Standard

The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method. / Botchev, Mikhail A.; Kabanikhin, Sergey I.; Shishlenin, Maxim A. и др.

в: Journal of Inverse and Ill-Posed Problems, Том 31, № 2, 01.04.2023, стр. 203-221.

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

Harvard

Botchev, MA, Kabanikhin, SI, Shishlenin, MA & Tyrtyshnikov, EE 2023, 'The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method', Journal of Inverse and Ill-Posed Problems, Том. 31, № 2, стр. 203-221. https://doi.org/10.1515/jiip-2022-0092

APA

Botchev, M. A., Kabanikhin, S. I., Shishlenin, M. A., & Tyrtyshnikov, E. E. (2023). The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method. Journal of Inverse and Ill-Posed Problems, 31(2), 203-221. https://doi.org/10.1515/jiip-2022-0092

Vancouver

Botchev MA, Kabanikhin SI, Shishlenin MA, Tyrtyshnikov EE. The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method. Journal of Inverse and Ill-Posed Problems. 2023 апр. 1;31(2):203-221. doi: 10.1515/jiip-2022-0092

Author

Botchev, Mikhail A. ; Kabanikhin, Sergey I. ; Shishlenin, Maxim A. и др. / The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method. в: Journal of Inverse and Ill-Posed Problems. 2023 ; Том 31, № 2. стр. 203-221.

BibTeX

@article{2cd8e6829daf4533b82af8f78f0c8bbb,
title = "The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method",
abstract = "The horizontally diagonalize and fit (HDF) method is proposed to solve the ill-posed Cauchy problem for the three-dimensional Poisson equation with data given on the part of the boundary (a continuation problem). The HDF method consists in discretization over horizontal variables and transformation of the system of differential equations to a diagonal form. This allows to uncouple the original three-dimensional continuation problem into a moderate number of one-dimensional problems in the vertical dimension. The problem size reduction can be carried taking into account the noise level, so that the number k of one-dimensional problems appears to be a regularization parameter. Our experiments show that HDF is applicable to large-scale problems and for n ≤ 2500 is significantly more efficient than Landweber iteration.",
keywords = "Continuation problem, inverse and ill-posed problem, regularization, singular values",
author = "Botchev, {Mikhail A.} and Kabanikhin, {Sergey I.} and Shishlenin, {Maxim A.} and Tyrtyshnikov, {Eugene E.}",
year = "2023",
month = apr,
day = "1",
doi = "10.1515/jiip-2022-0092",
language = "English",
volume = "31",
pages = "203--221",
journal = "Journal of Inverse and Ill-Posed Problems",
issn = "0928-0219",
publisher = "Walter de Gruyter GmbH",
number = "2",

}

RIS

TY - JOUR

T1 - The Cauchy problem for the 3D Poisson equation: Landweber iteration vs. horizontally diagonalize and fit method

AU - Botchev, Mikhail A.

AU - Kabanikhin, Sergey I.

AU - Shishlenin, Maxim A.

AU - Tyrtyshnikov, Eugene E.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - The horizontally diagonalize and fit (HDF) method is proposed to solve the ill-posed Cauchy problem for the three-dimensional Poisson equation with data given on the part of the boundary (a continuation problem). The HDF method consists in discretization over horizontal variables and transformation of the system of differential equations to a diagonal form. This allows to uncouple the original three-dimensional continuation problem into a moderate number of one-dimensional problems in the vertical dimension. The problem size reduction can be carried taking into account the noise level, so that the number k of one-dimensional problems appears to be a regularization parameter. Our experiments show that HDF is applicable to large-scale problems and for n ≤ 2500 is significantly more efficient than Landweber iteration.

AB - The horizontally diagonalize and fit (HDF) method is proposed to solve the ill-posed Cauchy problem for the three-dimensional Poisson equation with data given on the part of the boundary (a continuation problem). The HDF method consists in discretization over horizontal variables and transformation of the system of differential equations to a diagonal form. This allows to uncouple the original three-dimensional continuation problem into a moderate number of one-dimensional problems in the vertical dimension. The problem size reduction can be carried taking into account the noise level, so that the number k of one-dimensional problems appears to be a regularization parameter. Our experiments show that HDF is applicable to large-scale problems and for n ≤ 2500 is significantly more efficient than Landweber iteration.

KW - Continuation problem

KW - inverse and ill-posed problem

KW - regularization

KW - singular values

UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85147713447&partnerID=40&md5=07a0db71d848ea3408e53d1025f06ecd

UR - https://www.mendeley.com/catalogue/e7c3b01c-94ef-3042-b31e-e46f38a93d6f/

U2 - 10.1515/jiip-2022-0092

DO - 10.1515/jiip-2022-0092

M3 - Article

VL - 31

SP - 203

EP - 221

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 2

ER -

ID: 50058834