iterative methods Archives | Tiberiu Popoviciu Institute of Numerical Analysis

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.

Interpolation and Applications

29 Jul at 7:58 am

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

19 Jul at 9:25 am

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

13 Jul at 10:54 am

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

11 Oct 2018

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

27 Sep 2018

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

14 Mar 2018

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,

14 Mar 2018

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

10 Feb 2018

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

10 Feb 2018

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

10 Feb 2018

Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…