Multivariate Spline Approximation
Abstract
We started out with the goal of understanding approximation order in a multivariate context, including the approximation of surfaces. In addition, we wanted to understand better the use and analysis of our approach to multivariate polynomial interpolation. We ended up concentrating on approximation from shift- invariant spaces of functions on IR real space. Here, S is shift-invariant if f is an element S implies that also f(. - alpha) is an element S for any integer vector alpha. The simple, yet widely applicable, model we considered concerns the behavior, as H approaches 0, of the distance between f and s of a (suitably smooth) f from the scaled space S sub h := (f(./h) : f is an element S sub h), with each S sub h a shift-invariant space. Examples of such spaces are provided by finite elements on a regular grid, in particular, box spline spaces, also the spaces which make up the multiresolution analysis generated by wavelets.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 22, 1993
- Accession Number
- ADA276034
Entities
People
- Amos Ron
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison