How Good Are Global Newton Methods? Part 1

Abstract

1) Relying on a theorem of Nemerovsky and Yuden(1979) a lower bound is given for the efficiency of global Newton methods over the class C1(mu, Lambda). 2) The efficiency of Smale's global Newton method in a simple setting with a nonsingular, Lipschitz-continuous Jacobian is considered. The efficiency is characterized by 2 parameters, the condition number Q and the smoothness S. The efficiency is sensitive to S, and insensitive to Q.

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Document Details

Document Type
Technical Report
Publication Date
Feb 23, 1989
Accession Number
ADA208390

Entities

People

  • Allen A. Goldstein

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Computational Complexity
  • Computational Science
  • Convergence
  • Convex Programming
  • Efficiency
  • Equations
  • Hilbert Space
  • Inequalities
  • Mathematics
  • Military Research
  • Optimization
  • Sequences
  • Three Dimensional
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Solar Photovoltaics and Thermoelectric Devices.