## How many steps still left to x*?

Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac…

Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac…

Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by…

Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We…

Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form \(u^{p}\), \(p>1\) is considered. For \(p=3\), we deduce…

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…

Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…

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

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

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

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