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On the approximate solutions of implicit functions using the Steffensen method

8 years ago

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

Estimating the radius of an attraction ball

8 years ago

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

8 years ago

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

The inexact, inexact perturbed and quasi-Newton methods are equivalent models

8 years ago

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

Sufficient convergence conditions for certain accelerated successive approximations

8 years ago

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

On the superlinear convergence of the successive approximations method

8 years ago

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

Affine invariant conditions for the inexact perturbed Newton method

8 years ago

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

Inexact perturbed Newton methods and applications to a class of Krylov solvers

8 years ago

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

On accelerating the convergence of the successive approximations method

8 years ago

Abstract No q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when…

A note on the quadratic convergence of the inexact Newton methods

8 years ago

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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