iterative methods

the solution sought is a limit of a sequence of elements, and each element can be generated based on the previous ones. Initial elements are supposed to be given. Usual iterative methods are the Newton method, the successive approximations, etc.

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…

Interpolation and Applications

Book summarySummary of the book… Book coverContentsCh. 1 Keywordskeyword1, PDFpdf file Referencessee the expanding block below Cite this book as:Author,…

A mixed iteration for nonnegative matrix factorizations

Abstract We show that, under appropriate conditions, one can create a hybrid between two given iterations which can perform better…

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…

The numerical approximation to positive solution for some reaction-diffusion problems

Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form $$u^{p}$$, $$p>1$$ is considered. For $$p=3$$, we deduce…

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 KeywordsPDFScanned paper. Latex version of the paper. Cite this paper as:I. Păvăloiu, On computational complexity in solving…

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…