Extending the applicability of inexact Gauss--Newton method for solving underdetermined nonlinear least squares problems
J. Korean Math. Soc. 2019 Vol. 56, No. 2, 311-327
Published online 2019 Mar 01
Ioannis Konstantinos Argyros, Gilson do Nascimento Silva
Cameron University; CCET/UFOB
Abstract : The aim of this paper is to extend the applicability of Gauss-Newton method for solving underdetermined nonlinear least squares problems in cases not covered before. The novelty of the paper is the introduction of a restricted convergence domain. We find a more precise location where the Gauss-Newton iterates lie than in earlier studies. Consequently the Lipschitz constants are at least as small as the ones used before. This way and under the same computational cost, we extend the local as well the semilocal convergence of Gauss-Newton method. The new developmentes are obtained under the same computational cost as in earlier studies, since the new Lipschitz constants are special cases of the constants used before. Numerical examples further justify the theoretical results.
Keywords : Gauss-Newton method, restricted domain, nonlinear least squares problems, weaker majorant condition
MSC numbers : Primary 65K05, 65K15, 49M15, 49M37
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