On accelerating the convergence of the successive approximations method

Emil Cătinaş

doi:10.33993/jnaat301-675

Authors

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

DOI:

https://doi.org/10.33993/jnaat301-675

Keywords:

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

Abstract views: 295

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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