A Survey of Error Estimates for Iterative Solutions of Systems of Linear Equations with an Application to the Solution of Poisson's Equation

Abstract

In the solution of a set of linear equations Ax = b by an iterative method one would like an estimate of the error x - (x sub n) so that the iteration can be stopped after the error is within acceptable bounds. The author presents a review of several types of error estimates. In addition the author gives a new error estimate for the successive over-relaxation method which is a generalization of an estimate of Sassenfeld for the Gauss-Seidel method. The author presents a numerical example of an error estimate of Albrecht for the successive over-relaxation method applied to the iterative solution of the system of linear equations which arise from the finite difference formulation of the Poisson equation.

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Document Details

Document Type
Technical Report
Publication Date
Oct 03, 1972
Accession Number
AD0753463

Entities

People

  • Michael J. Vander Vorst

Organizations

  • Naval Ordnance Laboratory

Tags

Communities of Interest

  • Counter WMD

DTIC Thesaurus Topics

  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programs
  • Coordinate Systems
  • Difference Equations
  • Differential Equations
  • Equations
  • Fluid Flow
  • Iterations
  • Linear Systems
  • Munitions
  • Numerical Analysis
  • Ordnance Laboratories
  • Partial Differential Equations
  • Poisson Equation
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design