Results 151 to 160 of about 3,400 (193)

On the semilocal convergence behavior for Halley’s method

Computational Optimization and Applications, 2014
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Ling, Yonghui, Xu, Xiubin
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Semilocal convergence for Halley’s method under weak Lipschitz condition

Applied Mathematics and Computation, 2009
Let \(X,Y\) be Banach spaces, \(D\) be an open convex part of \(X\) and \(F:D\to Y\) be a continuous, twice Fréchet differentiable operator. The semilocal convergence of the Halley's method \[ x_{k+1}=x_k-(I-L_F(x_k))^{-1} F'(x_k)^{-1}F(x_k), \quad k\geq 0, \] towards the unique solution \(x^*\) of \(F(u)=0\) is established, under Lipschitz type ...
Xu, Xiubin, Ling, Yonghui
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Semilocal convergence and R-order for modified Chebyshev-Halley methods

Numerical Algorithms, 2012
A nonlinear equation \(F(x)=0\) in Banach spaces is to solve on a nonempty open convex subset of space \(X\), where \(F\) has values in a Banach space \(Y\). Newton's method converges quadratically. Third-order methods use the second Fréchet derivative of \(F\).
Wang, Xiuhua, Kou, Jisheng
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Semilocal convergence of a continuation method in Banach spaces

Numerical Analysis and Applications, 2017
Summary: This paper is concerned with the semilocal convergence of a continuation method between two third-order iterative methods, namely, the Halley's and the convex acceleration of Newton's method, also known as the Super-Halley's method. This convergence analysis is discussed using the recurrence relations approach.
Prashanth, Maroju, Motsa, Sandile
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New semilocal and local convergence analysis for the Secant method

Applied Mathematics and Computation, 2015
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Magreñán, Á. Alberto, Argyros, Ioannis K.   +1 more
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On semilocal convergence of two step Kurchatov method

International Journal of Computer Mathematics, 2018
In this article we present a new semilocal convergence analysis for the two step Kurchatov method by using recurrence relations under Lipschitz type conditions on first-order divided difference ope...
Himanshu Kumar, P. K. Parida
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Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions

East Asian Journal on Applied Mathematics, 2017
AbstractMulti-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established these MMN-HSS methods under Lipschitz conditions, and we now present a semilocal ...
Li, Yang, Guo, Xue-Ping
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SEMILOCAL CONVERGENCE OF A STIRLING-LIKE METHOD IN BANACH SPACES

International Journal of Computational Methods, 2010
The aim of this paper is to establish the semilocal convergence of a third order Stirling–like method employed for solving nonlinear equations in Banach spaces by using the first Fréchet derivative, which satisfies the Lipschitz continuity condition.
Parhi, S. K., Gupta, D. K.
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Semilocal convergence for Super-Halley’s method under $$\omega $$ ω -differentiability condition

Japan Journal of Industrial and Applied Mathematics, 2014
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Prashanth, Maroju, Gupta, D. K.
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Local and semilocal convergence for Kurchatov method under $$\omega$$-continuity conditions

The Journal of Analysis, 2022
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