# successive approximations

## 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: \tag{$C$} \lim \frac…

## Methods of Newton and Newton-Krylov type

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

## 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,…

## 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 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…
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