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