TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sungcharoen, Parada
A1  - Böckmann, Christine
T1  - Convergence rate of the modified Landweber method for solving inverse potential problems
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1034 
KW  - nonlinear operator
KW  - regularization
KW  - modified Landweber method
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471942
SN  - 1866-8372
IS  - 1034
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335 
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433
SN  - 1866-8372
IS  - 1335
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  -