High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation
Numerical Analysis
2024-05-02 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2405.00529,
title = {High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation},
author = {Sergey Medvedev and Irina Vaseva and Mikhail Fedoruk},
journal= {arXiv preprint arXiv:2405.00529},
year = {2024}
}