extended to the case of an Ishikawa iteration process.
Jia Yuting, Zhou Haiyun
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