Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems

This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise c...

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Main Authors:	Pornsawad, Pornsarp, Böckmann, Christine
Format:	Others
Language:	English
Published:	Universität Potsdam 2014
Subjects:	ill-posed problems Runge-Kutta methods regularization methods Hölder-type source condition stopping rules Mathematics
Online Access:	http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70834 http://opus.kobv.de/ubp/volltexte/2014/7083/

id	ndltd-Potsdam-oai-kobv.de-opus-ubp-7083
record_format	oai_dc
spelling	ndltd-Potsdam-oai-kobv.de-opus-ubp-70832015-01-06T04:07:02Z Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems Pornsawad, Pornsarp Böckmann, Christine ill-posed problems Runge-Kutta methods regularization methods Hölder-type source condition stopping rules Mathematics This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods. Universität Potsdam Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik 2014 Preprint application/pdf urn:nbn:de:kobv:517-opus-70834 http://opus.kobv.de/ubp/volltexte/2014/7083/ eng http://opus.kobv.de/ubp/doku/urheberrecht.php
collection	NDLTD
language	English
format	Others
sources	NDLTD
topic	ill-posed problems Runge-Kutta methods regularization methods Hölder-type source condition stopping rules Mathematics
spellingShingle	ill-posed problems Runge-Kutta methods regularization methods Hölder-type source condition stopping rules Mathematics Pornsawad, Pornsarp Böckmann, Christine Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
description	This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
author	Pornsawad, Pornsarp Böckmann, Christine
author_facet	Pornsawad, Pornsarp Böckmann, Christine
author_sort	Pornsawad, Pornsarp
title	Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
title_short	Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
title_full	Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
title_fullStr	Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
title_full_unstemmed	Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
title_sort	modified iterative runge-kutta-type methods for nonlinear ill-posed problems
publisher	Universität Potsdam
publishDate	2014
url	http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70834 http://opus.kobv.de/ubp/volltexte/2014/7083/
work_keys_str_mv	AT pornsawadpornsarp modifiediterativerungekuttatypemethodsfornonlinearillposedproblems AT bockmannchristine modifiediterativerungekuttatypemethodsfornonlinearillposedproblems
_version_	1716727693479772160

Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems

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