{"id":"https://openalex.org/W2974156201","doi":"https://doi.org/10.1145/3363520.3363522","title":"Row reduction process for matrices of scalar operators","display_name":"Row reduction process for matrices of scalar operators","publication_year":2019,"publication_date":"2019-09-18","ids":{"openalex":"https://openalex.org/W2974156201","doi":"https://doi.org/10.1145/3363520.3363522","mag":"2974156201"},"language":"en","primary_location":{"id":"doi:10.1145/3363520.3363522","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3363520.3363522","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-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/A5066677758","display_name":"\u0421. \u0410. \u0410\u0431\u0440\u0430\u043c\u043e\u0432","orcid":null},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Sergei A. Abramov","raw_affiliation_strings":["\"Computer Science and Control\" of the Russian Academy of Sciences;, Vavilova, Moscow, Russia",", Vavilova, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\"Computer Science and Control\" of the Russian Academy of Sciences;, Vavilova, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035"]},{"raw_affiliation_string":", Vavilova, Moscow, Russia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105411881","display_name":"Moulay A. Barkatou","orcid":"https://orcid.org/0000-0001-9892-9448"},"institutions":[{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Moulay A. Barkatou","raw_affiliation_strings":["Universit\u00e9 de Limoges;, Limoges, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges;, Limoges, France","institution_ids":["https://openalex.org/I65806277"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14999075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"1","first_page":"23","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.8546156287193298},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.785513162612915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7244197130203247},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6359023451805115},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5807294249534607},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5257022380828857},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4824398458003998},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47946131229400635},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39583027362823486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3540831208229065},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.27780961990356445}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8546156287193298},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.785513162612915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7244197130203247},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6359023451805115},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5807294249534607},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5257022380828857},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4824398458003998},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47946131229400635},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39583027362823486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3540831208229065},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.27780961990356445},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3363520.3363522","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3363520.3363522","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02393890v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02393890","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Communications in Computer Algebra, 2019, 53 (1), pp.23-30. &#x27E8;10.1145/3363520.3363522&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W78494858","https://openalex.org/W114689604","https://openalex.org/W1990226699","https://openalex.org/W1994728957","https://openalex.org/W2015697919","https://openalex.org/W2017249959","https://openalex.org/W2021258994","https://openalex.org/W2093914057","https://openalex.org/W2107951283","https://openalex.org/W2110836275","https://openalex.org/W2269795257","https://openalex.org/W2513157961","https://openalex.org/W2789870126","https://openalex.org/W2888260387","https://openalex.org/W2964290923","https://openalex.org/W4234000537"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W4289867043","https://openalex.org/W2784467519","https://openalex.org/W2504004674","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2963453621","https://openalex.org/W2498744856","https://openalex.org/W763418848","https://openalex.org/W1595229445"],"abstract_inverted_index":{"It":[0],"is":[1,17],"well":[2],"known":[3,42],"that":[4,121],"if":[5],"the":[6,20,32,63,67,70,74,77,89,93,101,110,114],"leading":[7,60],"matrix":[8,24,47,54],"of":[9,22,31,38,41,48,88,95,109],"a":[10,36,46,81],"linear":[11],"ordinary":[12],"differential":[13,71],"or":[14],"difference":[15,78],"system":[16],"nonsingular,":[18],"then":[19],"determinant":[21],"this":[23],"contains":[25],"some":[26,86,122],"useful":[27],"information":[28],"on":[29],"solutions":[30],"system.":[33],"We":[34,84,104],"investigate":[35],"kind":[37],"non-arithmetic":[39],"complexity":[40,90,111],"algorithms":[43,64],"for":[44],"transforming":[45],"scalar":[49],"operators":[50],"to":[51],"an":[52],"equivalent":[53],"which":[55],"has":[56],"non-singular":[57],"frontal,":[58],"or,":[59,97],"matrix.":[61],"In":[62],"under":[65],"consideration,":[66],"differentiation":[68],"in":[69,76,100],"case":[72,79],"and":[73,126],"shift":[75],"play":[80],"significant":[82],"role.":[83],"give":[85],"analysis":[87],"measured":[91],"as":[92],"number":[94],"differentiations":[96],"resp.,":[98],"shifts":[99],"worst":[102],"case.":[103],"not":[105,128],"only":[106],"offer":[107],"estimates":[108,123],"written":[112],"using":[113],"O":[115],"-notation,":[116],"but":[117],"we":[118],"also":[119],"show":[120],"are":[124],"sharp":[125],"can":[127],"be":[129],"improved.":[130]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
