## Abstract

The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant conditions. Using these results, we obtain affine invariant characterizations for the q-convergence orders of the inexact perturbed Newton iterates.

## Authors

Emil **Cătinaş**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

inexact perturbed Newton methods; affine invariant conditions; q-convergence orders.

## Cite this paper as:

E. Cătinaş, *Affine invariant conditions for the inexact perturbed Newton method*, Rev. Anal. Numér. Théor. Approx., **31** (2002) no. 1, pp. 17-20.

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## About this paper

##### Publisher Name

##### Paper on the journal website

##### Print ISSN

1222-9024

##### Online ISSN

2457-8126

##### MR

1222-9024

##### Online ISSN

2457-8126

## Google Scholar citations

[1] I. Argyros and F. Szidarovsky, *The Theory and Applications of Iteration Methods*, C.R.C. Press Inc., Boca Raton, FL, 1993.

[2] E. Catinas, *On the high convergence orders of the Newton-GMBACK methods*, Rev.Anal. Numer. Th ́eor. Approx.,28(1999) no. 2, 125-132, http://ictp.acad.ro/jnaat

[3] E. Catinas, *Newton and Newton-Krylov Methods for Solving Nonlinear Systems inRn, Ph.D. thesis*, “Babes–Bolyai” University of Cluj-Napoca, Romania, 1999.

[4] E. Catinas, *A note on the quadratic convergence of the inexact Newton methods*, Rev.Anal. Numer. Theor. Approx.,29(2000) no. 2, 129-133, http://ictp.acad.ro/jnaat

[5] E. Catinas, *Inexact perturbed Newton methods and applications to a class of Krylovsolvers*, J. Optim. Theory Appl.,108(2001) no. 3, 543-570, http://ictp.acad.ro/catinas/catinaspb.htm

[6] E. Catinas, *On the superlinear convergence of the successive approximations method*, J. Optim. Theory Appl.,113(2002) no. 3, 473-485, http://ictp.acad.ro/catinas/catinaspb.htm

[7] E. Catinas, *The inexact, inexact perturbed and quasi-Newton methods are equivalentmodels*, Math. Comp.74(2005) no. 249, 291-301, http://ictp.acad.ro/catinas/catinaspb.htm

[8] Dembo, R. S., Eisenstat, S. C. and Steihaug, T., *Inexact Newton methods*, SIAMJ. Numer. Anal.,19(1982), pp. 400-408.

[9] Deuflhard, P.and Heindl, G., *Affine invariant convergence theorems for Newton’smethod and extensions to related methods*, SIAM J. Numer. Anal.,16(1979), pp. 1-10.

[10] Deuflhard, P.and Potra, F. A., *Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem*, SIAM J. Numer. Anal.,29(1992), pp. 1395-1412.

[11] Ortega, J. M.and Rheinboldt, W. C., *Iterative Solution of Nonlinear Equations in Several Variables,* Academic Press, New York, 1970.

[12] Walker, H. F., *An approach to continuation using Krylov subspace methods*, Computational Science in the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J. L.Lions, J. Periaux and M. F. Wheeler, eds., John Wiley and Sons, Ltd., 1997, pp. 72-82.

[13] Ypma, T. J., *Local convergence of inexact Newton methods*, SIAM J. Numer. Anal.,21(1984), pp. 583-590.Received by the editors: October 3, 2001.