Results 161 to 170 of about 900 (183)

The semilocal convergence of a generalization of Brent's and Brown's methods

Numerical Algorithms, 1994
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An improved semilocal convergence analysis for the Chebyshev method

Journal of Applied Mathematics and Computing, 2013
The 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 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 \(F\).
Xiuhua Wang 0002, Jisheng Kou
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On the local and semilocal convergence of a parameterized multi-step Newton method

Journal of Computational and Applied Mathematics, 2020
This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of the equation \(F(x)=0\). The authors study the method defined for each \(n=0,1,2,\ldots\) (base part) by: \[ \begin{array}{l} F'(y_0^{(n)})\phi_1=F(y_0^{(n)}), \\[6pt] y_1^{(n)}=y_0^{(n)}-(1+\theta-\theta^2)\phi_1, \\[4pt] F'
Amat, null, Argyros, null, Busquier, null, Hernández-Verón, null, Yañez, null, 0000-0002-6206-1971   +5 more
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Semilocal convergence of a continuation method under ω-differentiability condition

International Journal of Computing Science and Mathematics, 2016
The 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, Dharmendra Kumar Gupta, Sandile Sydney Motsa   +2 more
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Concerning the semilocal convergence of Newton’s method and convex majorants

Rendiconti del Circolo Matematico di Palermo, 2008
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A Semilocal Convergence of a Secant–Type Method for Solving Generalized Equations

Positivity, 2006
Let \(X,Y\) 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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Semilocal convergence of Stirling's method for fixed points in Banach spaces

International Journal of Mathematics in Operational Research, 2016
The aim of this paper is to discuss the semilocal convergence of Stirling's method used to find fixed points of nonlinear operator equations in Banach spaces. This convergence is achieved using recurrence relations under the assumption that the first Frechet derivative of the involved operator satisfies the ω-continuity condition.
Dharmendra Kumar Gupta, Sanjaya Kumar Parhi, Sukhjit Singh   +2 more
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Semilocal convergence of Chebyshev Kurchatov type methods for non-differentiable operators

Computers and Mathematics With Applications
In this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator ...
Sukhjit Singh, Mehakpreet Singh
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Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

Journal of Optimization Theory and Applications, 2012
The authors consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. A system of recurrence relations for the methods is constructed, and based on it, an existence-uniqueness theorem ...
Xiuhua Wang 0002, Jisheng Kou, Chuanqing Gu   +2 more
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