Accession Number : AD0616867

Title :   ON COMPLEMENTARY VARIATIONAL PRINCIPLES.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Rall,L. B.

Report Date : MAY 1965

Pagination or Media Count : 20

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)

Descriptors :   (*FUNCTIONAL ANALYSIS, CALCULUS OF VARIATIONS), (*CALCULUS OF VARIATIONS, FUNCTIONAL ANALYSIS), OPERATORS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE