{"id":"https://openalex.org/W2008241326","doi":"https://doi.org/10.1145/1576702.1576723","title":"On finding multiplicities of characteristic polynomial factors of black-box matrices","display_name":"On finding multiplicities of characteristic polynomial factors of black-box matrices","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W2008241326","doi":"https://doi.org/10.1145/1576702.1576723","mag":"2008241326"},"language":"en","primary_location":{"id":"doi:10.1145/1576702.1576723","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576723","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 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0901.4747","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091337059","display_name":"Jean\u2010Guillaume Dumas","orcid":"https://orcid.org/0000-0002-2591-172X"},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Grenoble Universit\u00e9, Grenoble, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Grenoble Universit\u00e9, Grenoble, France","institution_ids":["https://openalex.org/I899635006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079752845","display_name":"Cl\u00e9ment Pernet","orcid":"https://orcid.org/0000-0001-6970-0417"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Pernet","raw_affiliation_strings":["Grenoble Universit\u00e9, Montbonnot, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Grenoble Universit\u00e9, Montbonnot, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057745748","display_name":"B. David Saunders","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. David Saunders","raw_affiliation_strings":["University of Delaware, Newark, DE, USA","University of Delaware, Newark, DE. USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]},{"raw_affiliation_string":"University of Delaware, Newark, DE. USA","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6103,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70595091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"135","last_page":"142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"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":0.9983000159263611,"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/integer-matrix","display_name":"Integer matrix","score":0.5804923176765442},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.550794243812561},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5313922166824341},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.5167333483695984},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.515503466129303},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48892632126808167},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4867298901081085},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.4715573787689209},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.448900431394577},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4371689558029175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4150146245956421},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3633657991886139},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3417397439479828},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.2151925265789032},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16953378915786743},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.09971478581428528}],"concepts":[{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.5804923176765442},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.550794243812561},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5313922166824341},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.5167333483695984},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.515503466129303},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48892632126808167},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4867298901081085},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.4715573787689209},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.448900431394577},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4371689558029175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4150146245956421},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3633657991886139},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3417397439479828},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2151925265789032},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16953378915786743},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.09971478581428528},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1576702.1576723","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576723","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 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:0901.4747","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.4747","pdf_url":"https://arxiv.org/pdf/0901.4747","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00357262v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00357262","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2009 - International Symposium on Symbolic and Algebraic Computation, Jul 2009, S\u00e9oul, South Korea. pp.135-142, &#x27E8;10.1145/1576702.1576723&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0901.4747","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.4747","pdf_url":"https://arxiv.org/pdf/0901.4747","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W149384130","https://openalex.org/W173029725","https://openalex.org/W1499171371","https://openalex.org/W1502124338","https://openalex.org/W1508580542","https://openalex.org/W1515261402","https://openalex.org/W1562183207","https://openalex.org/W1594960997","https://openalex.org/W1605088207","https://openalex.org/W1931801724","https://openalex.org/W1965506160","https://openalex.org/W1971862312","https://openalex.org/W1984987350","https://openalex.org/W1994635102","https://openalex.org/W2012620680","https://openalex.org/W2018433009","https://openalex.org/W2032080903","https://openalex.org/W2071483197","https://openalex.org/W2085819076","https://openalex.org/W2100300741","https://openalex.org/W2127412655","https://openalex.org/W2128978199","https://openalex.org/W2141363069","https://openalex.org/W2161330625","https://openalex.org/W2203317094","https://openalex.org/W2950606748","https://openalex.org/W3017039354","https://openalex.org/W6679103854"],"related_works":["https://openalex.org/W2335071938","https://openalex.org/W2905919007","https://openalex.org/W2023818677","https://openalex.org/W1489986405","https://openalex.org/W2382784327","https://openalex.org/W4391074879","https://openalex.org/W2041271016","https://openalex.org/W2087439748","https://openalex.org/W2377029957","https://openalex.org/W2058078107"],"abstract_inverted_index":{"We":[0],"present":[1],"algorithms":[2,64],"and":[3],"heuristics":[4],"to":[5,28,36],"compute":[6,29],"the":[7,40],"characteristic":[8],"polynomial":[9],"of":[10],"a":[11,22,26,44],"matrix":[12,18],"given":[13],"its":[14,30],"minimal":[15],"polynomial.":[16],"The":[17,33],"is":[19],"represented":[20],"as":[21],"black-box,":[23],"i.e.,":[24],"by":[25],"function":[27],"matrix-vector":[31],"product.":[32],"methods":[34,53],"apply":[35],"matrices":[37,73],"either":[38],"over":[39,43],"integers":[41],"or":[42],"large":[45],"enough":[46],"finite":[47],"field.":[48],"Experiments":[49],"show":[50],"that":[51],"these":[52,63],"perform":[54],"efficiently":[55],"in":[56,59,68,75],"practice.":[57],"Combined":[58],"an":[60,76],"adaptive":[61],"strategy,":[62],"reach":[65],"significant":[66],"speedups":[67],"practice":[69],"for":[70],"some":[71],"integer":[72],"arising":[74],"application":[77],"from":[78],"graph":[79],"theory.":[80]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
