## 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…

## 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…

## Inexact perturbed Newton methods and applications to a class of Krylov solvers

Abstract 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 method

Abstract 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 methods

Abstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…

## On the high convergence orders of the Newton-GMBACK methods

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

## On an Aitken-Newton type method

Abstract We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes…

## On a Newton-Steffensen type method

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