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…
Read MoreA survey on the high convergence orders and computational convergence orders of sequences
(survey), convergence orders, history, iterative methods, local convergence, nonlinear equations in Banach spaces, nonlinear equations in R, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations
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Abstract The convergence orders (convergence rates) of convergent sequences toward their limit are fundamental notions from Mathematical Analysis and Numerical…
Read MoreOn 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…
Read MoreEstimating 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…
Read MoreOn the convergence of some quasi-Newton iterates studied by I. Păvăloiu
Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…
Read MoreThe inexact, inexact perturbed and quasi-Newton methods are equivalent models
Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…
Read MoreAffine invariant conditions for the inexact perturbed Newton method
Abstract The high convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…
Read MoreInexact perturbed Newton methods and applications to a class of Krylov solvers
Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…
Read MoreOn accelerating the convergence of the successive approximations method
Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…
Read MoreA note on the quadratic convergence of the inexact Newton methods
Abstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…
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