Convergence of the Gauss–Newton method for a special class of systems of equations under a majorant condition
MLN Gonçalves, PR Oliveira - Optimization, 2015 - Taylor & Francis
Optimization, 2015•Taylor & Francis
In this paper, we study the Gauss–Newton method for a special class of systems of non-
linear equation. On the hypothesis that the derivative of the function under consideration
satisfies a majorant condition, semi-local convergence analysis is presented. In this
analysis, the conditions and proof of convergence are simplified by using a simple majorant
condition to define regions where the Gauss–Newton sequence is 'well behaved'. Moreover,
special cases of the general theory are presented as applications.
linear equation. On the hypothesis that the derivative of the function under consideration
satisfies a majorant condition, semi-local convergence analysis is presented. In this
analysis, the conditions and proof of convergence are simplified by using a simple majorant
condition to define regions where the Gauss–Newton sequence is 'well behaved'. Moreover,
special cases of the general theory are presented as applications.
Abstract
In this paper, we study the Gauss–Newton method for a special class of systems of non-linear equation. On the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. In this analysis, the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where the Gauss–Newton sequence is ‘well behaved’. Moreover, special cases of the general theory are presented as applications.
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