On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton-type methods Ώ]-[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]-[12], in some intersting cases. Numerical examples are also provided in this study.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2011
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300001 |
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