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