An Adaptive Algorithm for Multivariate Approximation Giving Optimal Convergence Rates.
Abstract
The distance dist(f, P sub n, K) of functions f with certain singularities from P sub n, K: = functions consisting of no more than K polynomial pieces of order n is shown to be O(K to the -nth power), i.e., of the same order as dist(f, P sub n, K) for F is an element of C(superscript n). It is shown that this optimal convergence rate is realized by approximations constructed with the aid of a simple adaptive algorithm. The paper offers a very simple mechanism for the analysis of the error achieved by such adaptive approximation schemes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1977
- Accession Number
- ADA046391
Entities
People
- Carl R. de Boor
- John R. Rice
Organizations
- University of Wisconsin–Madison