FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING. IX. VARIATIONAL ANALYSIS, ANALYTIC CONTINUATION, AND IMBEDDING OF OPERATORS

Abstract

In this paper it is shown how variational techniques can be applied to deduce properties for complex operators and for operators which are non- symmetric. For complex operators use is made of a min-max variation and analytic continuation, if necessary, while for non-symmetric operators an imbedding technique was used, along with analytic continuation when required. A non-symmetric operator is imbedded within a family of symmetric operators associated with a variational problem. Once the variational problem has been formulated one can apply the functional equation techniques of the theory of dynamic programming.

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Document Details

Document Type
Technical Report
Publication Date
Apr 07, 1958
Accession Number
AD0606859

Entities

People

  • Richard E. Bellman
  • Sherman Lehman

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Computer Programming
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Euler Equations
  • Hard Copy
  • Identities
  • Matrix Theory
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis