Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions (Q639348)
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scientific article; zbMATH DE number 5948612
| Language | Label | Description | Also known as |
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| English | Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions |
scientific article; zbMATH DE number 5948612 |
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Extending the applicability of the Gauss-Newton method under average Lipschitz-type conditions (English)
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20 September 2011
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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.
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Gauss-Newton method
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recurrent function
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local/semilocal convergence
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average Lipschitz conditions
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