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

Pornsawad, Pornsarp; Böckmann, Christine

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

Pornsarp Pornsawad, Christine Böckmann

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.

Metadaten
Author details:	Pornsarp Pornsawad, Christine Böckmann ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-70834
ISSN:	2193-6943
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (3 (2014) 7)
Publisher:	Universitätsverlag Potsdam
Place of publishing:	Potsdam
Publication type:	Preprint
Language:	English
Year of first publication:	2014
Publication year:	2014
Publishing institution:	Universität Potsdam
Publishing institution:	Universitätsverlag Potsdam
Release date:	2014/07/08
Tag:	Hölder-type source condition; Runge-Kutta methods; ill-posed problems; regularization methods; stopping rules
Volume:	3
Issue:	7
Number of pages:	30
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	47-XX OPERATOR THEORY / 47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX) / 47J06 Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]
	47-XX OPERATOR THEORY / 47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX) / 47J25 Iterative procedures [See also 65J15]
	65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J15 Equations with nonlinear operators (do not use 65Hxx)
	65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J22 Inverse problems
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2014
Publishing method:	Universitätsverlag Potsdam
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

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

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