On an Aitken-Steffensen-Newton type methodOctober 11, 2018Ion Păvăloiu(original), divided differences, inverse interpolation, iterative methods, local convergence, Newton method, nonlinear equations in R, Numerical Analysis, paper, Steffenssen methods2018Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We…Read More

On the r-convergence orders of the inexact perturbed Newton methodsFebruary 10, 2018Emil Cătinaş(original), convergence orders, inexact/perturbed iterations, iterative methods, local convergence, Numerical Analysis, paper1999Abstract The inexact perturbed Newton methods recently introduced by us are variant of Newton method, which assume that at each step…Read More

Estimating the radius of an attraction ballFebruary 10, 2018Emil Cătinaş(original), fixed point theory, inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations2009Abstract 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…Read More

On the convergence of some quasi-Newton iterates studied by I. PăvăloiuFebruary 10, 2018Emil Cătinaş(original), fixed point theory, iterative methods, local convergence, Newton method, nonlinear equations in Banach spaces, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations2015Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…Read More

The inexact, inexact perturbed and quasi-Newton methods are equivalent modelsFebruary 10, 2018Emil Cătinaş(original), inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper2005Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…Read More

Affine invariant conditions for the inexact perturbed Newton methodFebruary 10, 2018Emil Cătinaş(original), inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper2002Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…Read More

Inexact perturbed Newton methods and applications to a class of Krylov solversFebruary 10, 2018Emil Cătinaş(original), inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper2001Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…Read More

On accelerating the convergence of the successive approximations methodFebruary 10, 2018Emil Cătinaş(original), fixed point theory, inexact/perturbed iterations, iterative methods, local convergence, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations2001Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…Read More

A note on the quadratic convergence of the inexact Newton methodsFebruary 10, 2018Emil Cătinaş(original), inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper2000Abstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…Read More

On the high convergence orders of the Newton-GMBACK methodsFebruary 10, 2018Emil Cătinaşinexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper1999Abstract GMBACK is a Krylov solver for linear systems in \(\mathbb{R}^n\). We analyze here the high convergence orders (superlinear convergence)…Read More