Perov’s theorem applied to systems of equations
Abstract In this paper, we consider systems of equations having a linear part and also a nonlinear part. We give…
successive approximations
How many steps still left to x*?
We survey the convergence orders of sequences and show the orders of the basic iterative sequences for solving nonlinear equations…
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…