# Sufficient convergence conditions for certain accelerated successive approximations

## Abstract

We have recently characterized the q-quadratic convergence of the perturbed successive approximations. For a particular choice of the parameters, these sequences resulted as accelerated iterations toward a fixed point. We give here a Kantorovich-type result, which provides sufficient conditions ensuring the convergence of the accelerated iterates.

## Authors

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

fixed point; successive approximations; accelerated successive approximations; nonlinear system of equations in Rn; inexact Newton method; perturbed Newton method; ; local convergence; convergence order.

## PDF

Scanned paper.

##### Cite this paper as:

E. Cătinaş, Sufficient convergence conditions for certain accelerated successive approximations. In: Mache D.H., Szabados J., de Bruin M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151, pp. 71-75, 2005. Birkhäuser Basel

##### Book

Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151.

Birkhäuser Basel

##### Print ISBN

978-3-7643-7124-1

##### Online ISBN

978-3-7643-7356-6