Accurate enclosure of the zero set of multivariate polynomials (Q1415398)

Let \([p]\) be a complex multivariate polynomial with complex interval coefficients. Enclosures for the zeros of \([p]\) are derived. Actually these enclosures are defined as intersections of unions of funnel-shaped unbounded sets of type \(H^+_k(c)\), where for \(z\in \mathbb{C}^n\) and \(c\geq 0\), \(z\in H^+_k(c)\) iff \(| z|^k\geq c\) (multi-index-notation). \(k\) depends on the degree set of \([p]\), that is the set of (multi-) exponents occurring in \([p]\) and \(c\) is a rational expression in the moduli of the coefficients. -- The enclosures are refined in the case of bivariate polynomials. Zeros of systems of polynomials are considered as well.