On the superlinear convergence of the successive approximations method6 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…
Affine invariant conditions for the inexact perturbed Newton method6 years agoAbstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…
Inexact perturbed Newton methods and applications to a class of Krylov solvers6 years agoAbstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…
On accelerating the convergence of the successive approximations method6 years agoAbstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…
A note on the quadratic convergence of the inexact Newton methods6 years agoAbstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…
On an Aitken-Newton type method6 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 method6 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 polynomial6 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 three6 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 methods6 years agoAbstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…