Gaussian Elimination and Numerical Instability.

Abstract

Roundoff error in the solution of linear algebraic systems is studied using a more realistic notion of what it means to perturb a problem, namely that each datum is subject to a relatively small change. The condition number is determined for this approach. A good computable error bound is given for the 'backward error'. The effect of scaling on the stability of Gaussian elimination is studied, and it is discovered that the proper way to scale a system is dependent on knowing the solution. Finally it is shown that Gaussian elimination can be stabilized by doing iterative improvement. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1977
Accession Number
ADA042159

Entities

People

  • Robert D. Skeel

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Counter IED

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algorithms
  • Arithmetic
  • Computations
  • Computer Science
  • Computers
  • Error Analysis
  • Errors
  • Fish
  • Floating Point Operations
  • Iterations
  • Linear Systems
  • Numerical Analysis
  • Perturbations
  • Precision
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.