On the spectral set for a family of polynomials

The problem of generating the spectral set of two different families of polynomials, P-spherical families and polytopic families, is discussed. For the spherical case, a closed-form equation describing the boundary of the spectral set is obtained. In the polytopic case, 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 is shown. Two numerical examples are included