TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Sungcharoen, Parada
A1  - Böckmann, Christine
T1  - Convergence rate of the modified Landweber method for solving inverse potential problems
JF  - Mathematics : open access journal
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.
KW  - nonlinear operator
KW  - regularization
KW  - modified Landweber method
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2020
U6  - https://doi.org/10.3390/math8040608
SN  - 2227-7390
VL  - 8
IS  - 4
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Kammanee, Athassawat
A1  - Braunss, Andreas
T1  - Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem
JF  - Journal of inverse and ill-posed problems
N2  - We prove logarithmic convergence rate of the Levenberg-Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.
KW  - Levenberg-Marquardt method
KW  - inverse potential problems
KW  - logarithmic convergence rate
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2011
U6  - https://doi.org/10.1515/JIIP.2011.034
SN  - 0928-0219
VL  - 19
IS  - 3
SP  - 345
EP  - 367
PB  - De Gruyter
CY  - Berlin
ER  -