Results 161 to 170 of about 3,400 (193)

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.
openaire   +2 more sources

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, D.K. Gupta, S.S. Motsa
openaire   +1 more source

Extending the applicability of the local and semilocal convergence of Newton’s method

Applied Mathematics and Computation, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Argyros, Ioannis K., Magreñán, Á. Alberto   +1 more
openaire   +1 more source

Concerning the semilocal convergence of Newton’s method and convex majorants

Rendiconti del Circolo Matematico di Palermo, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Semilocal Convergence of Steffensen-Type Algorithms for Solving Nonlinear Equations

Numerical Functional Analysis and Optimization, 2014
In 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, Ioannis K. Argyros, Yeol Je Cho   +2 more
openaire   +1 more source

On the semilocal convergence of Newton–Kantorovich method under center-Lipschitz conditions

Applied Mathematics and Computation, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gutiérrez, J. M., Magreñán, Á. A., Romero, N.   +2 more
openaire   +2 more sources

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
openaire   +3 more sources

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

Asian-European Journal of Mathematics, 2014
We 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
openaire   +2 more sources

Semilocal convergence theorems for a certain class of iterative procedures

Korean Journal of Computational & Applied Mathematics, 2000
Semilocal convergence of Newton-like methods \(x_{k+1} = x_k - A(x_k)^\#F(x_k)\), \(k \geq 0\) is discussed for solving the nonlinear equation \(\Gamma F(x)=0\). Here \(F\) is a twice \(F\)-differentiable nonlinear operator between Banach spaces and \(\Gamma\) is a bounded linear operator, furthermore, \(A(x)\) is a bounded linear operator ...
openaire   +2 more sources

Correction: Semilocal convergence of the higher order method in riemannian manifolds

Rendiconti del Circolo Matematico di Palermo Series 2
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources