A NUMERICAL INVESTIGATION OF THE SIMPLEX METHOD

Abstract

The report analyzes the behavior of the round-off errors associated with three different computer implementations of the simplex method of linear programming. One of the three is representative of computer implementations in common use, and it is shown that the standard method of updating the basic- matrix inverse is numerically unstable. The remaining two implementations are suggested by the author and use triangular decompositions of the basic matrix as substitutes for its inverse. The implementations are shown to be stable, and one of them is shown to be competitive in speed with the standard simplex-method computer implementations. Error bounds which may be calculated from intermediate results are developed for each of the three implementations, and their use during computation for error monitoring and control is discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 31, 1968
Accession Number
AD0673010

Entities

People

  • Richard H. Bartels

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computational Processes
  • Computations
  • Computer Programming
  • Computer Programs
  • Computer Science
  • Computers
  • Eigenvalues
  • Equations
  • Error Analysis
  • Floating Point Operations
  • Linear Programming
  • Linear Systems
  • Notation
  • Numerical Analysis
  • Simplex Method

Fields of Study

  • Physics

Readers

  • Linear Algebra
  • Operations Research
  • Systems Analysis and Design