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)

Open PDF

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

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Classification
  • Construction
  • Contracts
  • Convergence
  • Convex Sets
  • Errors
  • Inequalities
  • Intervals
  • Mathematics
  • Military Research
  • North Carolina
  • Polynomials
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.