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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A polyhedral method for solving sparse polynomial systems

Authors: Birkett Huber and Bernd Sturmfels
Journal: Math. Comp. 64 (1995), 1541-1555
MSC: Primary 65H20; Secondary 65H10
MathSciNet review: 1297471
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Abstract: A continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations. We introduce mixed subdivisions of Newton polytopes, and we apply them to give a new proof and algorithm for Bernstein’s theorem on the expected number of roots. This results in a numerical homotopy with the optimal number of paths to be followed. In this homotopy there is one starting system for each cell of the mixed subdivision, and the roots of these starting systems are obtained by an easy combinatorial construction.

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Article copyright: © Copyright 1995 American Mathematical Society