Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices

Let a monic polynomial Pn(x) xn − a1xn-1 − ••• −an, aj %plane1D;49E;j = 1, 2,…, n, be given. Bounds for the eigenvalues and the computation of the singular values of some special companion matrices give bounds for the zeros of the polynomial Pn which improve classical and recently found ones. Also some new bounds for the zeros are given.