# 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