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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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A polyhedral method for solving sparse polynomial systems
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by Birkett Huber and Bernd Sturmfels PDF
Math. Comp. 64 (1995), 1541-1555 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1541-1555
  • MSC: Primary 65H20; Secondary 65H10
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1297471-4
  • MathSciNet review: 1297471