Using the Field of Values for Pseudospectra Generation

The generation of spectral portraits requires the speciication of a region in the complex plane which must be predetermined. For cases where little is known a priori about the spectral properties of a matrix, an accurate and eecient means to compute the outer boundaries of the pseudospectra is desirable. It is shown that the eld of values is an eeective way to determine the extremities of the pseudospectrum; and that it provides advantages over other possible techniques such as Gershgorin disks, matrix norms, and eigenvalue solvers. Numerical comparisons of the diierent approaches are presented.