Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions
Copyright policy )Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions
This paper deals with convergence analysis for the Gauss-Newton method. Using the new idea of recurrent functions, and a combination of average Lipschitz/central Lipschitz conditions, the authors provide a semilocal/local convergence analysis for the Gauss-Newton method to approximate a locally unique solution of a system of equations in finite dimensional spaces. The results obtained extended the work of \textit{C. Li, N. Hu} and \textit{J. Wang} [J. Complexity 26, No.~3, 268--295 (2010; Zbl 1192.65057)] under weaker or the same conditions. Larger convergence domains are provided.
- University of Poitiers France
- French National Centre for Scientific Research France
- Laboratoire de Mathématiques et Applications France
- Cameron University United States
Gauss-Newton method, Numerical computation of solutions to systems of equations, average Lipschitz conditions, recurrent function, local/semilocal convergence
Gauss-Newton method, Numerical computation of solutions to systems of equations, average Lipschitz conditions, recurrent function, local/semilocal convergence
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