Favard’s interpolation problem in one or more variables

Autor:	Thomas Kunkle
Rok vydání:	2002
Předmět:	Differential equation General Mathematics Mathematical analysis Univariate Multivariate interpolation Combinatorics Computational Mathematics Bounded function Divided differences Constant (mathematics) Real line Analysis Interpolation Mathematics
Zdroj:	Constructive Approximation. 18:467-478
ISSN:	1432-0940 0176-4276
DOI:	10.1007/s00365-001-0015-7
Popis:	Given scattered data on the real line, Favard [4] constructed an interpolant which depends linearly and locally on the data and whose nth derivative is locally bounded by the nth divided differences of the data times a constant depending only on n. It is shown that the (n —1)th derivative of Favard’s interpolant can be likewise bounded by divided differences, and that one can bound at best two consecutive derivatives of any interpolant by the corresponding divided differences. In this sense, Favard’s univariate interpolant is the best possible. Favard’s result has been extended [8] to a special case in several variables, and here the extent to which this can be repeated in a more general setting is proven exactly.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::59ddee17395697e78d183487ccf71687 https://doi.org/10.1007/s00365-001-0015-7 Zobrazit plný text záznamu Plný text ve formátu PDF