Affine invariant conditions for the inexact perturbed Newton method

Emil Cătinaş

doi:10.33993/jnaat311-704

Authors

Emil Cătinaş Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat311-704

Keywords:

inexact and inexact perturbed Newton methods, affine invariant conditions, convergence orders

Abstract views: 269

Abstract

The high 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 convergence orders of the inexact perturbed Newton iterates.

Downloads

Download data is not yet available.

References

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

E. Catinas, On the high convergence orders of the Newton-GMBACK methods, Rev. Anal. Numer. Theor. Approx.,28(1999) no. 2, 125-132, https://ictp.acad.ro/high-convergence-orders-newton-gmback-methods/

E. Catinas, Newton and Newton-Krylov Methods for Solving Nonlinear Systems in Rn, Ph.D. thesis, "Babes-Bolyai" University of Cluj-Napoca, Romania, 1999.

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

E. Catinas, Inexact perturbed Newton methods and applications to a class of Krylov solvers, J. Optim. Theory Appl.,108(2001) no. 3, 543-570, https://ictp.acad.ro/inexact-perturbed-newton-methods-applications-class-krylov-solvers/ DOI: https://doi.org/10.1023/A:1017583307974

E. Catinas, On the superlinear convergence of the successive approximations method, J. Optim. Theory Appl.,113(2002) no. 3, 473-485, https://ictp.acad.ro/superlinear-convergence-successive-approximations-method/ DOI: https://doi.org/10.1023/A:1015304720071

E. Catinas, The inexact, inexact perturbed and quasi-Newton methods are equivalent models, Math. Comp.74(2005) no. 249, 291-301, https://doi.org/10.1090/S0025-5718-04-01646-1 DOI: https://doi.org/10.1090/S0025-5718-04-01646-1

Dembo, R. S., Eisenstat, S. C. and Steihaug, T., Inexact Newton methods, SIAMJ. Numer. Anal.,19(1982), pp. 400-408, https://doi.org/10.1137/0719025 DOI: https://doi.org/10.1137/0719025

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, https://doi.org/10.1137/0716001 DOI: https://doi.org/10.1137/0716001

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, https://doi.org/10.1137/0729080 DOI: https://doi.org/10.1137/0729080

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

Walker, H. F., An approach to continuation using Krylov subspace methods, Compu-tational 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.

Ypma, T. J., Local convergence of inexact Newton methods, SIAM J. Numer. Anal., 21 (1984), pp. 583-590, https://doi.org/10.1137/0721040 DOI: https://doi.org/10.1137/0721040