The problem of bounding the zeros of a polynomial of degree n greater than
or equal to 2 with real or complex coefficients, is considered and an impro
ved Cauchy bound is proposed. This new bound is applied to two examples and
compared with existing approaches. The methodology is then extended to the
case of polynomials of degree n greater than or equal to 2 with interval C
oefficients. A counter-example to theorem 3.8 in Adjiman, Androulakis, Mara
nas and Floudas (1996), used in the alpha BB algorithm to compute a tight l
ower bound on the minimum real part of the zeros of an interval polynomial
is also presented. An alternative approach that uses the improved Cauchy bo
und as a starting point is developed. (C) 1999 Elsevier Science Ltd. All ri
ghts reserved.