A description can also be found in Ralston and [[Philip Rabinowitz (mathematician)|
Rabinowitz]]<ref>Ralston, A. and Rabinowitz, P. (1978), A First Course in Numerical Analysis, 2nd ed., McGraw-Hill, New York.</ref> p. 383.
The algorithm is similar in spirit to the two-stage algorithm studied by Traub.<ref>Traub, J. F. (1966), [http://linkswww.jstor.org/sici?sici=0025-5718(196601)20%3A93%3C113%3AACOGCI%3E2.0.CO%3B2-3stable/2004275 A Class of Globally Convergent Iteration Functions for the Solution of Polynomial Equations], Math. Comp., 20(93), 113–138.</ref>
=== Root-finding procedure ===
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==Real coefficients==
The Jenkins–Traub algorithm described earlier works for polynomials with complex coefficients. The same authors also created a three-stage algorithm for polynomials with real coefficients. See Jenkins and Traub [http://linkswww.jstor.org/sici?sici=0036-1429%28197012%297%3A4%3C545%3AATAFRP%3E2.0.CO%3B2-Jstable/2949376 A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration].<ref>Jenkins, M. A. and Traub, J. F. (1970), [http://linkswww.jstor.org/sici?sici=0036-1429%28197012%297%3A4%3C545%3AATAFRP%3E2.0.CO%3B2-Jstable/2949376 A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration], SIAM J. Numer. Anal., 7(4), 545–566.</ref> The algorithm finds either a linear or quadratic factor working completely in real arithmetic. If the complex and real algorithms are applied to the same real polynomial, the real algorithm is about four times as fast. The real algorithm always converges and the rate of convergence is greater than second order.
