We started the lecture mentioning two recent numerical root finders:

1. D.A. Bini and G. Fiorentino: "Design, analysis, and implementation of a multiprecision polynomial rootfinder". Numerical Algorithms 23:127-173, 2000. To download mpsolve; see also.
2. Steven Fortune: "Polynomial Root Finding Using Iterated Eigenvalue Computation". In Proceedings of ISSAC 2001, edited by Bernard Mourrain, pages 121-128, ACM 2001. To download eigensolve.

These root finders both use multiprecision arithmetic. An experiment with Maple (click here for the html version), shows the necessity of multiprecision, both for the evaluation of the coefficients and the arithmetic on the Wilkinson polynomial.