Application of Taylor’s Formula to Polynomial Approximation of a Function of Two Variables with Large Gradients

Application of Taylor’s Formula to Polynomial Approximation of a Function of Two Variables with Large Gradients Full article

Journal

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Output data

Year: 2025, Volume: 35, Number: 1, Pages: 87-92 Pages count : 6 DOI: 10.1134/s1055134425010079

Funding (1)

Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН».

FWNF-2022-0016

We consider approximation of a function of two variables with large gradients in a neighborhood of a point on the basis of Taylor’s formula. If the derivatives of this function are not bounded by a constant then the error of such an approximation can be significant. We represent the function as the sum of the regular and boundary layer components. Such a representation exists, for example, for solutions of singularly perturbed elliptic problems. The boundary layer component is regarded as a function of a general form. It is determined up to a factor and causes large gradientsof the function. We suggest to improve the accuracy of approximation on the basis of Taylor’s formula by constructing formulas that are exact on the boundary layer component. We prove that, in this case, the error estimate is independent of the derivatives of the boundary layer component.

Zadorin A.I.
Application of Taylor’s Formula to Polynomial Approximation of a Function of Two Variables with Large Gradients
Siberian Advances in Mathematics. 2025. V.35. N1. P.87-92. DOI: 10.1134/s1055134425010079 Scopus РИНЦ OpenAlex

Задорин А.И.
Применение формулы Тейлора для приближения многочленами функции двух переменных с большими градиентами
Математические труды. 2024. Т.27. №4. С.81-92. DOI: 10.25205/1560-750X-2024-27-4-81-92 РИНЦ

Submitted:	Sep 18, 2024
Accepted:	Oct 30, 2024
Published print:	Mar 19, 2025
Published online:	Jul 4, 2025

Scopus:	2-s2.0-105010141783
Elibrary:	82581690
OpenAlex:	W4412028542

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