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Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term

8 years ago

Abstract AuthorsIoannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu (Tiberiu…

On the approximate solutions of implicit functions using the Steffensen method

8 years ago

Abstract We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to…

Estimating the radius of an attraction ball

8 years ago

Abstract Given a nonlinear mapping \(G:D\subseteq \mathbb{R}^n\rightarrow \mathbb{R}^n\) differentiable at a fixed point \(x^\ast\), the Ostrowski theorem offers the sharp…

The inexact, inexact perturbed and quasi-Newton methods are equivalent models

8 years ago

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

Sufficient convergence conditions for certain accelerated successive approximations

8 years ago

Abstract We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

On the superlinear convergence of the successive approximations method

8 years ago

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

Affine invariant conditions for the inexact perturbed Newton method

8 years ago

Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…

On the high convergence orders of the Newton-GMBACK methods

8 years ago

Abstract GMBACK is a Krylov solver for linear systems in \(\mathbb{R}^n\). We analyze here the high convergence orders (superlinear convergence)…

On a Newton-Steffensen type method

8 years ago

Abstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…

Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three

8 years ago

Abstract We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable…

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