# On 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 $$G^\prime(x^\ast)$$ has no eigenvalue equal to 0, as shown by us in [8].

However, high q-convergence orders may be attained if one considers perturbed successive approximations.

We characterize the correction terms which must be added at each step in order to obtain convergence with q-order 2 of the resulted iterates.

## Authors

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

## Keywords

fixed point problems; acceleration of convergence; nonlinear system of equations in Rn; inexact Newton method; linear systems of equation in Rn; residual; local convergence; q-convergence order.

## Cite this paper as:

E. Cătinaş, On accelerating the convergence of the successive approximations method, Rev. Anal. Numér. Théor. Approx., 30 (2001) no. 1, pp. 3-8.

1222-9024

2457-8126

1222-9024

2457-8126