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http://dx.doi.org/10.4134/JKMS.2014.51.5.955

LOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD FOR INJECTIVE-OVERDETERMINED SYSTEMS  

Amat, Sergio (Departamento de Matematica Aplicada y Estadistica Universidad Politecnica de Cartagena)
Argyros, Ioannis Konstantinos (Department of Mathematics Sciences Cameron University)
Magrenan, Angel Alberto (Departamento de TFG/TFM Universidad Internacional de La Rioja)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 955-970 More about this Journal
Abstract
We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.
Keywords
the Gauss-Newton method; Hilbert spaces; majorant condition; local convergence; radius of convergence; injective-overdetermined systems;
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