Projection Tutorial (page 4)

• Step 4: Reduce the Safety value still further.

  As there was once again no difference, try reducing Safety again, this time to 0.5. If you look carefully at this plot, you can see that the pseudospectra are not the same as the previous plots at the left edge of the axes. If you reduce Safety still further, to 0.25, you should get the plot below, which again takes about 5 seconds to compute on my computer. The important thing to note here is that the pseudospectra of the projected matrix may be misleading when the invariant subspace that is projected upon makes a small angle with an eigenvector that is omitted from the projection; you must be careful not to project too far.
  

Pseudospectra GUI home page.