Semilocal convergence for Super-Halley’s method under $$\omega $$ ω -differentiability condition
Japan Journal of Industrial and Applied Mathematics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Prashanth, Maroju, Gupta, D. K.
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Local and semilocal convergence for Kurchatov method under $$\omega$$-continuity conditions
The Journal of Analysis, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An improved semilocal convergence analysis for the Chebyshev method
Journal of Applied Mathematics and Computing, 2013The article deals with the Chebyshev method (the method of tangent parabola) of the approximate solution of the nonlinear operator equation \(F(x) = 0\) with the twice differentiable nonlinear operator \(F\) acting between Banach spaces \(X\) and \(Y\). The Chebyshev method is defined as \[ x_{n+1} = y_n - \frac12 \, F'(x_n)^{-1}F''(x_n)(y_n - x_n)^2, \
Argyros, I. K., Khattri, S. K.
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Semilocal convergence of a continuation method under ω-differentiability condition
International Journal of Computing Science and Mathematics, 2016The aim of this paper is to study the semilocal convergence of a continuation method combining the Chebyshev's method and the convex acceleration of Newton's method for solving nonlinear operator equations in Banach spaces. This is carried out by deriving a family of recurrence relations based on two parameters under the assumption that the first ...
M. Prashanth, D.K. Gupta, S.S. Motsa
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Extending the applicability of the local and semilocal convergence of Newton’s method
Applied Mathematics and Computation, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Argyros, Ioannis K. +1 more
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Concerning the semilocal convergence of Newton’s method and convex majorants
Rendiconti del Circolo Matematico di Palermo, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Semilocal Convergence of Steffensen-Type Algorithms for Solving Nonlinear Equations
Numerical Functional Analysis and Optimization, 2014In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods ([7, 13]) using similar convergence conditions.
Hongmin Ren +2 more
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On the semilocal convergence of Newton–Kantorovich method under center-Lipschitz conditions
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gutiérrez, J. M. +2 more
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A Semilocal Convergence of a Secant–Type Method for Solving Generalized Equations
Positivity, 2006Let \(X,Y\) be two Banach spaces and let \(f:X\rightarrow Y\) be continuous and \(G:X\rightarrow \mathcal{P}(Y)\) be a set-valued map with closed graph. In order to solve the inclusion \[ 0\in f(x)+G(x), \] the authors consider the iterative method defined by \(x_0,x_1\in X\) and \[ y_k=\alpha x_k+(1-\alpha)x_{k-1},\;0\in f(x_k)+[y_k,x_k;f](x_{k+1}-x_k)
Hilout, Said, Piétrus, Alain
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ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS
Asian-European Journal of Mathematics, 2014We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J.
Argyros, Ioannis K., George, Santhosh
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