Standard

An algorithm for solving two-sided linear vector equations. / Кривулин, Николай Кимович.

International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. ed. / N. N. Vasilyev. Санкт-Петербург : Издательство «ВВМ», 2023. p. 68-74.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Кривулин, НК 2023, An algorithm for solving two-sided linear vector equations. in NN Vasilyev (ed.), International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. Издательство «ВВМ», Санкт-Петербург, pp. 68-74, Polynomial Computer Algebra 2023, Санкт-Петербург, Russian Federation, 17/04/23.

APA

Кривулин, Н. К. (2023). An algorithm for solving two-sided linear vector equations. In N. N. Vasilyev (Ed.), International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute (pp. 68-74). Издательство «ВВМ».

Vancouver

Кривулин НК. An algorithm for solving two-sided linear vector equations. In Vasilyev NN, editor, International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. Санкт-Петербург: Издательство «ВВМ». 2023. p. 68-74

Author

Кривулин, Николай Кимович. / An algorithm for solving two-sided linear vector equations. International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. editor / N. N. Vasilyev. Санкт-Петербург : Издательство «ВВМ», 2023. pp. 68-74

BibTeX

@inproceedings{bdc81fc72bb8401596b20b92884e1404,
title = "An algorithm for solving two-sided linear vector equations",
abstract = "We consider a two-sided vector equation that is defined in terms of tropical algebra as Ax=By, where A and B are given matrices, x and y are unknown vectors. We propose a new procedure to solve this equation, which is based on the minimization of the distance between vectors of tropical vector spaces generated by the columns of the given matrices. The procedure produces a pair of vectors that provide the minimum distance between the spaces. If the two-sided equation has nontrivial solutions, the obtained vectors present a solution. Otherwise, these vectors compose a pseudo-solution that minimizes the deviation between both sides of the equation.",
author = "Кривулин, {Николай Кимович}",
note = "Krivulin N. An algorithm for solving two-sided linear vector equations // International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. Ed. by N.N. Vassiliev. St. Petersburg, VVM Publishing, 2023. P. 68-74.; null ; Conference date: 17-04-2023 Through 22-04-2023",
year = "2023",
language = "English",
pages = "68--74",
editor = "Vasilyev, {N. N.}",
booktitle = "International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute",
publisher = "Издательство «ВВМ»",
address = "Russian Federation",
url = "https://pca-pdmi.ru/2023/submission",

}

RIS

TY - GEN

T1 - An algorithm for solving two-sided linear vector equations

AU - Кривулин, Николай Кимович

N1 - Krivulin N. An algorithm for solving two-sided linear vector equations // International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute. Ed. by N.N. Vassiliev. St. Petersburg, VVM Publishing, 2023. P. 68-74.

PY - 2023

Y1 - 2023

N2 - We consider a two-sided vector equation that is defined in terms of tropical algebra as Ax=By, where A and B are given matrices, x and y are unknown vectors. We propose a new procedure to solve this equation, which is based on the minimization of the distance between vectors of tropical vector spaces generated by the columns of the given matrices. The procedure produces a pair of vectors that provide the minimum distance between the spaces. If the two-sided equation has nontrivial solutions, the obtained vectors present a solution. Otherwise, these vectors compose a pseudo-solution that minimizes the deviation between both sides of the equation.

AB - We consider a two-sided vector equation that is defined in terms of tropical algebra as Ax=By, where A and B are given matrices, x and y are unknown vectors. We propose a new procedure to solve this equation, which is based on the minimization of the distance between vectors of tropical vector spaces generated by the columns of the given matrices. The procedure produces a pair of vectors that provide the minimum distance between the spaces. If the two-sided equation has nontrivial solutions, the obtained vectors present a solution. Otherwise, these vectors compose a pseudo-solution that minimizes the deviation between both sides of the equation.

UR - https://pca-pdmi.ru/2023/pca2023_book.pdf

M3 - Conference contribution

SP - 68

EP - 74

BT - International Conference Polynomial Computer Algebra '2023. St. Petersburg, April 17-22, 2023. Euler International Mathematical Institute

A2 - Vasilyev, N. N.

PB - Издательство «ВВМ»

CY - Санкт-Петербург

Y2 - 17 April 2023 through 22 April 2023

ER -

ID: 111057726