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 : MAY 1972

Pagination or Media Count : 12

Abstract : Given an operator P in a Banach space X with Lipschitz continuous derivative P primed, it is shown that the existence of 1/(P 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) - P(x sub n)/(P primed(s sub n)) will converge to a solution x of the equation P(x) = 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