Gaussian elimination

English

Noun

Gaussian elimination (countable and uncountable, plural Gaussian eliminations)

1. (linear algebra) A method of reducing an augmented matrix to row echelon form.
   • 1976, Thomas E. Rosmond, Frank D. Faulkner, Direct Solution of Elliptic Equations by Block Cyclic Reduction and Factorization, Monthly Weather Review, Volume 104, Issues 1-6, American Meteorological Society, page 644,

     We then repeat the Gaussian elimination procedure for the $({\boldsymbol {E}}-\alpha _{2}^{(2)})$ factor in (35), obtaining another intermediate solution vector. It is immediately apparent in this example that four Gaussian eliminations are necessary to obtain $\psi _{i,4}$.

   • 1989, Richard A. Blech, “Parallel Gaussian Elimination of a Block Tridiagonal Matrix Using Multiple Microcomputers”, in Technical Report, NASA, page 1:

     Theoretical partitioning and resource allocation for the Gaussian elimination method used to solve the matrix are discussed.

   • 1996, E. D'Hollander, G. R. Joubert, F. J. Peters, D. Trystram, Parallel Computing: State-of-the-art and Perspectives, Elsevier, page 642:

     The use of Gaussian eliminations limits the range of functionality of the algorithm, which operates only with square matrices A.

Translations

Gaussian elimination

• French: élimination de Gauss-Jordan (fr) f, méthode du pivot de Gauss f
• German: gaußsche Eliminationsverfahren n, Gauß-Verfahren n
• Italian: metodo di eliminazione di Gauss m, MEG m
• Russian: ме́тод Га́усса m (métod Gáussa)
• Swedish: Gausselimination

See also

• Cramer's rule