conditioning, diagonal dominance, pivoting strategies, accuracy, singular value decomposition.

Both lower triangular matrices inherit the diagonal dominance by columns and so their condition numbers satisfy the corresponding bound of Proposition 2.

As we have recalled in Section 2, diagonal dominance by columns is inherited by the Schur complements and hence L is diagonally dominant by columns.

If A is a nonsingular M-matrix strictly diagonally dominant by rows or columns, since strict diagonal dominance by columns is inherited by the Schur complements, one can deduce from the proof of the previous proposition and Remark 3.

We start by showing in Section 2 that diagonal dominance implies very well conditioning of both unit triangular matrices L, U.

16]) that diagonal dominance by rows or columns is inherited by the Schur complements obtained when performing Gauss elimination.

In [12] we defined a symmetric maximal absolute diagonal dominance (m.

Achieving Diagonal Dominance, System and Control Letter, Vol.

There is a slight decrease in the RGA number after ordering across the frequencies and therefore this implies that the selected I/O pairs will have an effect on the diagonal dominance of the system.

The Gershgorin diagonal dominance discs were used to assess interaction.

Input and output scaling are employed simultaneously to further reduce the level of ill conditioning in the system and also to obtain the best diagonal dominance across the frequency range of interest, especially near the system bandwidth.

New method of applying the Edmunds scaling is used to improve the diagonal dominance of the system and numerical conditioning.