## Three Ways to Compute Hankel Singular Values

Based on the above analysis one can see that there are three ways to obtain Hankel singular values for flexible structures in modal coordinates.

1. From the algorithm in Section 4.2. This algorithm gives the exact Hankel singular values. However, for large structures it could be time-consuming. Also, the relationship between the Hankel singular value and the natural mode it represents is not an obvious one: this requires one to examine the system matrix A in order to find the natural frequency related to the Hankel singular value in question.

2. From (4.43) and (4.44). This is an approximate value, and its determination can be time-consuming for large structures. However, there is a straightforward relationship between the Hankel singular values and natural frequencies (the Hankel singular value from (4.44) is found for the ith frequency).

3. From (4.46) or (4.59). This is an approximate value, but is determined fast, regardless of the size of the structure. Also, it is immediately known what mode it is associated with, and its closed-form allows for the parametric analysis and physical interpretation.

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