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Displaying 401 – 420 of 666

On mesh independence and Newton-type methods

Owe Axelsson (1993)

Applications of Mathematics

Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters $H$ and $h$ for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...

On multipoint iterative processes of efficiency index higher than Newton's method.

Argyros, Ioannis K., Hilout, Saïd (2009)

The Journal of Nonlinear Sciences and its Applications

On multivalued nonlinear variational inclusion problems with $(A, η)$ -accretive mappings in Banach spaces.

Lan, Heng-You (2006)

Journal of Inequalities and Applications [electronic only]

On Newton-Like Methods.

J.E. jr. DENNIS (1968)

Numerische Mathematik

On stability and growth of solutions for classes of initial and boundary value problems

L. E. Payne (1985)

Banach Center Publications

On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings.

Cai, Gang, Hu, Chang Song (2009)

Fixed Point Theory and Applications [electronic only]

On $T$ -stability of Picard iteration in cone metric spaces.

Asadi, M., Soleimani, H., Vaezpour, S.M., Rhoades, B.E. (2009)

Fixed Point Theory and Applications [electronic only]

On the application of Newton's and chord methods of bifurcation problems.

Elgindi, M.B.M. (1994)

International Journal of Mathematics and Mathematical Sciences

On the continuous dependence of the fixed points for $(ϕ, ψ)$ -contractive-type operators

Memudu Olaposi Olatinwo (2010)

Kragujevac Journal of Mathematics

On the convergence and application of Stirling's method

Ioannis K. Argyros (2003)

Applicationes Mathematicae

We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.

On the convergence for an iterative method for quasivariational inclusions.

Li, Yu, Wu, Changqun (2010)

Fixed Point Theory and Applications [electronic only]

On the convergence of an implicit iterative process for generalized asymptotically quasi-nonexpansive mappings.

Qin, Xiaolong, Kang, Shin Min, Agarwal, Ravi P. (2010)

Fixed Point Theory and Applications [electronic only]

On the convergence of implicit Ishikawa iterations with errors to a common fixed point of two mappings in convex metric spaces.

Rafiq, Arif, Zafar, Sundus (2006)

General Mathematics

On the convergence of implicit iterative processes for asymptotically pseudocontractive mappings in the intermediate sense.

Qin, Xiaolong, Kim, Jong Kyu, Wang, Tianze (2011)

Abstract and Applied Analysis

On the convergence of iterative sequences for a family of nonexpansive mappings and inverse-strongly monotone mappings.

Cho, Sun Young, Kang, Shin Min (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

On the convergence of Newton's method for analytic operators.

Argyros, Ioannis K. (2003)

Southwest Journal of Pure and Applied Mathematics [electronic only]

On the convergence of Newton's method under ω*-conditioned second derivative

Ioannis K. Argyros, Saïd Hilout (2011)

Applicationes Mathematicae

We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.

On the convergence of perturbed Newton-like methods in Banach space and applications.

Argyros, Ioannis K. (1996)

Southwest Journal of Pure and Applied Mathematics [electronic only]

On the convergence of the Ishikawa iterates to a common fixed point of two mappings

Ljubomir B. Ćirić, Jeong Sheok Ume, M. S. Khan (2003)

Archivum Mathematicum

Let $C$ be a convex subset of a complete convex metric space $X$ , and $S$ and $T$ be two selfmappings on $C$ . In this paper it is shown that if the sequence of Ishikawa iterations associated with $S$ and $T$ converges, then its limit point is the common fixed point of $S$ and $T$ . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].

On the convergence of the Ishikawa iteration in the class of quasi contractive operators.

Berinde, V. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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