Solution of a polylocal problem with a pseudospectral method
Abstract Consider the problem: $$y”(x) + f(x, y) = 0, \ \ x \in [0, 1], y(a) = \alpha, y(b)…
Numerical Analysis
On the convergence of some one step and multistep iterative methods
Abstract AuthorIon Păvăloiu (Tiberiu Popoviciu Institute of Numerical Analysis) Keywordsnonlinear equations in R; one step iterative methods; multistep iterative methods;…
On computational complexity in solving equations by Steffensen type methods
Abstract AuthorsIon Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy Keywordsnonlinear equations in R; iterative methods; Steffensen method.…
On computational complexity in solving equations by interpolation methods,
Abstract AuthorsIon Păvăloiu (Tiberiu Popoviciu Institute of Numerical Analysis) KeywordsPDFScanned paper: on the journal website. Latex version of the…
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…
Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term
Abstract AuthorsIoannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu (Tiberiu…
Perturbed-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…
On 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…
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,…