Semilocal Convergence of the Extension of Chun’s Method [PDF]
Axioms, 2021 In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method.
Alicia Cordero +4 more
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Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions [PDF]
The Scientific World Journal, 2015 Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt
Yueqing Zhao +5 more
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A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich [PDF]
Journal of Complexity, 2014 From Kantorovich's theory we establish a general semilocal convergence result for Newton's method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton's method and improve the a priori error estimates.
M A Hernández-Verón, J A Ezquerro
exaly +7 more sources
The cubic semilocal convergence on two variants of Newton's method [PDF]
Journal of Computational and Applied Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhongli Liu
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A semilocal convergence analysis for the method of tangent parabolas [PDF]
Journal of Numerical Analysis and Approximation Theory, 2005 We present a semilocal convergence analysis for the method of tangent parabolas (Euler-Chebyshev) using a combination of Lipschitz and center Lipschitz conditions on the Fréchet derivatives involved.
Ioannis K. Argyros
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Extended semilocal convergence for the Newton- Kurchatov method
Математичні Студії, 2020 We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general.
H.P. Yarmola +2 more
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On the semilocal convergence of efficient Chebyshev–Secant-type methods [PDF]
Journal of Computational and Applied Mathematics, 2011 We introduce a three-step ChebyshevSecant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM) using recurrence relations. Numerical examples validating our theoretical results are also provided in this study. © 2011 Elsevier B.V.
Ioannis K. Argyros +4 more
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Semilocal convergence of the secant method under mild convergence conditions of differentiability [PDF]
Computers & Mathematics with Applications, 2002 In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder continuous conditions. Also, we obtain a result for uniqueness of solutions.
Hernández, M.A., Rubio, M.J.
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Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method [PDF]
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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Extended sufficient semilocal convergence for the Secant method [PDF]
Computers & Mathematics with Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yeol Je Cho +2 more
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