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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. ред. / N. N. Vasiliev. Санкт-Петербург : Издательство «ВВМ», 2024. стр. 87-94.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
}
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