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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.