On a Dimensional Reduction Method. Some Approximation-Theoretic Results,

Abstract

This paper is the second in a series of three that analyze a method of dimensional reduction. It contains some results for approximation of functions on the interval -1,1 with elements from the nullspace of p to the n power, n greater than or equal to 1, where P is a second order ordinary differential operator. A special case of this is approximation by polynomials. The one-dimensional results are used as a tool to prove similar versions in several dimensions. These multi-dimensional results are directly related to the approximate method of dimensional reduction, and they lead to statements about the convergence properties of this approach. The third paper, which analyzes the adaptive aspects of the method, is forthcoming.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA104966

Entities

People

  • Ivo Babuška
  • M. Vogelius

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Hilbert Space
  • Inequalities
  • Interpolation
  • Numerical Analysis
  • Periodic Functions
  • Polynomials
  • Sequences
  • Standards
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Systems Analysis and Design