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On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible

dc.creatorArgyros, Ioannis K.
dc.creatorHilout, Saïd
dc.date2011-10-01
dc.identifierhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1359
dc.identifier10.4067/S0719-06462011000300001
dc.descriptionWe 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 Fr´echet– derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton–type methods [1]–[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.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1359/1213
dc.sourceCUBO, A Mathematical Journal; Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal; 1–15en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 13 Núm. 3 (2011): CUBO, A Mathematical Journal; 1–15es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectNewton–type methodsen-US
dc.subjectBanach spaceen-US
dc.subjectsmall divisorsen-US
dc.subjectnon–invertible operatorsen-US
dc.subjectsemilocal convergenceen-US
dc.subjectNewton–Kantorovich–type hypothesisen-US
dc.titleOn the semilocal convergence of Newton–type methods, when the derivative is not continuously invertibleen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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