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Solution of tropical best approximation problems. / Кривулин, Николай Кимович.

International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024. ed. / N. N. Vasiliev. Санкт-Петербург : Издательство «ВВМ», 2024. p. 87-94.

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

Harvard

Кривулин, НК 2024, Solution of tropical best approximation problems. in NN Vasiliev (ed.), International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024. Издательство «ВВМ», Санкт-Петербург, pp. 87-94, Polynomial Computer Algebra 2024, Санкт-Петербург, Russian Federation, 15/04/24.

APA

Кривулин, Н. К. (2024). Solution of tropical best approximation problems. In N. N. Vasiliev (Ed.), International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024 (pp. 87-94). Издательство «ВВМ».

Vancouver

Кривулин НК. Solution of tropical best approximation problems. In Vasiliev NN, editor, International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024. Санкт-Петербург: Издательство «ВВМ». 2024. p. 87-94

Author

Кривулин, Николай Кимович. / Solution of tropical best approximation problems. International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024. editor / N. N. Vasiliev. Санкт-Петербург : Издательство «ВВМ», 2024. pp. 87-94

BibTeX

@inproceedings{369ff82b839f4a5882161a63a8564bd0,
title = "Solution of tropical best approximation problems",
abstract = "We consider discrete best approximation problems in the framework of tropical algebra, which focuses on semirings and semifields with idempotent addition. Given a set of samples from input and output of an unknown function defined on an idempotent semifield, the problem is to find a best approximation of the function by tropical Puiseux polynomial and rational functions. We describe a solution approach that transforms the problem into the best approximation of linear vector equations. Application of this approach yields a direct analytical solution for the polynomial approximation problem and an iterative algorithmic solution for approximation by rational functions. As an illustration, we present results of the best Chebyshev approximation by piecewise linear functions.",
author = "Кривулин, {Николай Кимович}",
note = "Krivulin N. Solution of tropical best approximation problems. In N. N. Vasiliev, Ed. International Conference Polynomial Computer Algebra '2024. Euler International Mathematical Institute, April 15-20, 2024. St. Petersburg, VVM Publishing, 2024. P. 87-94.; Polynomial Computer Algebra 2024, PCA '2024 ; Conference date: 15-04-2024 Through 20-04-2024",
year = "2024",
language = "English",
pages = "87--94",
editor = "Vasiliev, {N. N.}",
booktitle = "International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024",
publisher = "Издательство «ВВМ»",
address = "Russian Federation",
url = "https://pca-pdmi.ru/2024/",

}

RIS

TY - GEN

T1 - Solution of tropical best approximation problems

AU - Кривулин, Николай Кимович

N1 - Conference code: 17

PY - 2024

Y1 - 2024

N2 - We consider discrete best approximation problems in the framework of tropical algebra, which focuses on semirings and semifields with idempotent addition. Given a set of samples from input and output of an unknown function defined on an idempotent semifield, the problem is to find a best approximation of the function by tropical Puiseux polynomial and rational functions. We describe a solution approach that transforms the problem into the best approximation of linear vector equations. Application of this approach yields a direct analytical solution for the polynomial approximation problem and an iterative algorithmic solution for approximation by rational functions. As an illustration, we present results of the best Chebyshev approximation by piecewise linear functions.

AB - We consider discrete best approximation problems in the framework of tropical algebra, which focuses on semirings and semifields with idempotent addition. Given a set of samples from input and output of an unknown function defined on an idempotent semifield, the problem is to find a best approximation of the function by tropical Puiseux polynomial and rational functions. We describe a solution approach that transforms the problem into the best approximation of linear vector equations. Application of this approach yields a direct analytical solution for the polynomial approximation problem and an iterative algorithmic solution for approximation by rational functions. As an illustration, we present results of the best Chebyshev approximation by piecewise linear functions.

UR - https://pca-pdmi.ru/2024/pca2024_book.pdf

M3 - Conference contribution

SP - 87

EP - 94

BT - International Conference Polynomial Computer Algebra '2024. St. Petersburg, Russia. April 15-20, 2024

A2 - Vasiliev, N. N.

PB - Издательство «ВВМ»

CY - Санкт-Петербург

T2 - Polynomial Computer Algebra 2024

Y2 - 15 April 2024 through 20 April 2024

ER -

ID: 124160014