On the Location of Pseudozeros of a Complex Interval Polynomial

Abstract.

Given a univariate complex interval polynomial F, we provide a rigorous method for deciding whether there exists a pseudozero of F in a prescribed closed complex domain D. Here a pseudozero of F is defined to be a zero of some polynomial in F. We use circular intervals and assume that the boundary C of D is a simple curve and that C is the union of a finite number of arcs, each of which is represented by a rational function. When D is not bounded, we assume further that all the polynomials in F are of the same degree. Examples of such domains are the outside of an open disk and a half-plane with boundary. Our decision method uses the representation of C and the property that a polynomial in F is of degree 1 with respect to each coefficient regarded as a variable.