## 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…

Abstract The inexact perturbed Newton methods recently introduced by us are variant of Newton method, which assume that at each step…

Abstract AuthorsIoannis K. Argyros (Cameron University, USA) Emil Cătinaş (Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy) Ion Păvăloiu (Tiberiu…

Abstract We use perturbed Steffensen-Aitken methods to approximate a locally unique solution of an operator equation in a Banach space. Using…

Abstract We use inexact Steffensen-Aitken-type methods to approximate implicit functions in a Banach space. Using a projection operator our equation reduces to…

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…

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

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

Abstract We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these…

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…

Book summarySummary of the book… Book coverContentsCh. 1 Keywordskeyword1, PDFpdf file Referencessee the expanding block below Cite this book as:Author, title, publisher, year. Book TitlePublisherPrint ISBNAuthorsV. Soporan, C. Vamos, C.…

Read More AbstractWe consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our previous analysis in [Numer. Math. 144, 451–477, 2020] to the convection-dominated regime.…

Read More Book summarySummary of the book… Book coverContents1.Variational formulations 1.1. A 1D model problem 1.2. A 2D model problem (lapace eqution) 1.3. Some other boundary value problems 1.4. An eigenvalue problem…

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