On the Superlinear Convergence of the Successive Approximations Method

  • E. Cătinaş
Article

Abstract

The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+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 convergence orders in terms of some spectral elements of G′(x*); 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.

Successive approximations convergence orders inexact Newton iterates 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • E. Cătinaş
    • 1
  1. 1.Romanian Academy of SciencesT. Popoviciu Institute of Numerical AnalysisCluj-NapocaRomania

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