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158 CHAPTER 9. H 2 MODEL-ORDER REDUCTION FROM ORDER N TO N-1
(9.4% filled), i =1,...,N. The matrix A T V H
contains 550100 non-zeros (52.5% filled).
See Figure 9.3 for a representation of the sparsity structure of the matrices A T x 1
, A T x 2
and of the matrix A T V H
, respectively.
Figure 9.3: Sparsity representation of the matrices A T x 1
(9.4% filled), A T x 2
(9.4% filled)
and A T V H
(52.5% filled)
To compute only the smallest non-zero real eigenvalue/eigenvector of the operator
A T V H
using an nD-systems approach, the iterative eigenvalue solvers JDQR, JDQZ and
Eigs are used. These solvers are introduced and discussed in Chapter 6. Because
the condition numbers of the operators involved are very large, a similar balancing
technique is used as described in [27], and employed before in Section 7.1.
The smallest real non-zero eigenvalue computed matrix-free using the operator,
is equal to the eigenvalue computed before, with the only exception that the computation
only takes about 200 seconds and the memory requirements are minimal
because the matrix is never constructed explicitly. The memory requirements for this