1197	 Finding Zeros of a Polynomial by the Q-D Algorithm	 A method which finds simultaneously all the zeros of a polynomial developed by H. Rutishauser has been tested on a number of polynomials with real coefficients. This slowly converging method the Quotient-Difference Q-D algorithm provides starting values for a Newton or a Bairstow algorithm for more rapid convergence. Necessary and sufficient conditions for the existence of the Q-D scheme are not completely known however failure may occur when zeros have equal or nearly equal magnitudes. Success was achieved in most of the cases tried with the failures usually traceable to the equal magnitude difficulty. In some cases computer roundoff may result in errors which spoil the scheme. Even if the Q-D algorithm does not give all the zeros it will usually find a majority of them.
