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arXiv · 2405.00529

High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation

Sergey Medvedev·Irina Vaseva·Mikhail Fedoruk
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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.

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Sergey Medvedev, Irina Vaseva, Mikhail Fedoruk. 2024-05-01. High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation. https://arxiv.org/abs/2405.00529

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