{"id":"https://openalex.org/W2027212082","doi":"https://doi.org/10.1145/29380.214343","title":"Algorithm 652","display_name":"Algorithm 652","publication_year":1987,"publication_date":"1987-09-01","ids":{"openalex":"https://openalex.org/W2027212082","doi":"https://doi.org/10.1145/29380.214343","mag":"2027212082"},"language":"en","primary_location":{"id":"doi:10.1145/29380.214343","is_oa":true,"landing_page_url":"https://doi.org/10.1145/29380.214343","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/29380.214343","source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/29380.214343","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068161656","display_name":"Layne T. Watson","orcid":"https://orcid.org/0000-0003-2009-107X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Layne T. Watson","raw_affiliation_strings":["Departments of Electrical Engineering and Computer Science, Industrial and Operations Engineering and Mathematics, University of Michigan, Ann Arbor, MI and Virginia Polytechnic Institute and State University"],"affiliations":[{"raw_affiliation_string":"Departments of Electrical Engineering and Computer Science, Industrial and Operations Engineering and Mathematics, University of Michigan, Ann Arbor, MI and Virginia Polytechnic Institute and State University","institution_ids":["https://openalex.org/I859038795","https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026811780","display_name":"Stephen C. Billups","orcid":"https://orcid.org/0000-0003-3627-0793"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen C. Billups","raw_affiliation_strings":["Safety Assessment Technologies Division 7233, Sandia National Laboratories, Albuquerque, NM","Safety Assessment Technologies Division 7233, Sandia National Laboratories, Albuquerque, NM#TAB#"],"affiliations":[{"raw_affiliation_string":"Safety Assessment Technologies Division 7233, Sandia National Laboratories, Albuquerque, NM","institution_ids":["https://openalex.org/I4210104735"]},{"raw_affiliation_string":"Safety Assessment Technologies Division 7233, Sandia National Laboratories, Albuquerque, NM#TAB#","institution_ids":["https://openalex.org/I192454743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111715135","display_name":"Alexander P. Morgan","orcid":null},"institutions":[{"id":"https://openalex.org/I118136607","display_name":"General Motors (United States)","ror":"https://ror.org/05addee68","country_code":"US","type":"company","lineage":["https://openalex.org/I118136607"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander P. Morgan","raw_affiliation_strings":["Mathematics Department, General Motors Research Laboratories, Warren, MI"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, General Motors Research Laboratories, Warren, MI","institution_ids":["https://openalex.org/I118136607"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068161656"],"corresponding_institution_ids":["https://openalex.org/I27837315","https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":21.0705,"has_fulltext":true,"cited_by_count":382,"citation_normalized_percentile":{"value":0.99672158,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"3","first_page":"281","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9983999729156494,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9947999715805054,"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8001061677932739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7815960645675659},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.5701050758361816},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5443929433822632},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.535914421081543},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5175946950912476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4641280174255371},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4509512782096863},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.4352928400039673},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4328386187553406},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4179735779762268},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32610881328582764},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3243219256401062},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22592505812644958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20298728346824646}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8001061677932739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7815960645675659},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5701050758361816},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5443929433822632},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.535914421081543},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5175946950912476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4641280174255371},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4509512782096863},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.4352928400039673},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4328386187553406},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4179735779762268},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32610881328582764},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3243219256401062},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22592505812644958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20298728346824646},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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:10.1145/29380.214343","is_oa":true,"landing_page_url":"https://doi.org/10.1145/29380.214343","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/29380.214343","source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/29380.214343","is_oa":true,"landing_page_url":"https://doi.org/10.1145/29380.214343","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/29380.214343","source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1199476271","display_name":null,"funder_award_id":"DE-AC04-76","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3345247719","display_name":"Mathematical Software For Homotopy Algorithms","funder_award_id":"8207217","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5570696538","display_name":null,"funder_award_id":"DE-AC04-76DP00789","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6971178474","display_name":null,"funder_award_id":"DP00789","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8414908677","display_name":null,"funder_award_id":"DE-AC0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2027212082.pdf","grobid_xml":"https://content.openalex.org/works/W2027212082.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1358817","https://openalex.org/W1517659762","https://openalex.org/W1583979427","https://openalex.org/W1596150805","https://openalex.org/W1971897569","https://openalex.org/W1973310172","https://openalex.org/W1976222070","https://openalex.org/W1976231053","https://openalex.org/W1979416293","https://openalex.org/W1979490178","https://openalex.org/W1983443215","https://openalex.org/W1995148226","https://openalex.org/W1998444222","https://openalex.org/W1999281516","https://openalex.org/W2001414735","https://openalex.org/W2021131708","https://openalex.org/W2024685678","https://openalex.org/W2025259350","https://openalex.org/W2028099324","https://openalex.org/W2028931640","https://openalex.org/W2029911309","https://openalex.org/W2053550367","https://openalex.org/W2057641327","https://openalex.org/W2060087716","https://openalex.org/W2066409969","https://openalex.org/W2068484625","https://openalex.org/W2076067331","https://openalex.org/W2081634353","https://openalex.org/W2091186243","https://openalex.org/W2128470309","https://openalex.org/W2133086779","https://openalex.org/W2137837586","https://openalex.org/W2156722294","https://openalex.org/W2164452006","https://openalex.org/W2243893708","https://openalex.org/W2320253350","https://openalex.org/W2330913512","https://openalex.org/W2344958626","https://openalex.org/W2608505863","https://openalex.org/W3163705782","https://openalex.org/W4230656725","https://openalex.org/W4235625704","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2007405763","https://openalex.org/W1486373823","https://openalex.org/W3136087161","https://openalex.org/W2053762185","https://openalex.org/W2119578520","https://openalex.org/W2018238589","https://openalex.org/W2145980196","https://openalex.org/W2362256999","https://openalex.org/W2007245702","https://openalex.org/W2048873866"],"abstract_inverted_index":{"There":[0],"are":[1,15,78],"algorithms":[2,32,60],"for":[3,18,61,81,92],"finding":[4],"zeros":[5],"or":[6],"fixed":[7],"points":[8],"of":[9,12,29,36,51,96],"nonlinear":[10],"systems":[11],"equations":[13],"that":[14],"globally":[16],"convergent":[17],"almost":[19],"all":[20,30],"starting":[21],"points,":[22],"i.e.,":[23],"with":[24],"probability":[25],"one.":[26],"The":[27],"essence":[28],"such":[31],"is":[33,90],"the":[34,48,63,93],"construction":[35],"an":[37],"appropriate":[38],"homotopy":[39,53,64],"map":[40],"and":[41,72,83],"then":[42],"tracking":[43,62],"some":[44],"smooth":[45],"curve":[46],"in":[47],"zero":[49,65],"set":[50],"this":[52],"map.":[54],"HOMPACK":[55],"provides":[56],"three":[57],"qualitatively":[58],"different":[59],"curve:":[66],"ordinary":[67],"differential":[68],"equation-based,":[69],"normal":[70],"flow,":[71],"augmented":[73],"Jacobian":[74,85],"matrix.":[75],"Separate":[76],"routines":[77],"also":[79],"provided":[80],"dense":[82],"sparse":[84],"matrices.":[86],"A":[87],"high-level":[88],"driver":[89],"included":[91],"special":[94],"case":[95],"polynomial":[97],"systems.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
