The Gauss-Jordan elimination is not quite stable numerically. In order to get better and more stable schemes, a common practice is to use pivoting. Basically, pivoting is a scaling procedure by dividing all the elements in a row by the element with the largest magnitude or norm. If necessary...
The analysis of computational complexity indicates that our algorithm is more efficient than the existing Gauss-Jordan elimination algorithms for \\(A_{R(G),N(G)}^{(2)}\\) in the literature for a large class of problems. Especially for the case when G is a Hermitian matrix, our ...