## 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…

## Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media

AbstractIn this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled flow…

## 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…

## Numerical benchmark study for flow in highly heterogeneous aquifers

AbstractThis article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in…

## A survey on the high convergence orders and computational convergence orders of sequences

Abstract Let $$x_k\rightarrow x^\ast\in{\mathbb R}^N$$; denote the errors by $$e_k: = \|x^\ast – x_k\|$$ and the quotient factors…

## On the convergence of some one step and multistep iterative methods

Abstract AuthorIon Păvăloiu Keywordsnonlinear equations in R; one step iterative methods; multistep iterative methods; convergence order. ReferencesPDFScanned manuscript (in Romanian).…

## 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…

## Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences

Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…

## On the convergence order of the iterative methods

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…

## Optimal algorithms concerning the solving of equations by interpolation

Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for…