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):

• Rall,L. B.

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:

• (*ITERATIONS
• CONVERGENCE)
• BANACH SPACE
• SEQUENCES(MATHEMATICS)
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE