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

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
Revision date

2007-05-23
Description

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.
Subjects

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

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]
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Homotopy_Polynomial2.nb (433.3 KB) - Mathematica Notebook [for Mathematica 5.2]