On multivariate approximation by integer translates of a basis function |
| |
Authors: | N Dyn I R H Jackson D Levin A Ron |
| |
Institution: | (1) School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel;(2) Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, England;(3) School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel;(4) Computer Sciences Department, University of Wisconsin-Madison, 53706 Madison, WI, USA |
| |
Abstract: | Approximation properties of the dilations of the integer translates of a smooth function, with some derivatives vanishing
at infinity, are studied. The results apply to fundamental solutions of homogeneous elliptic operators and to “shifted” fundamental
solutions of the iterated Laplacian. Following the approach from spline theory, the question of polynomial reproduction by
quasi-interpolation is addressed first. The analysis makes an essential use of the structure of the generalized Fourier transform
of the basis function. In contrast with spline theory, polynomial reproduction is not sufficient for the derivation of exact
order of convergence by dilated quasi-interpolants. These convergence orders are established by a careful and quite involved
examination of the decay rates of the basis function. Furthermore, it is shown that the same approximation orders are obtained
with quasi-interpolants defined on a bounded domain.
Supported in part by the United States under contract No. DAAL-87-K-0030, and by Carl de Boor’s Steenbock Professorship, University
of Wisconsin-Madison. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|