A numerical method for reconstructing the potential in fractional Calder\'on problem with a single measurement
<|reference_start|>A numerical method for reconstructing the potential in fractional Calder\'on problem with a single measurement: In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calder\'{o}n problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient method is utilized to solve the variational problem. Moreover, we also provide a suggestion to choose the regularization parameter. Numerical experiments are performed to illustrate the efficiency and effectiveness of the developed method and verify the theoretical results.<|reference_end|>
@article{li2024a,
    title={A numerical method for reconstructing the potential in fractional
  Calder\'{o}n problem with a single measurement},
    author={Xinyan Li},
    journal={arXiv preprint arXiv:2409.16711},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16711},
    primaryClass={math.NA cs.NA}
}