Can Any Stationary Iteration Using Linear Information be Globally Convergent.

Abstract

All known globally convergent interations for the solution of a nonlinear operator equation f(x) = 0 are either non-stationary or use nonlinear information. We ask whether there exists a globally convergent stationary iteration which uses linear information. We prove that even if global convergence is defined in a weak sense, there exists no such iteration for as simple a class of problems as the set of all analytic complex functions having only simple zeros. We conjecture that even for the class of all real polynomials which have real simple zeros there does not exist a globally convergent stationary iteration using linear information. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1978
Accession Number
ADA064295

Entities

People

  • G. W. Wasilkowski

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebraic Functions
  • Classification
  • Computer Science
  • Computers
  • Convergence
  • Equations
  • Iterations
  • Mathematical Analysis
  • Military Research
  • New York
  • Numerical Analysis
  • Polynomials
  • Sequences
  • Stationary
  • Universities

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Statistical inference.