On accelerating the convergence of the successive approximations method

Authors

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

Keywords:

successive approximations, inexact Newton methods, quadratic convergence, acceleration of the convergence of successive approximations

Abstract

In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one considers perturbed successive approximations.
We characterize the correction terms which must be added at each step in order to obtain convergence with q-order 2 of the resulted iterates.

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Published

2001-02-01

How to Cite

Cătinaş, E. (2001). On accelerating the convergence of the successive approximations method. Rev. Anal. Numér. Théor. Approx., 30(1), 3–8. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art1

Issue

Vol. 30 No. 1 (2001)

Section

Articles

License

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.