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Mathematics of Computation

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Solving real polynomial systems with real homotopies


Authors: T. Y. Li and Xiao Shen Wang
Journal: Math. Comp. 60 (1993), 669-680
MSC: Primary 65H20
DOI: https://doi.org/10.1090/S0025-5718-1993-1160275-5
MathSciNet review: 1160275
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Abstract: When a real homotopy is used for solving a polynomial system with real coefficients, bifurcation of some of the homotopy paths at singular points is inevitable. The main result of this paper shows that, generically, the solution set of a real homotopy contains no singular point other than a finite number of quadratic turning points. At a quadratic turning point, the bifurcation phenomenon is quite simple. It consists of two bifurcation branches with their tangent vectors being perpendicular to each other.


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DOI: https://doi.org/10.1090/S0025-5718-1993-1160275-5
Article copyright: © Copyright 1993 American Mathematical Society

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