Spaces of distributions, interpolation by translates of a basis function and error estimates

Authors
Citation
W. Light et H. Wayne, Spaces of distributions, interpolation by translates of a basis function and error estimates, NUMER MATH, 81(3), 1999, pp. 415-450
Citations number
19
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
NUMERISCHE MATHEMATIK
ISSN journal
0029-599X → ACNP
Volume
81
Issue
3
Year of publication
1999
Pages
415 - 450
Database
ISI
SICI code
0029-599X(199901)81:3<415:SODIBT>2.0.ZU;2-O
Abstract
Interpolation with translates of a basis function is a common process in ap proximation theory. The most elementary form of the interpolant consists of a linear combination of all translates by interpolation points of a single basis function. Frequently, low degree polynomials are added to the interp olant. One of the significant features of this type of interpolant is that it is often the solution of a variational problem. In this paper we concent rate on developing a wide variety of spaces for which a variational theory is available. For each of these spaces, we show that there is a. natural ch oice of basis function. We also show how the theory leads to efficient ways of calculating the interpolant and to new error estimates.