Rates of Convergence of Newton's Method.

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)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1972
Accession Number
AD0744335

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Convergence
  • Equations
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Human-Computer Interaction (HCI).

Technology Areas

  • Space