Multivariate Approximation
Abstract
Methods for representing multi-dimensional objects, such as functions of several variables and, more generally, (hyper-)surfaces is the main objective. One goal of such representation, whether approximate or exact, is the efficient evaluation of the object: Multivariate Polynomial Interpolation as well as Scattered Data Approximation both fall into this category. Another goal is a representation that allows one to identify and access easily and simultaneously relevant aspects of the object. The topics of wavelets and Weyl-Heisenberg systems belong to this second category. As to multivariate polynomial interpolation, we hope ultimately to duplicate the success of univariate polynomial interpolation as a basic tool in scientific computing. Current focus is the derivation of error formulae, using a multivariate divided difference just developed. Scattered data approximation is to be accomplished by extending well-known and efficient techniques for fitting to data on uniform meshes. Concerning Wavelets and Weyl-Heisenberg systems, the goal is to make new inroads in these important areas by applying tools and techniques from Approximation Theory, particularly those developed during studies of Shift-Invariant Spaces, a centerpiece of our previous research.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 29, 1998
- Accession Number
- ADA364536
Entities
People
- Amos Ron
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison