{"id":"https://openalex.org/W2038857114","doi":"https://doi.org/10.1145/2331684.2331710","title":"Empirical study of an evaluation-based subdivision algorithm for complex root isolation","display_name":"Empirical study of an evaluation-based subdivision algorithm for complex root isolation","publication_year":2012,"publication_date":"2012-06-07","ids":{"openalex":"https://openalex.org/W2038857114","doi":"https://doi.org/10.1145/2331684.2331710","mag":"2038857114"},"language":"en","primary_location":{"id":"doi:10.1145/2331684.2331710","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331710","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation","raw_type":"proceedings-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/A5013416639","display_name":"Narayan Kamath","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I4210113297","display_name":"Google (United Kingdom)","ror":"https://ror.org/024bc3e07","country_code":"GB","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210113297","https://openalex.org/I4210128969"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Narayan Kamath","raw_affiliation_strings":["Google, Inc. and Oxford Computing Lab, UK","Google, Inc. and Oxford Computing Lab, UK#TAB#"],"affiliations":[{"raw_affiliation_string":"Google, Inc. and Oxford Computing Lab, UK","institution_ids":["https://openalex.org/I4210113297"]},{"raw_affiliation_string":"Google, Inc. and Oxford Computing Lab, UK#TAB#","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055611196","display_name":"Irina Voiculescu","orcid":"https://orcid.org/0000-0002-9104-8012"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Irina Voiculescu","raw_affiliation_strings":["Oxford University, UK","Oxford University (UK)#TAB#"],"affiliations":[{"raw_affiliation_string":"Oxford University, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Oxford University (UK)#TAB#","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078989577","display_name":"Chee Yap","orcid":"https://orcid.org/0000-0003-2952-3545"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chee K. Yap","raw_affiliation_strings":["Courant Institute, NYU and Oxford Computing Lab, UK"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU and Oxford Computing Lab, UK","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013416639"],"corresponding_institution_ids":["https://openalex.org/I1291425158","https://openalex.org/I4210113297"],"apc_list":null,"apc_paid":null,"fwci":1.399,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80730127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"155","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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":0.9986000061035156,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/subdivision","display_name":"Subdivision","score":0.8900389075279236},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6626589298248291},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.585726797580719},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5310937166213989},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5260087251663208},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.388011634349823},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21513631939888},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15763503313064575}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8900389075279236},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6626589298248291},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.585726797580719},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5310937166213989},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5260087251663208},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.388011634349823},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21513631939888},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15763503313064575},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2331684.2331710","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331710","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:8de35d81-ccd4-43aa-a1f7-6d656b4f6d8d","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:8de35d81-ccd4-43aa-a1f7-6d656b4f6d8d","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science","raw_type":"Conference item"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:dde981a3-6888-40a9-8fcb-762ad67a642a","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:dde981a3-6888-40a9-8fcb-762ad67a642a","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6723795458","display_name":null,"funder_award_id":"CCF-0728977CCF-0917093","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W37596728","https://openalex.org/W203551860","https://openalex.org/W1483874187","https://openalex.org/W1532036648","https://openalex.org/W1572875162","https://openalex.org/W1595351456","https://openalex.org/W1604917823","https://openalex.org/W1702387807","https://openalex.org/W1832583097","https://openalex.org/W1941717577","https://openalex.org/W1986748775","https://openalex.org/W1995250895","https://openalex.org/W2021573332","https://openalex.org/W2031999868","https://openalex.org/W2033703141","https://openalex.org/W2043237762","https://openalex.org/W2054292870","https://openalex.org/W2068167196","https://openalex.org/W2070381457","https://openalex.org/W2073158267","https://openalex.org/W2074068518","https://openalex.org/W2075367494","https://openalex.org/W2077961479","https://openalex.org/W2085063566","https://openalex.org/W2106719661","https://openalex.org/W2120694921","https://openalex.org/W2123503236","https://openalex.org/W2130952444","https://openalex.org/W2131327682","https://openalex.org/W2144493917","https://openalex.org/W2167849855","https://openalex.org/W2169964384","https://openalex.org/W2185262283","https://openalex.org/W2251133682","https://openalex.org/W4244574515","https://openalex.org/W4249516290","https://openalex.org/W4290864872","https://openalex.org/W4300873693","https://openalex.org/W6628933813","https://openalex.org/W6634407384","https://openalex.org/W6635834624","https://openalex.org/W6668975508"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2140072033","https://openalex.org/W2163269603","https://openalex.org/W4205312897","https://openalex.org/W1106115901","https://openalex.org/W2055560755","https://openalex.org/W2386836336"],"abstract_inverted_index":{"We":[0,75,85],"provide":[1],"an":[2,60],"empirical":[3],"study":[4],"of":[5,13,22,29,42,70,80],"subdivision":[6,43],"algorithms":[7,30,44],"for":[8],"isolating":[9],"the":[10,23,77,90,97],"simple":[11],"roots":[12],"a":[14,53],"polynomial":[15],"in":[16,82],"any":[17],"desired":[18],"box":[19],"region":[20],"B0":[21],"complex":[24],"plane.":[25],"One":[26],"such":[27,112],"class":[28,41],"is":[31,45,56],"based":[32,46,58],"on":[33,47,59],"Newton-like":[34],"interval":[35],"methods":[36,111],"(Moore,":[37],"Krawczyk,":[38],"Hansen-Sengupta).":[39],"Another":[40],"function":[48],"evaluation.":[49],"Here,":[50],"Yakoubsohn":[51],"discussed":[52],"method":[54],"that":[55,108],"purely":[57],"exclusion":[61],"predicate.":[62],"Recently,":[63],"Sagraloff":[64],"and":[65,94,103,117],"Yap":[66],"introduced":[67],"another":[68],"algorithm":[69],"this":[71],"type,":[72],"called":[73],"Ceval.":[74],"describe":[76],"first":[78],"implementation":[79],"Ceval":[81,114],"Core":[83],"Library.":[84],"compare":[86],"its":[87],"performance":[88],"to":[89,96],"above":[91],"mentioned":[92],"algorithms,":[93],"also":[95],"well-known":[98],"MPSolve":[99],"software":[100],"from":[101],"Bini":[102],"Florentino.":[104],"Our":[105],"results":[106],"suggest":[107],"certified":[109],"evaluation-based":[110],"as":[113],"are":[115],"encouraging":[116],"deserve":[118],"further":[119],"exploration.":[120]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}