Root Exclusion Research Articles

Regions of polynomial root clustering

A criterion for root exclusion from a region composed as a union of elemental regions—discs and halfplanes—is established. Associated with each elemental region is a derived polynomial which must be by the criterion a strictly Hurwitz polynomial. The criterion is the basis for a root exclusion test, obtained by invoking the equivalence of the strict Hurwitz property of a polynomial and the positivity of a set of inners [equivalently, Hurwitz] determinants associated with the polynomial.