Accession Number : AD0675791

Title :   ON THE APPROXIMATE MINIMIZATION OF FUNCTIONALS.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES

Personal Author(s) : Daniel,James W.

Report Date : SEP 1968

Pagination or Media Count : 23

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)

Descriptors :   (*FUNCTIONAL ANALYSIS, OPTIMIZATION), APPROXIMATION(MATHEMATICS), DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS, SET THEORY, HILBERT SPACE, TOPOLOGY, SEQUENCES(MATHEMATICS), CONVERGENCE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE