We present several examples which illustrate some of the features of the symmetric indefinite Lanczos procedure described above. In particular, the examples below illustrate three points:

- When is singular, premultiplying the starting vector by provides a dramatic improvement in the quality of the computed Ritz pairs.
- When is singular, the postprocessing step described in equation (8.27) may further improve the Ritz pairs.
- Partial reorthogonalization provides substantial savings over complete reorthogonalization.

The first model is an acoustics problem representing a speaker box. Two sets of matrices have been generated from the model. In the first set, the linearized problem has order 1076. In a smaller second set of matrices, modal reduction has been employed and the associated matrices have order 668.

The second model represents a shaft on bearing supports with a translational viscous damper attached at the midpoint of the shaft. By controlling the mesh size, two sets of matrices have been produced for this model. With a finer mesh, the order of is 800, while a coarser mesh yields matrices with order 160. In each case, the resulting matrix is singular with this model.