How many steps still left to x*?
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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…
local convergence
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…
On an Aitken-Steffensen-Newton type method
Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We…
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…
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,…
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…