On a family of high-order iterative methods under gamma conditions with applications in denoising
- Amat, S. 1
- Hernández, M.A. 2
- Romero, N. 2
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1
Universidad Politécnica de Cartagena
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2
Universidad de La Rioja
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ISSN: 0029-599X
Année de publication: 2014
Volumen: 127
Número: 2
Pages: 201-221
Type: Article
beta Ver similares en nube de resultadosD'autres publications dans: Numerische Mathematik
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Résumé
We study a class of at least third order iterative methods for nonlinear equations on Banach spaces. A characterization of the convergence under Gamma-type conditions is presented. Though, in general, these methods are not very extended due to their computational costs, we can find examples in which they are competitive and even cheaper than other simpler methods. Indeed, we propose a new nonlinear mathematical model for the denoising of digital images, where the best method in the family has fourth order of convergence. Moreover, our family includes two-step Newton type methods with good numerical behavior in general. We center our analysis in both, analytic and computational, aspects. © 2013 Springer-Verlag Berlin Heidelberg.