Finding roots by deflated polynomial approximation
A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, multiple or nearly equal roots being easily dealt with and a high degree of flexibility in coping with non-convergent iterations. The method is simple to use and is based upon a Routh Array-type algorithm familiar to control engineers. Numerical examples demonstrate its application to various polynomials.
Lucas, T.N. 1990. Finding roots by deflated polynomial approximation. Journal of the Franklin Institute. 327(5): pp.819-830. Available from http://dx.doi.org/10.1016/0016-0032(90)90085-W