ON THE SPECTRAL SET FOR A FAMILY OF POLYNOMIALS

Given a family of real nth-order polynomials P, the spectral set of P is de fined as sigma-(P) is approximately equal to {z-epsilon-C: p(z) = 0 for some p(.)-epsilon-P}. The focal point of this note is the problem of generating the spectral set for two different families of polynomials P - spheric al families and polytopic families. For the spherical case, a closed form equation describing the boundary of the spectral set is obtained. In the polytopic case, we show a computationally feasible technique which requires only a two-dimensional gridding of a bounded subset of the complex plane rather than a high-dimensional gridding of the parameter set. Two numerical examples conclude the note.