Projection Tutorial (page 2)

• Step 2: Select the portion of the complex plane of interest.

  This plot shows the pseudospectra in a region of the complex plane which contains the entire spectrum of the matrix B. Our interest, however, is in the rightmost eigenvalues, the ones with largest real part. To focus on these, we change the axis limits (using the text boxes towards the bottom left of the GUI) so that the real axis ranges from -100 to 50 and the imaginary axis from 0 to 150.

  After changing these limits, click on `Go!' to recompute the pseudospectra on this new domain. You will get a message saying that there are no contours to plot in the range specified, and that `Smart' levels have been used instead; this is because the original levels are no longer appropriate. You should end up with something like the following image, which my Sun Ultra 5 takes about 10 seconds to compute:

  

Pseudospectra GUI home page.