Minimizing multi-homogeneous Bézout numbers by a local search method
type: Item
instance of: scholarly article
zbMATH Open document ID: 1013.65046
DOI: 10.1090/S0025-5718-00-01303-X
published in: Mathematics of Computation
publication date: 2001-02-19T00:00:00Z
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 1566131
zbMATH Keywords: multi-homogeneous Bézout number
zbMATH Keywords: polynomial system
zbMATH Keywords: homotopy method
zbMATH Keywords: local search method
zbMATH Keywords: numerical examples
author: Tiejun Li
author: Fengshan Bai
MaRDI profile type: Publication
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title: Minimizing multi-homogeneous Bézout numbers by a local search method
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.
reviewed by: Hermann G. Matthies
description: scientific article