Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Gaussian elimination

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_376

A computational procedure for reducing a set of (m × m) linear equations Axv = bv to the form MAxv = Mb,v where MAv = Uv is an upper triangular matrix. The variables of the solution vector are found by solving the resulting triangular system for one variable in the last equation, and back-substituting in the next to last equation, and so on. Some form of elimination is central to the simplex method for solving linear-programming problems. Matrices and matrix algebra; Simplex method.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA