The Strength of Nonstationary Iteration.

Abstract

This is the second of three papers in which we study global convergence of iterations using linear information for the solution of nonlinear equations. In Wasilkowski we proved that for the class of all analytic scalar complex functions having only simple zeros there exists no globally convergent stationary iteration using linear information. Here we exhibit a nonstationary iteration using linear information which is globally convergent even for the multivariate and abstract cases. This demonstrates the strength of nonstationary iteration. In Wasilkowski we shall prove that any globally convergent iteration using linear information has infinite complexity even for the class of scalar complex polynomials having only simple zeros. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1979
Accession Number
ADA081450

Entities

People

  • G. W. Wasilkowski

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Computer Science
  • Computers
  • Convergence
  • Equations
  • Iterations
  • Mathematical Analysis
  • Military Research
  • New York
  • Numbers
  • Polynomials
  • Real Numbers
  • Sequences
  • Stationary
  • Universities

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.