On Optimal Approximation of Geophysical Fields

Autor:	I. V. Boikov, V. A. Ryazantsev
Rok vydání:	2021
Předmět:	Domain of a function Gravitation Numerical Analysis Constant coefficients Numerical analysis Thermal Heat equation Class (philosophy) Geophysics Optimal methods Mathematics
Zdroj:	Numerical Analysis and Applications. 14:13-29
ISSN:	1995-4247 1995-4239
Popis:	In this paper, optimal methods of approximation of some geophysical fields, in particular gravitational and thermal fields, are considered. A review of the results on this problem is presented. An algorithm of approximation for the multidimensional thermal fields described by a heat equation with constant coefficients is developed. For this, classes of functions including the solutions of heat equations are introduced, and continuous splines uniformly approximating the functions from the classes in the whole domain of definition are constructed. Upper bounds for the Kolmogorov widths of these classes of functions are given. For a wider class of the thus introduced classes of functions, a lower estimate of the Kolmogorov width is presented.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::989b38d63751c709fcdc3b977a4342ab https://doi.org/10.1134/s199542392101002x Zobrazit plný text záznamu Full text from SpringerLink