## Abstract

The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations *x*_{k+1} = *G*(*x*_{k}) near a fixed point *x**. Different conditions [ultimately on the magnitude of *G*′(*x**)] provide lower bounds for the convergence order of the process as a whole.

In this paper, we consider only one such sequence and we characterize its high q-convergence orders in terms of some spectral elements of *G*′(*x**); we obtain that the set of trajectories with high q-convergence orders is restricted to some affine subspaces, regardless of the nonlinearity of *G*.

We analyze also the stability of the successive approximations under perturbation assumptions.

## Authors

Emil Cătinaş

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

fixed point; successive approximations; nonlinear system of equations in Rn; inexact Newton method; perturbed Newton method; linear systems of equation in Rn; residual; local convergence; q-convergence orders.

## Cite this paper as:

E. Cătinaş, *On the superlinear convergence of the successive approximations method*, J. Optim. Theory Appl., **113** (2002) no. 3, pp. 473-485.

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## About this paper

##### Publisher Name

Kluwer Academic Publishers-Plenum Publishers

##### Print ISSN

0022-3239

##### Online ISSN

1573-2878

##### MR

0022-3239

##### Online ISSN

1573-2878

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## References

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