{"id":"https://openalex.org/W2134013328","doi":"https://doi.org/10.1145/1577190.1577202","title":"Experimental evaluation and cross-benchmarking of univariate real solvers","display_name":"Experimental evaluation and cross-benchmarking of univariate real solvers","publication_year":2009,"publication_date":"2009-08-03","ids":{"openalex":"https://openalex.org/W2134013328","doi":"https://doi.org/10.1145/1577190.1577202","mag":"2134013328"},"language":"en","primary_location":{"id":"doi:10.1145/1577190.1577202","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577202","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00340887/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047174420","display_name":"Michael Hemmer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Hemmer","raw_affiliation_strings":["MPI for Informatics, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MPI for Informatics, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elias P. Tsigaridas","raw_affiliation_strings":["INRIA, Sophia-Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Sophia-Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012936317","display_name":"Zafeirakis Zafeirakopoulos","orcid":"https://orcid.org/0000-0002-9632-6325"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Zafeirakis Zafeirakopoulos","raw_affiliation_strings":["Johannes Kepler University, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johannes Kepler University, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088969863","display_name":"Menelaos I. Karavelas","orcid":null},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]},{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Menelaos I. Karavelas","raw_affiliation_strings":["University of Crete + FORTH, Heraklion, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Crete + FORTH, Heraklion, Greece","institution_ids":["https://openalex.org/I142617266","https://openalex.org/I8901234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003683965","display_name":"Bernard Mourrain","orcid":"https://orcid.org/0000-0002-8813-1368"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernard Mourrain","raw_affiliation_strings":["INRIA, Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5047174420"],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":null,"apc_paid":null,"fwci":7.4441,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.97665131,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"45","last_page":"54"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9980999827384949,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/univariate","display_name":"Univariate","score":0.9113773107528687},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.6533876657485962},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6264272928237915},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.6183009147644043},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.47024813294410706},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4534958302974701},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39271023869514465},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35892602801322937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32473334670066833},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.323908269405365},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15852311253547668},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12356480956077576},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.07693469524383545}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.9113773107528687},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.6533876657485962},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6264272928237915},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.6183009147644043},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.47024813294410706},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4534958302974701},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39271023869514465},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35892602801322937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32473334670066833},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.323908269405365},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15852311253547668},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12356480956077576},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.07693469524383545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1577190.1577202","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577202","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:inria-00340887v2","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00340887","pdf_url":"https://inria.hal.science/inria-00340887/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Workshop SNC, ACM, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577202⟩","raw_type":"Conference papers"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.715.1704","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.715.1704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.tem.uoc.gr/%7Emkaravel/files/papers/eecur-snc09.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:518267","is_oa":false,"landing_page_url":"http://edoc.mpg.de/518267","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"SNC '09: Proceedings of the 2009 conference on Symbolic numeric computation, ACM, 45-54 (2009)","raw_type":"Conference-Paper"},{"id":"pmh:oai:pure.mpg.de:item_1324109","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-1846-F","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SNC '09: Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00340887v2","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00340887","pdf_url":"https://inria.hal.science/inria-00340887/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Workshop SNC, ACM, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577202⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2134013328.pdf","grobid_xml":"https://content.openalex.org/works/W2134013328.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W74955198","https://openalex.org/W98795181","https://openalex.org/W131450502","https://openalex.org/W1511166374","https://openalex.org/W1552350973","https://openalex.org/W1577339277","https://openalex.org/W1591895435","https://openalex.org/W1598339794","https://openalex.org/W1603065468","https://openalex.org/W1748106532","https://openalex.org/W1832583097","https://openalex.org/W1868080791","https://openalex.org/W1987590225","https://openalex.org/W2003860131","https://openalex.org/W2025810010","https://openalex.org/W2041844522","https://openalex.org/W2048184489","https://openalex.org/W2049417271","https://openalex.org/W2067705970","https://openalex.org/W2077961479","https://openalex.org/W2084459701","https://openalex.org/W2097217811","https://openalex.org/W2100399244","https://openalex.org/W2144619406","https://openalex.org/W2146199242","https://openalex.org/W2158622794","https://openalex.org/W2168222442","https://openalex.org/W2338982075","https://openalex.org/W2441241344","https://openalex.org/W2736255692","https://openalex.org/W3032086160","https://openalex.org/W4239443128","https://openalex.org/W4285719527","https://openalex.org/W6602933805","https://openalex.org/W6632910055","https://openalex.org/W7075739727"],"related_works":["https://openalex.org/W4238897586","https://openalex.org/W435179959","https://openalex.org/W2619091065","https://openalex.org/W2341842940","https://openalex.org/W2059640416","https://openalex.org/W1490753184","https://openalex.org/W2284465472","https://openalex.org/W2291782699","https://openalex.org/W1993948687","https://openalex.org/W2329895846"],"abstract_inverted_index":{"Real":[0],"solving":[1,211],"of":[2,20,23,30,53,91,98,119,129,198,206],"univariate":[3,31,209],"polynomials":[4,32,100],"is":[5,15,171,202],"a":[6],"fundamental":[7],"problem":[8],"with":[9,79],"several":[10],"important":[11],"applications.":[12],"This":[13],"paper":[14],"focused":[16],"on":[17,43,187],"the":[18,34,62,72,92,115,120,130,147,184,192,196,203],"comparison":[19],"black-box":[21],"implementations":[22,41,128],"state-of-the-art":[24],"algorithms":[25],"for":[26,181,208],"isolating":[27],"real":[28,210],"roots":[29],"over":[33],"integers.":[35],"We":[36,75],"have":[37,106],"tested":[38],"9":[39],"different":[40,103],"based":[42,186],"symbolic-numeric":[44],"methods,":[45],"Sturm":[46],"sequences,":[47],"Continued":[48,188],"Fractions":[49,189],"and":[50,71,114,152],"Descartes'":[51],"rule":[52],"sign.":[54],"The":[55],"methods":[56,133],"under":[57],"consideration":[58],"were":[59],"developed":[60],"at":[61,65,69],"GALAAD":[63],"group":[64,68],"INRIA,the":[66],"VEGAS":[67],"LORIA":[70],"MPI":[73],"Saarbr\u00fccken.":[74],"compared":[76],"their":[77],"sensitivity":[78],"respect":[80],"to":[81,111,155,163,213],"various":[82],"aspects":[83],"such":[84],"as":[85],"degree,":[86],"bitsize":[87,109],"or":[88],"root":[89],"separation":[90],"input":[93],"polynomials.":[94],"Our":[95,166],"datasets":[96],"consist":[97],"5,000":[99],"from":[101],"many":[102],"settings,":[104],"which":[105,160],"maximum":[107],"coefficient":[108],"up":[110,212],"bits":[112],"8,000,":[113],"total":[116],"running":[117],"time":[118],"experiments":[121],"was":[122],"about":[123],"50":[124],"hours.":[125],"Thereby,":[126],"all":[127],"theoretically":[131],"exact":[132],"always":[134],"provided":[135],"correct":[136],"results":[137,167],"throughout":[138],"this":[139,201],"extensive":[140],"study.":[141],"For":[142],"each":[143,158],"scenario":[144],"we":[145,153],"identify":[146],"currently":[148],"most":[149,182],"adequate":[150],"method,":[151],"point":[154],"weaknesses":[156],"in":[157],"approach,":[159],"should":[161],"lead":[162],"further":[164],"improvements.":[165],"indicate":[168],"that":[169,180],"there":[170],"no":[172],"\"best":[173],"method\"":[174],"overall,":[175],"but":[176],"one":[177],"can":[178],"say":[179],"instances":[183],"solvers":[185],"are":[190],"among":[191],"best":[193,197],"methods.":[194],"To":[195],"our":[199],"knowledge,":[200],"largest":[204],"number":[205],"tests":[207],"date.":[214]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}