Scattered date interpolation from principal shift-invariant spaces

Authors:
Michael J. Johnson
Affiliations:
Department of Mathematics and Computer Science, Kuwait University, Safat, Kuwait
Venue:
Journal of Approximation Theory
Year:
2001

Citing 3
Cited 1

Approximation by multiinteger translates of functions having global support

Journal of Approximation Theory
Box splines

Box splines
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Scattered data reconstruction by regularization in B-spline and associated wavelet spaces

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Under certain assumptions on the compactly supported function φ ∈ C(Rd), we propose two methods of selecting a function s from the scaled principal shift-invariant space Sh(φ) such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme amounts to solving a quadratic programming problem and we are able to prove error estimates similar to those obtained by Duchon for surface spline interpolation.