Remarkable Haar spaces of multivariate piecewise polynomials

Autor:	Giampietro Allasia
Rok vydání:	2017
Předmět:	Discrete mathematics Sequence Box spline Applied Mathematics Univariate Basis function 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Normal distribution Probability theory Piecewise 0101 mathematics Mathematics Interpolation
Zdroj:	Numerical Algorithms. 78:661-672
ISSN:	1572-9265 1017-1398
DOI:	10.1007/s11075-017-0394-x
Popis:	Some families of Haar spaces in $\mathbb {R}^{d},~ d\ge 1,$ whose basis functions are d-variate piecewise polynomials, are highlighted. The starting point is a sequence of univariate piecewise polynomials, called Lobachevsky splines, arised in probability theory and asymptotically related to the normal density function. Then, it is shown that d-variate Lobachevsky splines can be expressed as products of Lobachevsky splines. All these splines have simple analytic expressions and subsets of them are suitable for scattered data interpolation, allowing efficient computation and plain error analysis.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a0ccf06eb47de96fb5d7368070e626aa https://doi.org/10.1007/s11075-017-0394-x Zobrazit plný text záznamu Full text from SpringerLink