The nearest polynomial with a zero in a given domain

Abstract: For a real univariate polynomial and a closed domain whose boundary is represented by a piecewise rational function, we provide a rigorous method for finding a real univariate polynomial such that has a zero in and is minimal. First, we prove that if a nearest polynomial exists, there is a nearest polynomial such that the absolute value of every coefficient of is with at most one exception. Using this property and the representation of , we reduce the problem to solving systems of algebraic equations, each of which consists of two equations with two variables. [Copyright &y& Elsevier]