TY  - GEN
A1  - Böckmann, Christine
A1  - Osterloh, Lukas
T1  - Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 907 
KW  - inverse ill-posed problem
KW  - integral equation
KW  - laser remote sensing
KW  - inverse scattering
KW  - aerosol size distribution
KW  - 65R32
KW  - 47A52
KW  - 65R20
KW  - 78A46
KW  - iterative regularization
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-441200
SN  - 1866-8372
IS  - 907
SP  - 150
EP  - 165
ER  - 
TY  - INPR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
T1  - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 
KW  - ill-posed problems
KW  - Runge-Kutta methods
KW  - regularization methods
KW  - Hölder-type source condition
KW  - stopping rules
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834
SN  - 2193-6943
VL  - 3
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -