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.


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


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.


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