On a Dimensional Reduction Method. The Optimal Selection of Basis Functions,

Abstract

This paper is the first in a series of three, which analyze an adaptive approximate approach for solving (n+1)- dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this approach the unknown functions of (n+1)- variables are projected onto finite linear combinations of functions of just n-variables. This paper shows how the coefficients of these linear combinations can be chosen optimally. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1980
Accession Number
ADA092999

Entities

People

  • Ivo Babuška
  • M. Vogelius

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Series
  • Band Structures
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Computer Science
  • Equations
  • Errors
  • Fourier Series
  • Hilbert Space
  • Military Research
  • Numerical Analysis
  • Physical Sciences
  • Polynomials
  • Sequences
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research
  • Statistical inference.

Technology Areas

  • Space