The inexact, inexact perturbed and quasi-Newton methods are equivalent models8 years agoAbstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…
On the superlinear convergence of the successive approximations method8 years agoAbstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…
Inexact perturbed Newton methods and applications to a class of Krylov solvers8 years agoAbstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…
On an Aitken-Newton type method8 years agoAbstract We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes…
On a Newton-Steffensen type method8 years agoAbstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…
On a robust Aitken-Newton method based on the Hermite polynomial8 years agoAbstract We introduce an Aitken–Newton iterative method for nonlinear equations, which is obtained by using the Hermite inverse interpolation polynomial…
Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three8 years agoAbstract We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable…
A unified treatment of the modified Newton and chord methods8 years agoAbstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…
On a Steffensen-Hermite method of order three8 years agoAbstract In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the…
On a Steffensen type method8 years agoAbstract We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show…