Approximation of the Derivatives of a Function in Lagrange Interpolation on Low-Dimensional Simplices

Autor:	N. V. Baidakova, Yu. N. Subbotin
Rok vydání:	2021
Předmět:	Polynomial symbols.namesake Mathematics (miscellaneous) Simplex Lagrange polynomial symbols Mathematics::Metric Geometry Applied mathematics Differentiable function Function (mathematics) Grid Interpolation Mathematics
Zdroj:	Proceedings of the Steklov Institute of Mathematics. 312:261-269
ISSN:	1531-8605 0081-5438
DOI:	10.1134/s008154382101017x
Popis:	We address the problem of approximating the derivatives of a differentiable function of $$m$$ variables ( $$m=3,4$$ ) by the derivatives of a polynomial on an $$m$$ -simplex for the standard method of interpolation by Lagrange polynomials at the points of a uniform grid on this simplex. For the error of approximation of these derivatives by the derivatives of the interpolation polynomial, we obtain upper bounds expressed in terms of new geometric characteristics of the simplex. The proposed characteristics of the simplex are clear and easy to calculate.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4e627730c449c0c10a6136e8dcb39813 https://doi.org/10.1134/s008154382101017x Zobrazit plný text záznamu Full text from SpringerLink