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

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High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation. / Medvedev, S. B.; Vaseva, I. A.; Fedoruk, M. P.

в: Communications in Nonlinear Science and Numerical Simulation, Том 138, 108255, 11.2024.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{0ace96178f2244248a919879c3e0a3c7,

title = "High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation",

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. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.",

keywords = "Gelfand–Levitan–Marchenko equation, Gregory quadrature formulas, Inverse scattering transform, Nonlinear Fourier transform, Toeplitz Inner-Bordering method, Woodbury formula",

author = "Medvedev, {S. B.} and Vaseva, {I. A.} and Fedoruk, {M. P.}",

note = "M.P. Fedoruk was supported by the Russian Science Foundation (Grant No. 20-11-20040).",

year = "2024",

month = nov,

doi = "10.1016/j.cnsns.2024.108255",

language = "English",

volume = "138",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation

AU - Medvedev, S. B.

AU - Vaseva, I. A.

AU - Fedoruk, M. P.

N1 - M.P. Fedoruk was supported by the Russian Science Foundation (Grant No. 20-11-20040).

PY - 2024/11

Y1 - 2024/11

N2 - 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. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.

AB - 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. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.

KW - Gelfand–Levitan–Marchenko equation

KW - Gregory quadrature formulas

KW - Inverse scattering transform

KW - Nonlinear Fourier transform

KW - Toeplitz Inner-Bordering method

KW - Woodbury formula

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200551638&origin=inward&txGid=87df3ae9cb42929584050163bfbdceef

UR - https://www.mendeley.com/catalogue/326d9eba-af7d-3889-b79b-fe16b41cd000/

U2 - 10.1016/j.cnsns.2024.108255

DO - 10.1016/j.cnsns.2024.108255

M3 - Article

VL - 138

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 108255

ER -

ID: 60385546