{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:47:43Z","timestamp":1776725263040,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"234","license":[{"start":{"date-parts":[[2001,10,18]],"date-time":"2001-10-18T00:00:00Z","timestamp":1003363200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous B\u00e9zout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous B\u00e9zout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method.<\/p>","DOI":"10.1090\/s0025-5718-00-01303-x","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:46Z","timestamp":1027707466000},"page":"767-787","source":"Crossref","is-referenced-by-count":11,"title":["Minimizing multi-homogeneous B\u00e9zout numbers by a local search method"],"prefix":"10.1090","volume":"70","author":[{"given":"Tiejun","family":"Li","sequence":"first","affiliation":[]},{"given":"Fengshan","family":"Bai","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,10,18]]},"reference":[{"key":"1","isbn-type":"print","first-page":"77","article-title":"A homotopy method for locating all zeros of a system of polynomials","author":"Chow, Shui Nee","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/3540095187"},{"key":"2","doi-asserted-by":"crossref","unstructured":"T. A. Gao, T. Y. Li, X. S. 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