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On the superlinear convergence of the successive approximations method

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Emil Catinas

Editorial: Journal of Optimization Theory and Applications, 113, no. 3, p.473-485, 2002.


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 $x^ast$. Different conditions (ultimately on the magnitude of $G(x^ast)$) 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 convergence orders in terms of some spectral elements of $G(x^ast)$; we obtain that the set of trajectories with high 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.

Cuvinte cheie: aproximatii succesive, ordine de convergenta, iteratii Newton inexacte // successive approximations, convergence orders, inexact Newton iterates