Pivoting strategies leading to diagonal dominance by rows

Abstract.

Pivoting strategies for Gaussian elimination leading to upper triangular matrices which are diagonally dominant by rows are studied. Forward error analysis of triangular systems whose coefficient matrices are diagonally dominant by rows is performed. We also obtain small bounds of the backward errors for the pivoting strategies mentioned above. Our examples of matrices include H-matrices and some generalizations of diagonally dominant matrices, and scaled partial pivoting for the 1-norm is an example of these pivoting strategies. In the case of an $n\times n$ M-matrix, a pivoting strategy of computational complexity $O(n^2)$ is proposed, which satisfies all the results of the paper.