Gaussian elimination

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

   • 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.

• Cramer's rule