Mixed volume computation via linear programming (Q5928410)
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scientific article; zbMATH DE number 1582617
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mixed volume computation via linear programming |
scientific article; zbMATH DE number 1582617 |
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Mixed volume computation via linear programming (English)
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12 June 2001
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mixed volume
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polynomial system
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linear programming
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isolated zeros
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subdivision
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algorithm
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simplex algorithm
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numerical results
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The mixed volume of the support \(\mathcal A = (\mathcal A_1, \ldots, \mathcal A_n)\) of a polynomial system \(P(x)=(p_1(x),\dots\), \(p_n(x))\) is important for the approximation of the isolated zeros of \(P(x)\). It can be computed from the fine mixed cells of a subdivision of \(\mathcal A\). NEWLINENEWLINENEWLINEThis subdivison can be obtained via lifting functions and lower facets. The authors present a new algorithm where the lower facets are computed using a tailored version of the simplex algorithm for linear programming. They show the superiority of their methods over others by numerical results.
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