Accession Number:
AD0744335
Title:
Rates of Convergence of Newton's Method.
Descriptive Note:
Technical summary rept.,
Corporate Author:
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s):
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
Descriptors:
Subject Categories:
- Theoretical Mathematics