On the Gauss-Newton Method for Solving Equations


  • Ioannis K. Argyros Cameron University.
  • Saïd Hilout Poitiers University.




Gauss—Newton method, semilocal convergence, Frechet—derivative, Lipschitz/center—Lipschitz condition, convergence domain, método de Gauss-Newton, convergencia semilocal, derivada de Frechet, condición de Lipschitz, centro de Lipschitz.


We use a combination of the center—Lipschitz condition with the Lipschitz condition condition on the Frechet—derivative of the opera­tor involved to provide a semilocal convergence analysis ofthe Gauss-Newton method to a solution ofan 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 [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution.

Author Biographies

Ioannis K. Argyros, Cameron University.

Department of Mathematics Sciences.

Saïd Hilout, Poitiers University.

Laboratoire de Mathématiques et Applications.


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[10] Y. Yuan, W. Sun, Optimization theory and methods. Nonlinear Programming. Springer Optimization and Its Applications, Springer, New York, (2006).



How to Cite

I. K. Argyros and S. Hilout, “On the Gauss-Newton Method for Solving Equations”, Proyecciones (Antofagasta, On line), vol. 31, no. 1, pp. 11-24, Jan. 2012.




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