Results 91 to 100 of about 3,400 (193)
Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
Journal of Computational and Applied Mathematics, 2000 This study obtains two semilocal convergence results for the well-known Chebyshev method, which is a third-order iterative process. The hypotheses required are modifications to the normal Kantorovich ones. The results obtained are applied to the reduction of nonlinear integral equations of the Fredholm type and first kind.
Hernández, M.A., Salanova, M.A.
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Semilocal Convergence for new Chebyshev-type iterative methods
, 2019 [EN] In this paper, the convergence of improved Chebyshev-Secant-type iterative methods are studied for solving nonlinear equations in Banach space settings. Its semilocal convergence is established using recurrence relations under weaker continuity conditions on first order divided differences.
Kumar, Abhimanyu +4 more
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On the convergence of Steffensen-type methods using recurrent functions nonexpansive mappings
Journal of Numerical Analysis and Approximation Theory, 2009 We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Steffensen-type methods (STM) in a Banach space setting.
Ioannis K. Argyros, Saïd Hilout
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On an iterative algorithm of Ulm-type for solving equations
Journal of Numerical Analysis and Approximation Theory, 2013 We provide a semilocal convergence analysis of an iterative algorithm for solving nonlinear operator equations in a Banach space setting. This algorithm is of order \(1.839\ldots\), and has already been studied in [3, 8, 18, 20].
Ioannis K. Argyros, Sanjay K. Khattri
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On a third order iterative method for solving polynomial operator equations
Journal of Numerical Analysis and Approximation Theory, 2002 We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree \(2\). The method consists in fact in evaluating the Jacobian at every two steps, and it has the \(r\)-convergence order at least \(3\).
Emil Cătinaş, Ion Păvăloiu
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Convergence estimates for the Magnus expansion I. Banach algebras
, 2019 We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made.
Lakos, Gyula
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On the semilocal convergence of derivative free methods for solving nonlinear equations
Journal of Numerical Analysis and Approximation Theory, 2012 We introduce a Derivative Free Method (DFM) for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for DFM using recurrence relations. Numerical examples validating our theoretical results are also provided
Ioannis K. Argyros, Hongmin Ren
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Cubo, 2011 We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This
Ioannis K Argyros, Saïd Hilout
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Local convergence of Newton's method using Kantorovich convex majorants
Journal of Numerical Analysis and Approximation Theory, 2010 We are concerned with the problem of approximating a solution of an operator equation using Newton's method. Recently in the elegant work by Ferreira and Svaiter [6] a semilocal convergence analysis was provided which makes clear the relationship of the
Ioannis K. Argyros
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Weaker conditions for the convergence of Newton-like methods
Journal of Numerical Analysis and Approximation Theory, 2007 We provide a semilocal convergence analysis for a certain class of Newton-like methods for the solution of a nonlinear equation containing a non differentiable term. Our approach provides: weaker sufficient conditions; finer error bounds on the distances
Ioannis K. Argyros
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