Validating Polynomial Numerical Computations with Complementary Automatic Methods

Finite precision computations affect the accuracy of computed solutions and sometimes the stability of iterative algorithms. Automatic approaches exist to control and to reduce these effects. Examples are the CESTAC and the CENA methods and the more general interval approaches. We focus here on a complementary use of these methods to localize unstable behavior of the algorithm, to improve the accuracy of the solutions, to identify and explain finite precision effects. We present computational experiments on ill-conditioned polynomial roots approximated with Newton's iteration that illustrate the well-known influence of coefficient perturbations