versão impressa ISSN 0716-0917
Proyecciones (Antofagasta) vol.31 no.1 Antofagasta mar. 2012
Proyecciones Journal of Mathematics Vol. 31, No 1, pp. 11-24, March 2012. Universidad Catolica del Norte Antofagasta - Chile
On the GaussNewton method for solving equations
Ioaniss K. Argyros
Cameron University, U.S.A.
Poitiers University, France
We use a combination of the centerLipschitz condition with the Lipschitz condition condition on the Frechetderivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss Newton method with the following advantages over the corresponding results in : larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution
AMS Subject Classification. 65F20, 65G99, 65H10, 49M15.
Key Words. GaussNewton method, semilocal convergence, Frechet derivative, Lipschitz/centerLipschitz condition, convergence domain.
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Ioannis K. Argyros
Department of Mathematics Sciences Cameron university
Lawton, OK 73505, U.S.A.
e-mail : firstname.lastname@example.org
Laboratoire de Mathematiques et Applications
Bd. Pierre et Marie Curie,
Teleport 2, B.P. 30179
86962 Futuroscope Chasseneuil Cedex,
e-mail : email@example.com
Received : January 2011. Accepted : October 2011