## 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 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 We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…