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…
Read MoreA survey on the high convergence orders and computational convergence orders of sequences
Abstract Twenty years after the classical book of Ortega and Rheinboldt was published, five definitions for the (Q)-convergence orders of…
Read MoreOn the convergence of some one step and multistep iterative methods
Abstract Author Ion Păvăloiu Keywords nonlinear equations in R; one step iterative methods; multistep iterative methods; convergence order. References PDF…
Read MoreOn 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…
Read MoreImproving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term
Abstract Authors Ioannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu…
Read MorePerturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators
Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…
Read MoreOn the approximate solutions of implicit functions using the Steffensen method
Abstract We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to…
Read MoreEstimating 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…
Read MoreOn 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,…
Read MoreThe 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,…
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