High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation
<|reference_start|>High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation: We propose a high precision algorithm for solving the Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson's type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations.<|reference_end|>
@article{medvedev2024high-order,
    title={High-Order Block Toeplitz Inner-Bordering method for solving the
  Gelfand-Levitan-Marchenko equation},
    author={Sergey Medvedev, Irina Vaseva, Mikhail Fedoruk},
    journal={arXiv preprint arXiv:2405.00529},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00529},
    primaryClass={math.NA cs.NA}
}