A complicated Polynomial Root-finding algorithm which is used in the IMSL (IMSL, Houston, TX) library and which Press et al. (1992) describe as ``practically a standard in black-box Polynomial Root-finders.''
References
IMSL, Inc. IMSL Math/Library User's Manual. Houston, TX: IMSL, Inc.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, p. 369, 1992.
Ralston, A. and Rabinowitz, P. §8.9-8.13 in A First Course in Numerical Analysis, 2nd ed.
New York: McGraw-Hill, 1978.