ON THE APPROXIMATE MINIMIZATION OF FUNCTIONALS.

Abstract

The paper considers in general the problem of finding the minimum of a given functional f(u) over a set B by approximately minimizing a sequence of functionals f sub n(u sub n) over a 'discretized' set B sub n; theorems are given proving the convergence of the approximating points u sub n in B sub n to the desired point u in B. Applications are given to the Rayleigh-Ritz method, regularization, Chebyshev solution of differential equations, and the calculus of variations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1968
Accession Number
AD0675791

Entities

People

  • James W. Daniel

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Convergence
  • Differential Equations
  • Equations
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.