Zeros of Polynomials, Inequalities, Cauchy bound, Companion Matrix, Compound Matrix
The Cauchy bound is one of the best known upper bounds for the modulus of the zeros of a polynomial. The Fujiwara bound is another useful upper bound for the modulus of the zeros of a polynomial. In this paper, compound matrices are used to derive a generalization of both the Cauchy bound and the Fujiwara bound. This generalization yields upper bounds for the modulus of the product of $m$ zeros of the polynomial.
Pereira, Rajesh and Vali, Mohammad Ali.
"Generalizations of the Cauchy and Fujiwara Bounds for Products of Zeros of a Polynomial",
Electronic Journal of Linear Algebra,
Volume 31, pp. 565-571.