{"id":"https://openalex.org/W4297021879","doi":"https://doi.org/10.1093/imamci/dnac017","title":"Iterative algorithms for reducing inversion of discrete algebraic riccati matrix equation","display_name":"Iterative algorithms for reducing inversion of discrete algebraic riccati matrix equation","publication_year":2022,"publication_date":"2022-09-23","ids":{"openalex":"https://openalex.org/W4297021879","doi":"https://doi.org/10.1093/imamci/dnac017"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnac017","is_oa":true,"landing_page_url":"https://doi.org/10.1093/imamci/dnac017","pdf_url":"https://academic.oup.com/imamci/article-pdf/39/4/985/47735369/dnac017.pdf","source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://academic.oup.com/imamci/article-pdf/39/4/985/47735369/dnac017.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103207599","display_name":"Jianzhou Liu","orcid":"https://orcid.org/0000-0003-1056-0274"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianzhou Liu","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-1056-0274","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100401100","display_name":"Zheng Wang","orcid":"https://orcid.org/0000-0002-4222-1659"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Wang","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhiming Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiming Xie","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University , Xiangtan, 411105 Hunan, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100336091","display_name":"Li Wang","orcid":"https://orcid.org/0000-0002-7489-3441"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan University of Science and Technology , Xiangtan, 411105 Hunan, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan University of Science and Technology , Xiangtan, 411105 Hunan, P. R. China","institution_ids":["https://openalex.org/I121296143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103207599"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":{"value":2582,"currency":"GBP","value_usd":3167},"fwci":1.2932,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8220567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"39","issue":"4","first_page":"985","last_page":"1007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6607964038848877},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6121695041656494},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.606623649597168},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.5554900765419006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5503545999526978},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.488295316696167},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48444700241088867},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4651309847831726},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.45113545656204224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4469635486602783},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44146278500556946},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34941524267196655},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34525424242019653},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12809821963310242},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10837754607200623},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08633694052696228},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06042167544364929}],"concepts":[{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6607964038848877},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6121695041656494},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.606623649597168},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.5554900765419006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5503545999526978},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.488295316696167},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48444700241088867},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4651309847831726},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.45113545656204224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4469635486602783},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44146278500556946},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34941524267196655},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34525424242019653},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12809821963310242},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10837754607200623},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08633694052696228},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06042167544364929},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnac017","is_oa":true,"landing_page_url":"https://doi.org/10.1093/imamci/dnac017","pdf_url":"https://academic.oup.com/imamci/article-pdf/39/4/985/47735369/dnac017.pdf","source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1093/imamci/dnac017","is_oa":true,"landing_page_url":"https://doi.org/10.1093/imamci/dnac017","pdf_url":"https://academic.oup.com/imamci/article-pdf/39/4/985/47735369/dnac017.pdf","source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2239969262","display_name":null,"funder_award_id":"91430213","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G2449565384","display_name":null,"funder_award_id":"11801164","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3762157797","display_name":null,"funder_award_id":"91430213","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4926683670","display_name":null,"funder_award_id":"11971413","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5184971586","display_name":null,"funder_award_id":"2015JJ2134","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5267561973","display_name":null,"funder_award_id":"11571292","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5398052954","display_name":null,"funder_award_id":"2015JJ2134","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7140317294","display_name":null,"funder_award_id":"15C1320","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4297021879.pdf","grobid_xml":"https://content.openalex.org/works/W4297021879.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W125612427","https://openalex.org/W1486025375","https://openalex.org/W1542938076","https://openalex.org/W1766888123","https://openalex.org/W1918128066","https://openalex.org/W1939044097","https://openalex.org/W1965640670","https://openalex.org/W1976988880","https://openalex.org/W1979164898","https://openalex.org/W1980740683","https://openalex.org/W1982955548","https://openalex.org/W1991511812","https://openalex.org/W1992997200","https://openalex.org/W2007322084","https://openalex.org/W2009502436","https://openalex.org/W2012057157","https://openalex.org/W2017401723","https://openalex.org/W2025519154","https://openalex.org/W2048134878","https://openalex.org/W2057921229","https://openalex.org/W2059221098","https://openalex.org/W2060190738","https://openalex.org/W2061553277","https://openalex.org/W2065575594","https://openalex.org/W2071824735","https://openalex.org/W2078060826","https://openalex.org/W2084401098","https://openalex.org/W2089724807","https://openalex.org/W2104717209","https://openalex.org/W2109726170","https://openalex.org/W2110596895","https://openalex.org/W2112801564","https://openalex.org/W2116877555","https://openalex.org/W2122055952","https://openalex.org/W2124210402","https://openalex.org/W2133866750","https://openalex.org/W2139861130","https://openalex.org/W2163334725","https://openalex.org/W2318722778","https://openalex.org/W2330619591","https://openalex.org/W2463195734","https://openalex.org/W2969415742","https://openalex.org/W3013246119","https://openalex.org/W3026626891","https://openalex.org/W4224717528","https://openalex.org/W4229706427","https://openalex.org/W6628931229","https://openalex.org/W6640241883","https://openalex.org/W6777850683","https://openalex.org/W6811034908"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433","https://openalex.org/W2096105566"],"abstract_inverted_index":{"Abstract":[0],"In":[1,27],"practical":[2],"engineering,":[3],"many":[4],"control":[5],"problems":[6],"usually":[7],"can":[8],"be":[9],"transformed":[10],"into":[11,54,78],"solutions":[12],"of":[13,36,44,72,110,133],"the":[14,32,37,49,84,108,129],"discrete":[15],"algebraic":[16],"Riccati":[17],"equation":[18],"(DARE),":[19],"which":[20],"has":[21],"two":[22],"matrix":[23,38],"inverse":[24,45],"operations":[25],"formally.":[26],"this":[28,76,120],"paper,":[29],"first,":[30],"by":[31],"relationship":[33],"between":[34],"properties":[35],"Schur":[39],"complement":[40],"and":[41,61,106,131],"partitioned":[42],"representation":[43],"matrix,":[46],"we":[47,74,87,101],"change":[48],"DARE":[50,77],"with":[51,58,115],"twice":[52],"inversions":[53],"an":[55,94],"equivalent":[56,81,85],"form":[57],"once":[59],"inversion":[60],"propose":[62,88],"a":[63,69,79,89],"corresponding":[64,122],"iterative":[65,91],"algorithm.":[66],"Next,":[67],"for":[68,98],"special":[70],"case":[71],"DARE,":[73],"deformed":[75],"new":[80,90],"one.":[82],"For":[83],"form,":[86],"algorithm":[92],"in":[93],"inversion-free":[95],"way.":[96],"Furthermore,":[97],"these":[99],"algorithms,":[100],"prove":[102],"their":[103,111],"monotone":[104],"convergence":[105],"give":[107],"analysis":[109],"errors.":[112],"Last,":[113],"comparing":[114],"some":[116],"existing":[117],"work":[118],"on":[119],"topic,":[121],"numerical":[123],"examples":[124],"are":[125],"given":[126],"to":[127],"illustrate":[128],"superiority":[130],"effectiveness":[132],"our":[134],"results.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2025-10-10T00:00:00"}
