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Homotopy Continuation Method to Find All Real Roots of a Polynomial Equation

Housam Binous
Organization: National Institute of Applied Sciences and Technology
Department: Chemical Engineering Department
URL: http://pageperso.aol.fr/binoushousam/index.html
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Using homotopy continuation methods such as the fixed point and the Newton homotopy methods, one can find all real solutions of a polynomial equation. Two examples are presented here. In notebook Homotopy_Polynomial2.nb, we also reproduce Figure 4 in the excellent paper by M. Kuno and J. D. Seader, Computing All Real Solutions to Systems of Nonlinear Equations with a Global Fixed-Point Homotopy, Ind. Eng. Chem. Res., 1988, 27, 1320-1329.

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering
*Science > Chemistry

Newton homotopy method, fixed point homotopy method, homotopy continuation method, polynomial equation
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Homotopy_Polynomial.nb (137.8 KB) - Mathematica Notebook [for Mathematica 5.2]
Homotopy_Polynomial2.nb (433.3 KB) - Mathematica Notebook [for Mathematica 5.2]

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