Accession Number : AD0678976

Title :   NORM MINIMIZATION ON NONLINEAR MANIFOLDS IN HILBERT SPACE,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH INFORMATION SCIENCES LAB

Personal Author(s) : Johnson,Frederick C.

Report Date : OCT 1968

Pagination or Media Count : 15

Abstract : A problem in estimation theory that frequently arises in aerospace technology is the determination of a 'best estimate' of a set of parameters x given a sequence of noisy measurements y sub 1, y sub 2,...,y sub n and the fact that, in the absence of noise, a nonlinear equation of the form f(x,y sub i) = 0 is satisfied. The solution to this nonlinear estimation problem is dependent upon finding a computational method for minimizing norm z subject to a nonlinear constraint g(z) = 0. This paper considers the problem of minimizing norm z on the manifold M = (z: g(z) = 0), where g is a suitably differentiable function mapping the Hilbert space E into the Hilbert space F. A method is given for generating a sequence of points (in braces: z sub k) in E such that g(z sub k) converges to zero and which, under suitable additional assumptions, converges to an element in M of minimum norm. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, DECISION THEORY), HILBERT SPACE, INFORMATION THEORY, NONLINEAR SYSTEMS, OPERATORS(MATHEMATICS), OPTIMIZATION, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE