{"id":"https://openalex.org/W1980102753","doi":"https://doi.org/10.1016/s0096-3003(99)00115-0","title":"Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods","display_name":"Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods","publication_year":2000,"publication_date":"2000-09-01","ids":{"openalex":"https://openalex.org/W1980102753","doi":"https://doi.org/10.1016/s0096-3003(99)00115-0","mag":"1980102753"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(99)00115-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(99)00115-0","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008328991","display_name":"Tangan Gao","orcid":null},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tangan Gao","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045521450","display_name":"Taiyong Li","orcid":"https://orcid.org/0000-0002-1546-8015"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T.Y. Li","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112224754","display_name":"Jan Verschelde","orcid":null},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jan Verschelde","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033080130","display_name":"Mengnien Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mengnien Wu","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics,Michigan State University,East Lansing,MI 48824-1027,USA","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112224754"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":3.2874,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.91570938,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"114","issue":"2-3","first_page":"233","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9847999811172485,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9800000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7699407339096069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7463181614875793},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.7018479704856873},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6834595203399658},{"id":"https://openalex.org/keywords/tracing","display_name":"Tracing","score":0.6789692044258118},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6418858766555786},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5137375593185425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5037767291069031},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4804672598838806},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.47478029131889343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30322542786598206},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22515910863876343},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1781635880470276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17385005950927734}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7699407339096069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7463181614875793},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.7018479704856873},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6834595203399658},{"id":"https://openalex.org/C138673069","wikidata":"https://www.wikidata.org/wiki/Q322229","display_name":"Tracing","level":2,"score":0.6789692044258118},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6418858766555786},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5137375593185425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5037767291069031},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4804672598838806},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.47478029131889343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30322542786598206},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22515910863876343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1781635880470276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17385005950927734},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s0096-3003(99)00115-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(99)00115-0","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},{"id":"pmh:oai:tkuir.lib.tku.edu.tw:987654321/107563","is_oa":false,"landing_page_url":"https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/107563","pdf_url":null,"source":{"id":"https://openalex.org/S4406922698","display_name":"Tamkang University Institutional Repository (TKUIR)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:tkuir.lib.tku.edu.tw:987654321/58693","is_oa":false,"landing_page_url":"https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/58693","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1512237513","https://openalex.org/W1561337879","https://openalex.org/W1977415556","https://openalex.org/W1985548249","https://openalex.org/W1989923040","https://openalex.org/W2034955763","https://openalex.org/W2035516724","https://openalex.org/W2066130115","https://openalex.org/W2081659888","https://openalex.org/W2087336107","https://openalex.org/W2088758224","https://openalex.org/W2143023483","https://openalex.org/W2143628714","https://openalex.org/W4206077821","https://openalex.org/W4238102028","https://openalex.org/W4301168154"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2391752819","https://openalex.org/W2012352190","https://openalex.org/W4225310406","https://openalex.org/W2362256999","https://openalex.org/W2007245702","https://openalex.org/W2048873866"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
