Error-bounds for zeroes of polynomials using complex circular arithmetic (Q1094096)

Let p be a complex polynomial of degree n having exactly n distinct zeros \(x_ 1,...,x_ n\) for which one is given approximations \(w_ 1,...,w_ n\). Several known methods for establishing upper bounds on \(| x_ i-w_ i|\), \(i=1,...,n\), are based on Brouwer's fixed point theorem. These methods are modified by using complex circular arithmetic. It is shown that in two cases the modified methods give better bounds for \(| x_ i-w_ i|\), whereas there is no improvement in a third case. Numerical examples are included.