Minimizing multi-homogeneous Bézout numbers by a local search method (Q2701563): Difference between revisions
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Minimizing multi-homogeneous Bézout numbers by a local search method (English) | |||
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This paper is about the preparations for computing the zeros of polynomial systems via a homotopy method. For this it is important that the number of homotopy paths is as small as possible. This number is bounded by the Bézout and the multi-homogeneous Bézout numbers. For the latter it is important to partition the variables into disjoint classes. The authors develop a ``topology'' on these classes, and starting from a certain point proceed to improve the multi-homogeneous Bézout number through local searches. They demonstrate the effectiveness with a few examples and conjecture that the problem of finding the minimal multi-homogeneous Bézout number may be NP-hard. | |||
| Property / review text: This paper is about the preparations for computing the zeros of polynomial systems via a homotopy method. For this it is important that the number of homotopy paths is as small as possible. This number is bounded by the Bézout and the multi-homogeneous Bézout numbers. For the latter it is important to partition the variables into disjoint classes. The authors develop a ``topology'' on these classes, and starting from a certain point proceed to improve the multi-homogeneous Bézout number through local searches. They demonstrate the effectiveness with a few examples and conjecture that the problem of finding the minimal multi-homogeneous Bézout number may be NP-hard. / rank | |||
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| Property / reviewed by: Hermann G. Matthies / rank | |||
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Latest revision as of 14:36, 10 April 2025
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimizing multi-homogeneous Bézout numbers by a local search method |
scientific article |
Statements
19 February 2001
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multi-homogeneous Bézout number
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polynomial system
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homotopy method
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local search method
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numerical examples
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Minimizing multi-homogeneous Bézout numbers by a local search method (English)
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This paper is about the preparations for computing the zeros of polynomial systems via a homotopy method. For this it is important that the number of homotopy paths is as small as possible. This number is bounded by the Bézout and the multi-homogeneous Bézout numbers. For the latter it is important to partition the variables into disjoint classes. The authors develop a ``topology'' on these classes, and starting from a certain point proceed to improve the multi-homogeneous Bézout number through local searches. They demonstrate the effectiveness with a few examples and conjecture that the problem of finding the minimal multi-homogeneous Bézout number may be NP-hard.
0 references
