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.
openaire +2 more sources
On the local and semilocal convergence of a parameterized multi-step Newton method
Journal of Computational and Applied Mathematics, 2020This 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 +5 more
openaire +4 more sources
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.
openaire +1 more source
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 +2 more
openaire +2 more sources
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
openaire +3 more sources
Semilocal convergence of Stirling's method for fixed points in Banach spaces
International Journal of Mathematics in Operational Research, 2016The 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 +2 more
openaire +2 more sources
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.
José Manuel Gutiérrez Jiménez +2 more
openaire +2 more sources
A refined semilocal convergence analysis of an algorithm for solving the Ricatti equation
Journal of Applied Mathematics and Computing, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Correction: Semilocal convergence of the higher order method in riemannian manifolds
Rendiconti del Circolo Matematico di Palermo Series 2zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
INTRODUCTION TO SEMILOCAL AND GLOBAL CONVERGENCE
1970J.M. Ortega, W.C. Rheinboldt
openaire +1 more source