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  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Kammanee, Athassawat
T1  - Broyden method for inverse non-symmetric Sturm-Liouville problems
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of boundary value methods obtained as an extension of Numerov's method is the major tool for approximating the eigenvalues in each Broyden iteration step. Numerical examples demonstrate that the method is able to reduce the number of iteration steps, in particular for non-symmetric potentials, without accuracy loss.
KW  - Inverse Sturm-Liouville problem
KW  - Non-symmetric potential
KW  - Broyden's method
KW  - Boundary value method
Y1  - 2011
U6  - https://doi.org/10.1007/s10543-011-0317-5
SN  - 0006-3835
VL  - 51
IS  - 3
SP  - 513
EP  - 528
PB  - Springer
CY  - Dordrecht
ER  -