Numerical stability of barycentric Hermite root-finding
Piers W. Lawrence, Robert M. Corless · 2012
Computing the roots of a polynomial expressed in the Lagrange basis or a Hermite interpolational basis can be reduced to computing the eigenvalues of the corresponding companion matrix [2]. The result we present here is that roots of a polynomial computed via this method are exactly the roots of a polynomial with slightly perturbed coefficients.