Newton's Method as a Dynamical System: Global Convergence and Predictability.

Abstract

Newton's method as an iterative scheme to compute both unstable and stable fixed points of a discrete dynamical system is considered. It is shown for Newton iterations that the basins of attraction are intertwined in a complicated manner. This complex structure appears to be fractal, and its dimension is estimated. Consequences of predictability for the final state are given in terms of imprecision in the initial data. Keywords include: Newton's method, Predictability, Basin boundaries, Fractal, Nonlinear dynamic.

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Document Details

Document Type
Technical Report
Publication Date
May 13, 1985
Accession Number
ADA155170

Entities

People

  • I. B. Schwartz
  • R. G. Holt

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Classification
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fungi
  • Iterations
  • Military Research
  • Physics
  • Scaling Laws
  • Security
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design
  • Wave Propagation and Nonlinear Chaotic Dynamics.