SOME STABILITY THEOREMS FOR ORDINARY DIFFERENCE EQUATIONS.

Abstract

LaSalle and others have developed a generalization of the 'second method' of Liapunov which utilizes certain invariance properties of solutions of ordinary differential equations. Invariance properties of solutions of ordinary difference equations are utilized here to develop stability theorems similar to those in LaSalle. As illustrations of the application of these theorems, a region of convergence is derived for the Newton-Raphson and Secant iteration methods. A modification of one of these theorems is given and applied to study the effect of roundoff errors in the Newton-Raphson and Gauss-Seidel iteration methods.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1966
Accession Number
AD0653013

Entities

People

  • James Hurt

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Convergence
  • Difference Equations
  • Differential Equations
  • Equations
  • Invariance
  • Iterations
  • Mathematical Analysis

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra