On the r-convergence orders of the inexact perturbed Newton methods
Abstract The inexact perturbed Newton methods recently introduced by us are variant of Newton method, which assume that at each step…
Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term
Abstract Authors Ioannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu…
Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators
Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…
On the approximate solutions of implicit functions using the Steffensen method
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
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…
On the convergence of some quasi-Newton iterates studied by I. Păvăloiu
Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…
The inexact, inexact perturbed and quasi-Newton methods are equivalent models
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
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
Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(x k ) near a fixed…
Affine invariant conditions for the inexact perturbed Newton method
Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…