Accession Number:
AD0678976
Title:
NORM MINIMIZATION ON NONLINEAR MANIFOLDS IN HILBERT SPACE,
Descriptive Note:
Corporate Author:
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH INFORMATION SCIENCES LAB
Personal Author(s):
Report Date:
1968-10-01
Pagination or Media Count:
15.0
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 fx,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 gz 0. This paper considers the problem of minimizing norm z on the manifold M z gz 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 gz sub k converges to zero and which, under suitable additional assumptions, converges to an element in M of minimum norm. Author
Descriptors:
Subject Categories:
- Theoretical Mathematics