{"id":"https://openalex.org/W2059248461","doi":"https://doi.org/10.1090/s0025-5718-00-01303-x","title":"Minimizing multi-homogeneous B\u00e9zout numbers by a local search method","display_name":"Minimizing multi-homogeneous B\u00e9zout numbers by a local search method","publication_year":2000,"publication_date":"2000-10-18","ids":{"openalex":"https://openalex.org/W2059248461","doi":"https://doi.org/10.1090/s0025-5718-00-01303-x","mag":"2059248461"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01303-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01303-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01303-X/S0025-5718-00-01303-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01303-X/S0025-5718-00-01303-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111365454","display_name":"Tiejun Li","orcid":"https://orcid.org/0000-0003-4881-812X"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tiejun Li","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102215816","display_name":"Fengshan Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fengshan Bai","raw_affiliation_strings":["Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China","Department of Mathematics, Tsinghua University, Beijing, 100084, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematics, Tsinghua University, Beijing, 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111365454"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":0.5541,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.69081838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"70","issue":"234","first_page":"767","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8989542126655579},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7459019422531128},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.7282959818840027},{"id":"https://openalex.org/keywords/partition-problem","display_name":"Partition problem","score":0.5347586870193481},{"id":"https://openalex.org/keywords/local-search","display_name":"Local search (optimization)","score":0.5084027647972107},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.4829501509666443},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.4224448502063751},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38478323817253113},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36354804039001465},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24956366419792175},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12579703330993652},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06559735536575317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8989542126655579},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7459019422531128},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.7282959818840027},{"id":"https://openalex.org/C35995877","wikidata":"https://www.wikidata.org/wiki/Q1065968","display_name":"Partition problem","level":3,"score":0.5347586870193481},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.5084027647972107},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4829501509666443},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.4224448502063751},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38478323817253113},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36354804039001465},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24956366419792175},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12579703330993652},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06559735536575317},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-00-01303-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01303-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01303-X/S0025-5718-00-01303-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01303-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01303-x","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01303-X/S0025-5718-00-01303-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2059248461.pdf","grobid_xml":"https://content.openalex.org/works/W2059248461.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1972040900","https://openalex.org/W1975041748","https://openalex.org/W1985548249","https://openalex.org/W1989923040","https://openalex.org/W2002312285","https://openalex.org/W2005936052","https://openalex.org/W2010906827","https://openalex.org/W2011026283","https://openalex.org/W2034955763","https://openalex.org/W2048277184","https://openalex.org/W2076067331","https://openalex.org/W2088758224","https://openalex.org/W2091186243","https://openalex.org/W2109596995","https://openalex.org/W2137837586","https://openalex.org/W2494797023","https://openalex.org/W4238102028","https://openalex.org/W6604267941"],"related_works":["https://openalex.org/W2025912669","https://openalex.org/W2057299700","https://openalex.org/W1549987457","https://openalex.org/W2014615094","https://openalex.org/W1977789739","https://openalex.org/W2351778335","https://openalex.org/W4240458717","https://openalex.org/W2497180562","https://openalex.org/W2379495598","https://openalex.org/W2047470742"],"abstract_inverted_index":{"Consider":[0],"the":[1,18,23,34,69,78],"multi-homogeneous":[2,19,51],"homotopy":[3],"continuation":[4],"method":[5,42],"for":[6,43],"solving":[7],"a":[8,39,45,64],"system":[9],"of":[10,16,25,47,80],"polynomial":[11],"equations.":[12],"For":[13],"any":[14,56],"partition":[15,46],"variables,":[17],"B\u00e9zout":[20,52],"number":[21,24],"bounds":[22],"isolated":[26],"solution":[27],"curves":[28],"one":[29],"has":[30],"to":[31],"follow":[32],"in":[33],"method.":[35,84],"This":[36],"paper":[37],"presents":[38],"local":[40,58,65,82],"search":[41,59,83],"finding":[44],"variables":[48],"with":[49,55],"minimal":[50],"number.":[53],"As":[54],"other":[57],"method,":[60],"it":[61],"may":[62],"give":[63],"minimum":[66,70],"rather":[67],"than":[68],"over":[71],"all":[72],"possible":[73],"homogenizations.":[74],"Numerical":[75],"examples":[76],"show":[77],"efficiency":[79],"this":[81]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}