{"id":"https://openalex.org/W2158516852","doi":"https://doi.org/10.1145/2331130.2331136","title":"Algorithm 921","display_name":"Algorithm 921","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2158516852","doi":"https://doi.org/10.1145/2331130.2331136","mag":"2158516852"},"language":"en","primary_location":{"id":"doi:10.1145/2331130.2331136","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331130.2331136","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007214938","display_name":"Jonathan D. Hauenstein","orcid":"https://orcid.org/0000-0002-9252-8210"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonathan D. Hauenstein","raw_affiliation_strings":["Texas A&M University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078229263","display_name":"Frank Sottile","orcid":"https://orcid.org/0000-0003-0087-7120"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frank Sottile","raw_affiliation_strings":["Texas A&M University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.7665,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.98880083,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"38","issue":"4","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9972000122070312,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/overdetermined-system","display_name":"Overdetermined system","score":0.6488162279129028},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5711161494255066},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5561208724975586},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5249776244163513},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.5221205949783325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5218545198440552},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.4544459283351898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4452565014362335},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4292660355567932},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2838120460510254}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.6488162279129028},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5711161494255066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5561208724975586},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5249776244163513},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.5221205949783325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5218545198440552},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.4544459283351898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4452565014362335},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4292660355567932},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2838120460510254},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2331130.2331136","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331130.2331136","pdf_url":null,"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":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7076854086","display_name":null,"funder_award_id":"DMS-0915211DMS-0922866DMS-1114336","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W59564462","https://openalex.org/W1495088152","https://openalex.org/W1550331971","https://openalex.org/W1570420806","https://openalex.org/W1571614612","https://openalex.org/W1607862333","https://openalex.org/W1627871703","https://openalex.org/W1969213662","https://openalex.org/W1974806647","https://openalex.org/W1979462002","https://openalex.org/W1983221496","https://openalex.org/W1989369020","https://openalex.org/W2019363796","https://openalex.org/W2028576930","https://openalex.org/W2030727463","https://openalex.org/W2049665423","https://openalex.org/W2062754393","https://openalex.org/W2066409969","https://openalex.org/W2067437385","https://openalex.org/W2077129956","https://openalex.org/W2081901537","https://openalex.org/W2089003198","https://openalex.org/W2105458451","https://openalex.org/W2127042188","https://openalex.org/W2136480649","https://openalex.org/W2158358539","https://openalex.org/W2159461250","https://openalex.org/W2167360454","https://openalex.org/W2170485468","https://openalex.org/W2175098281","https://openalex.org/W2494491604","https://openalex.org/W2592503220","https://openalex.org/W2792841820","https://openalex.org/W2798909945","https://openalex.org/W2952107645","https://openalex.org/W4210648061","https://openalex.org/W4231932295","https://openalex.org/W4301168154","https://openalex.org/W6672845998"],"related_works":["https://openalex.org/W4382516418","https://openalex.org/W2990591761","https://openalex.org/W4386576538","https://openalex.org/W1981326443","https://openalex.org/W2347376008","https://openalex.org/W2383044727","https://openalex.org/W4287998014","https://openalex.org/W28907793","https://openalex.org/W2000063485","https://openalex.org/W2055757595"],"abstract_inverted_index":{"Smale\u2019s":[0],"\u03b1":[1,34],"-theory":[2,35],"uses":[3],"estimates":[4],"related":[5],"to":[6,12,20,22,36,64,70,74,80],"the":[7,82],"convergence":[8],"of":[9,39],"Newton\u2019s":[10],"method":[11],"certify":[13,37,58],"that":[14,57],"Newton":[15],"iterations":[16],"will":[17],"converge":[18],"quadratically":[19],"solutions":[21,38,73],"a":[23,60,65],"square":[24],"polynomial":[25,40],"system.":[26],"The":[27],"program":[28],"alphaCertified":[29],"implements":[30,55],"algorithms":[31,56,69],"based":[32],"on":[33],"systems":[41],"using":[42],"both":[43],"exact":[44],"rational":[45],"arithmetic":[46],"and":[47,68],"arbitrary":[48],"precision":[49],"floating":[50],"point":[51,62],"arithmetic.":[52],"It":[53],"also":[54],"whether":[59],"given":[61],"corresponds":[63],"real":[66],"solution,":[67],"heuristically":[71],"validate":[72],"overdetermined":[75],"systems.":[76],"Examples":[77],"are":[78],"presented":[79],"demonstrate":[81],"algorithms.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}