Gauss Elimination: Workhorse of Linear Algebra.

Abstract

This report brings together many different aspects of Gauss elimination. The basic Gauss elimination (GE) algorithm is a fundamental tool of linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also included. Finally, GE is considered within the context of 'noisy' matrices. The effect of the noise in matrix entries on the effective rank of the matrix is the central aspect considered here.

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Document Details

Document Type
Technical Report
Publication Date
Aug 05, 1995
Accession Number
ADA313547

Entities

People

  • Peter R. Turner

Organizations

  • Naval Air Warfare Center

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes
  • Sensors
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algebra
  • Algorithms
  • Arithmetic
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Architecture
  • Computers
  • Computing System Architectures
  • Detection
  • Elimination
  • Floating Point Operations
  • Linear Algebra
  • Rational Numbers
  • Real Numbers

Readers

  • Computer Programming and Software Development.
  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design