Gauss-Jordan elimination

Gauss-Jordan elimination

[¦gau̇s ¦jȯrd·ən ə‚lim·ə′nā·shən]
(mathematics)
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The most known direct methods are: Cramer, Gaussian elimination, Gauss-Jordan elimination, LU factorization, QR decomposition etc.
Gauss-Jordan elimination produces an array containing only three unknowns.
Let us also recall that there are problems where the conditioning of the lower and upper triangular matrices can have different importance: this happens, for instance, in the backward stability of Gauss-Jordan elimination, where the conditioning of the upper triangular matrix is crucial (see [10], [13] and [14]).
1] by a procedure similar to Gauss-Jordan elimination, but using column elementary operations instead of row elementary operations and starting from the last row, we can easily obtain the following bound for the absolute value of [([T.
MALYSHEV, A note on the stability of Gauss-Jordan elimination for diagonally dominant matrices, Computing, 65 (2000), pp.
1], via the Gauss-Jordan elimination algorithm with partial pivoting [Golub and van Loan 1989; Wilkinson 1961].