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LIST OF FIGURES 271
7.7 Residual norms against MVs with A p1 for the JD and JDCOMM methods . . 123
7.8 Eigenvalue spectra of the matrices A p1 and A xi ,i=1,...,4........ 124
7.9 Eigenvalue spectra of the matrices A p1 and A xi ,i=1,...,5........ 125
7.10 Sparsity structure of the matrices A p1 and A xi , i =1,...,4 ........ 127
7.11 Eigenvalue spectra of the matrices A p1 and A xi , i =1,...,4........ 128
7.12 Residual norms against MVs with A p1 for the JD and JDCOMM methods . . 129
9.1 All eigenvalues of the matrix A T V H
...................... 157
9.2 Zoomed in on the smallest real eigenvalues of the matrix A T V H
....... 157
9.3 Sparsity representation of the matrices A T x 1
, A T x 2
and A T V H
......... 158
10.1 Sparsity and structure of the matrix Ãã N−1
(ρ 1 ) T .............. 183
10.2 Sparsity structure of the matrices B and C ................. 183
10.3 The poles of H(s) and G(s) .......................... 185
10.4 The poles of H(s), G 1 (s), and G 2 (s) ..................... 186
10.5 Impulse responses of H(s), G(s), and G 2 (s) ................. 187
10.6 Bode diagrams of H(s), G(s), and G 2 (s) ................... 187
10.7 Structure of the matrix Ãã N−1
(ρ 1 ) T ..................... 189
10.8 Poles of H(s) and approximation G(s) .................... 191
10.9 Poles of H(s) and approximations G 1 (s) and G 2 (s) ............. 191
10.10Impulse responses of H(s) and G(s) ..................... 192
10.11Bode diagrams of H(s) and G(s) ....................... 192
10.12Poles of H(s), G 1 (s), G 2 (s), and G(s) .................... 193
10.13Impulse responses of H(s), G 2 (s), and G(s) ................. 194
10.14Bode diagrams of H(s), G 2 (s), and G(s) ................... 194
11.1 Sparsity structure of the matrices Ãã N−1
(ρ 1 ,ρ 2 ) T and Ãã N−2
(ρ 1 ,ρ 2 ) T . . 223
11.2 Real eigenvalue pairs (ρ 1 ,ρ 2 ) of the matrices ................ 224
11.3 Five important real eigenvalue pairs (ρ 1 ,ρ 2 ) of the matrices ........ 225