{"id":"https://openalex.org/W1569588109","doi":"https://doi.org/10.23919/ecc.2003.7086598","title":"Approximate greatest common divisor of many polynomials and generalised resultants","display_name":"Approximate greatest common divisor of many polynomials and generalised resultants","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W1569588109","doi":"https://doi.org/10.23919/ecc.2003.7086598","mag":"1569588109"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2003.7086598","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7086598","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","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/A5048478636","display_name":"N. Karcanias","orcid":"https://orcid.org/0000-0002-1889-6314"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"N. Karcanias","raw_affiliation_strings":["Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK"],"affiliations":[{"raw_affiliation_string":"Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK","institution_ids":["https://openalex.org/I180825142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054923997","display_name":"Stavros Fatouros","orcid":null},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. Fatouros","raw_affiliation_strings":["Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK"],"affiliations":[{"raw_affiliation_string":"Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK","institution_ids":["https://openalex.org/I180825142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009517859","display_name":"Marilena Mitrouli","orcid":null},"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":"M. Mitrouli","raw_affiliation_strings":["Department of Mathematics, University of Athens, Panepistemiopolis 15784, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Athens, Panepistemiopolis 15784, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004895976","display_name":"George Halikias","orcid":"https://orcid.org/0000-0003-1260-1383"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G. Halikias","raw_affiliation_strings":["Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK"],"affiliations":[{"raw_affiliation_string":"Control Engineering Centre, School of Engineering, City University, Northampton Square, London, EC1V0HB, UK","institution_ids":["https://openalex.org/I180825142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048478636"],"corresponding_institution_ids":["https://openalex.org/I180825142"],"apc_list":null,"apc_paid":null,"fwci":1.0635,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74747701,"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":"3583","last_page":"3586"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9997000098228455,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/greatest-common-divisor","display_name":"Greatest common divisor","score":0.8753454089164734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8711214065551758},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5743709802627563},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5398927927017212},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5226923227310181},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4263344407081604},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4139268398284912},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41250288486480713},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2987065315246582},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28453290462493896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08537298440933228}],"concepts":[{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.8753454089164734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8711214065551758},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5743709802627563},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5398927927017212},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5226923227310181},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4263344407081604},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4139268398284912},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41250288486480713},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2987065315246582},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28453290462493896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08537298440933228},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2003.7086598","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2003.7086598","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2003 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W130500341","https://openalex.org/W1572189095","https://openalex.org/W2020156690","https://openalex.org/W2116318259","https://openalex.org/W2140279008","https://openalex.org/W2140710461","https://openalex.org/W2614481108","https://openalex.org/W7056756531"],"related_works":["https://openalex.org/W2011129019","https://openalex.org/W2464170562","https://openalex.org/W2011432541","https://openalex.org/W2890926087","https://openalex.org/W2769688358","https://openalex.org/W2079183647","https://openalex.org/W2391305499","https://openalex.org/W2038478051","https://openalex.org/W2170050979","https://openalex.org/W2051087136"],"abstract_inverted_index":{"In":[0],"this":[1,94],"paper,":[2],"a":[3,45,84,106,155],"new":[4,29,78,95],"characterisation":[5],"of":[6,10,20,22,40,44,47,65,74,101,105,122,143],"the":[7,18,23,38,41,57,63,99,102,115,119,126,134,141,151],"approximate":[8,144],"GCD":[9,26,59],"many":[11],"polynomials":[12,48],"is":[13,31,111],"given":[14,128],"that":[15],"also":[16],"allows":[17,62],"evaluation":[19,110],"accuracy":[21],"corresponding":[24],"\u2018approximate":[25,66,72,103,130],"computation\u2019.":[27],"This":[28,61,77,109],"approach":[30,79],"based":[32],"on":[33,37,118,154],"some":[34],"recent":[35],"results":[36],"factorisation":[39],"generalised":[42,75],"resultant":[43],"set":[46,121],"into":[49],"reduced":[50],"resultants":[51],"and":[52],"appropriate":[53],"Toeplitz":[54],"matrices":[55],"representing":[56],"exact":[58,132,152],"[1].":[60],"reduction":[64],"GCD\u2019":[67,104,131],"computation":[68],"to":[69,97,113,150],"an":[70],"equivalent":[71,112],"factorisation\u2019":[73],"resultants.":[76],"may":[80],"be":[81],"formulated":[82],"as":[83],"structured":[85,90],"optimization":[86],"problem":[87],"(distance":[88],"between":[89],"matrices).":[91],"We":[92],"use":[93],"framework":[96],"evaluate":[98],"\u2018accuracy\u2019":[100],"certain":[107],"degree.":[108],"finding":[114],"minimal":[116],"perturbation":[117],"original":[120],"polynomials,":[123],"which":[124],"make":[125],"selected":[127],"degree":[129],"for":[133],"perturbed":[135,156],"set.":[136,157],"The":[137],"later":[138],"makes":[139],"precise":[140],"meaning":[142],"GCD,":[145],"since":[146],"it":[147,149],"relates":[148],"notion":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
