{"id":"https://openalex.org/W2786204129","doi":"https://doi.org/10.1137/18m1168522","title":"An Algorithmic Characterization of P-matricity II: Adjustments, Refinements, and Validation","display_name":"An Algorithmic Characterization of P-matricity II: Adjustments, Refinements, and Validation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2786204129","doi":"https://doi.org/10.1137/18m1168522","mag":"2786204129"},"language":"en","primary_location":{"id":"doi:10.1137/18m1168522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1168522","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-01672197/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046043088","display_name":"Ibtihel Ben Gharbia","orcid":"https://orcid.org/0000-0002-9002-1985"},"institutions":[{"id":"https://openalex.org/I265217849","display_name":"IFP \u00c9nergies nouvelles","ror":"https://ror.org/03gcbhc33","country_code":"FR","type":"facility","lineage":["https://openalex.org/I265217849"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"I. Ben Gharbia","raw_affiliation_strings":["IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Pr\u00e9au\r\n92500 Rueil-Malmaison - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IFPEN - IFP Energies nouvelles (1-4 avenue de Bois Pr\u00e9au\r\n92500 Rueil-Malmaison - France)","institution_ids":["https://openalex.org/I265217849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033475682","display_name":"Jean Charles Gilbert","orcid":"https://orcid.org/0000-0002-0375-4663"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Ch. Gilbert","raw_affiliation_strings":["Inria de Paris (2 rue Simone Iff -\r\nCS 42112 -\r\n75589 Paris Cedex 12 - France)"],"raw_orcid":"https://orcid.org/0000-0002-0375-4663","affiliations":[{"raw_affiliation_string":"Inria de Paris (2 rue Simone Iff -\r\nCS 42112 -\r\n75589 Paris Cedex 12 - France)","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4007,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.94881994,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"40","issue":"2","first_page":"800","last_page":"813"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.8002583384513855},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.649069607257843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6458673477172852},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5899823904037476},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5320219993591309},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5216567516326904},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.50334233045578},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.4580584466457367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3923206925392151},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.378980815410614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10006365180015564},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08677870035171509},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06361472606658936}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8002583384513855},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.649069607257843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6458673477172852},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5899823904037476},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5320219993591309},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5216567516326904},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.50334233045578},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.4580584466457367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3923206925392151},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.378980815410614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10006365180015564},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08677870035171509},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06361472606658936},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1168522","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1168522","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01672197v4","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01672197","pdf_url":"https://inria.hal.science/hal-01672197/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":"SIAM Journal on Matrix Analysis and Applications, 2019, 40 (2), pp.800-813. ⟨10.1137/18M1168522⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01672197v2","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-01672197","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":"https://hal.inria.fr/hal-01672197","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01672197v4","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01672197","pdf_url":"https://inria.hal.science/hal-01672197/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":"SIAM Journal on Matrix Analysis and Applications, 2019, 40 (2), pp.800-813. ⟨10.1137/18M1168522⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2786204129.pdf","grobid_xml":"https://content.openalex.org/works/W2786204129.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W875426949","https://openalex.org/W1977135073","https://openalex.org/W1992688650","https://openalex.org/W2026365342","https://openalex.org/W2035345211","https://openalex.org/W2052611587","https://openalex.org/W2075205943","https://openalex.org/W2076887500","https://openalex.org/W2085202100","https://openalex.org/W2092963025","https://openalex.org/W2113734366","https://openalex.org/W2128234186","https://openalex.org/W2135978105","https://openalex.org/W2169988972","https://openalex.org/W2287259016","https://openalex.org/W2321923742"],"related_works":["https://openalex.org/W2276648117","https://openalex.org/W819098253","https://openalex.org/W2599483915","https://openalex.org/W1548220668","https://openalex.org/W15122084","https://openalex.org/W2765841216","https://openalex.org/W2607337407","https://openalex.org/W1566966152","https://openalex.org/W169948756","https://openalex.org/W2078891263"],"abstract_inverted_index":{"The":[0,91,140],"paper":[1,109],"\u201cAn":[2],"Algorithmic":[3],"Characterization":[4],"of":[5,39,53,65,93,107],"P-Matricity\u201d":[6],"[":[7],"SIAM":[8],"J.":[9],"Matrix":[10],"Anal.":[11],"Appl.,":[12],"34":[13],"(2013),":[14],"pp.":[15],"904--916],":[16],"by":[17,29,49],"the":[18,26,30,80,83,94,104,127],"same":[19],"authors":[20],"as":[21],"here,":[22],"implicitly":[23],"assumes":[24],"that":[25,68,108,115],"iterates":[27],"generated":[28],"Newton-min":[31,128],"algorithm":[32,129],"for":[33,62],"solving":[34],"a":[35,63,116,121],"linear":[36],"complementarity":[37],"problem":[38],"dimension":[40],"$n$,":[41],"which":[42,150],"reads":[43],"$0\\leq":[44],"x\\perp(Mx+q)\\geq0$,":[45],"are":[46,151],"uniquely":[47],"determined":[48],"some":[50,148],"index":[51],"subsets":[52],"$\\llbracket":[54],"1,n":[55],"\\rrbracket$.":[56],"Even":[57],"if":[58,123,126],"this":[59,73,102],"is":[60,69,75,86,97,110,120,142],"satisfied":[61],"subset":[64],"vectors":[66],"$q$":[67,85,138],"dense":[70],"in":[71,77,79],"$\\mathbb{R}^n$,":[72],"assumption":[74],"improper,":[76],"particular":[78],"statements":[81],"where":[82],"vector":[84],"not":[87,131,143],"subject":[88],"to":[89,98],"restrictions.":[90],"goal":[92],"present":[95],"contribution":[96],"show":[99],"that,":[100],"despite":[101],"blunder,":[103],"main":[105],"result":[106],"preserved.":[111],"This":[112],"one":[113],"claims":[114],"nondegenerate":[117],"matrix":[118],"$M$":[119],"P-matrix":[122],"and":[124],"only":[125,147],"does":[130],"cycle":[132],"between":[133],"two":[134],"distinct":[135],"points,":[136],"whatever":[137],"is.":[139],"proof":[141],"more":[144],"complex,":[145],"requiring":[146],"adjustments,":[149],"essential,":[152],"however.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}