@article{BoeckmannKammaneeBraunss2011,
  author    = {B{\"o}ckmann, Christine and Kammanee, Athassawat and Braunss, Andreas},
  title     = {Logarithmic convergence rate of Levenberg-Marquardt method with application to an inverse potential problem},
  series = {Journal of inverse and ill-posed problems},
  volume    = {19},
  journal   = {Journal of inverse and ill-posed problems},
  number    = {3},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0928-0219},
  doi       = {10.1515/JIIP.2011.034},
  pages     = {345 -- 367},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{BoeckmannKammanee2011,
  author    = {B{\"o}ckmann, Christine and Kammanee, Athassawat},
  title     = {Broyden method for inverse non-symmetric Sturm-Liouville problems},
  series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
  volume    = {51},
  journal   = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
  number    = {3},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0006-3835},
  doi       = {10.1007/s10543-011-0317-5},
  pages     = {513 -- 528},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Kammanee2010,
  author    = {Kammanee, Athassawat},
  title     = {Some inverse potential problems},
  address   = {Potsdam},
  pages     = {XIV, 128 S.},
  year      = {2010},
  language  = {en}
}
@article{KammaneeBoeckmann2009,
  author    = {Kammanee, Athassawat and B{\"o}ckmann, Christine},
  title     = {Boundary value method for inverse Sturm-Liouville problems},
  issn      = {0096-3003},
  doi       = {10.1016/j.amc.2009.04.002},
  year      = {2009},
  abstract  = {In this paper we present a method to recover symmetric and non-symmetric potential functions of inverse Sturm- Liouville problems from the knowledge of eigenvalues. The linear multistep method coupled with suitable boundary conditions known as boundary value method (BVM) is the main tool to approximate the eigenvalues in each iteration step of the used Newton method. The BVM was extended to work for Neumann-Neumann boundary conditions. Moreover, a suitable approximation for the asymptotic correction of the eigenvalues is given. Numerical results demonstrate that the method is able to give good results for both symmetric and non-symmetric potentials.},
  language  = {en}
}