A bound for the zeros of polynomials

A new kind of circular bound on the zeros of polynomials is derived by determining Cauchy´s bound on zeros of its transformed pair first. The transformation is based on a nonlinear transformation of the variable, which conceptually should give a better upper bound. The advantage of such a transformation is illustrated through several examples that show the improvement over the existing bounds. Convergence of the bound after iterative transformations of the original polynomial is also examined.