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.

CACM September, 1965

Henrich, P.
Watkins, B. O.

CA650908 JB March 6, 1978  7:21 PM

1197	5	1197
1197	5	1197
1197	5	1197
1524	5	1197
879	6	1197
1197	6	1197
311	6	1197