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# Accession Number:

## AD0744335

# Title:

## Rates of Convergence of Newton's Method.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1972-05-01

# Pagination or Media Count:

##
12.0

# Abstract:

## Given an operator P in a Banach space X with Lipschitz continuous derivative P primed, it is shown that the existence of 1P primed x 1 is necessary and sufficient to predict on the basis of the theorem of L. V. Kantorovic that the Newton sequence x sub n 1 x sub n - Px sub nP primeds sub n will converge to a solution x of the equation Px o quadratically. Some examples are given of convergent Newton sequences for which convergence and the rate of convergence cannot be predicted by the Kantorovic theorem. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#