ON COMPLEMENTARY VARIATIONAL PRINCIPLES.

Abstract

Variational problems which are formulated in terms of finding maxima or minima of functionals usually lead to only one-sided bounds for approximate solutions. It has been shown recently by B. Noble that a number of variational problems may be formulated in terms of complementary variational problems, the approximate solutions of which give both upper and lower bounds for the desired stationary value. In this paper, complementary variational principles are formulated abstractly in Hilbert space. Necessary and sufficient conditions are given for a system of two equations to represent a variational principle, and sufficient conditions are given for the variational principle to be complementary. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1965
Accession Number
AD0616867

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Real Variables
  • Stationary
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra

Technology Areas

  • Space