{"id":"https://openalex.org/W1983184346","doi":"https://doi.org/10.1137/050647669","title":"Iterative Solution of a Nonsymmetric Algebraic Riccati Equation","display_name":"Iterative Solution of a Nonsymmetric Algebraic Riccati Equation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1983184346","doi":"https://doi.org/10.1137/050647669","mag":"1983184346"},"language":"en","primary_location":{"id":"doi:10.1137/050647669","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647669","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100956974","display_name":"Chun\u2010Hua Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I194028371","display_name":"University of Regina","ror":"https://ror.org/03dzc0485","country_code":"CA","type":"education","lineage":["https://openalex.org/I194028371"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Chun\u2010Hua Guo","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada","institution_ids":["https://openalex.org/I194028371"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069339254","display_name":"Nicholas J. Higham","orcid":"https://orcid.org/0000-0001-5956-4976"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicholas J. Higham","raw_affiliation_strings":["Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100956974"],"corresponding_institution_ids":["https://openalex.org/I194028371"],"apc_list":null,"apc_paid":null,"fwci":7.8621,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.97660514,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"2","first_page":"396","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T12303","display_name":"Tensor decomposition and applications","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9693999886512756,"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.9343483448028564},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8766922354698181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8471508026123047},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6306589245796204},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.621372640132904},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.4984562397003174},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4609563648700714},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4425562620162964},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41997432708740234},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.41687339544296265},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.416849285364151},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2975333333015442},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22650030255317688},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.22362002730369568},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.13953760266304016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13586172461509705}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.9343483448028564},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8766922354698181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8471508026123047},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6306589245796204},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.621372640132904},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.4984562397003174},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4609563648700714},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4425562620162964},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41997432708740234},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.41687339544296265},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.416849285364151},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2975333333015442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22650030255317688},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.22362002730369568},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13953760266304016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13586172461509705},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/050647669","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647669","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:pure.atira.dk:openaire_cris_publications/32860e76-f275-4dd6-9fe8-69e9f57e745d","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/32860e76-f275-4dd6-9fe8-69e9f57e745d","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Guo, C H & Higham, N J 2007, 'Iterative solution of a nonsymmetric algebraic riccati equation', SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 2, pp. 396-412. https://doi.org/10.1137/050647669","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:130","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.117.7977","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.7977","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.ma.man.ac.uk/760/01/covered/MIMS_ep2005_48.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.7556","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.7556","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.ma.man.ac.uk/309/01/covered/MIMS_ep2005_48.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.9152","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.9152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.ma.man.ac.uk/130/01/covered/MIMS_ep2005_48.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/32860e76-f275-4dd6-9fe8-69e9f57e745d","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/iterative-solution-of-a-nonsymmetric-algebraic-riccati-equation(32860e76-f275-4dd6-9fe8-69e9f57e745d).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Guo, C H & Higham, N J 2007, 'Iterative solution of a nonsymmetric algebraic riccati equation', SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 2, pp. 396-412. https://doi.org/10.1137/050647669","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320291","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1560592371","https://openalex.org/W1569509623","https://openalex.org/W1600349401","https://openalex.org/W1970674091","https://openalex.org/W1971875357","https://openalex.org/W1988425433","https://openalex.org/W2007703035","https://openalex.org/W2013108889","https://openalex.org/W2017636104","https://openalex.org/W2022067462","https://openalex.org/W2023471726","https://openalex.org/W2025657264","https://openalex.org/W2035684733","https://openalex.org/W2039532495","https://openalex.org/W2052323297","https://openalex.org/W2056589646","https://openalex.org/W2059100658","https://openalex.org/W2069500104","https://openalex.org/W2070689535","https://openalex.org/W2080497978","https://openalex.org/W2102352719","https://openalex.org/W2114188988","https://openalex.org/W2114349947","https://openalex.org/W2167493384","https://openalex.org/W2170005034","https://openalex.org/W2171106345"],"related_works":["https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2005019312","https://openalex.org/W2727200542","https://openalex.org/W2003686272","https://openalex.org/W1969667742","https://openalex.org/W2144429983"],"abstract_inverted_index":{"We":[0,34,54],"study":[1],"the":[2,12,30,62,77,94,103,123,132,137,141,145,149,157,178,187,193,197,205,214,224],"nonsymmetric":[3],"algebraic":[4],"Riccati":[5,104,124,150,198,221],"equation":[6,105,113,125,139,151,199,222],"whose":[7],"four":[8],"coefficient":[9],"matrices":[10],"are":[11],"blocks":[13],"of":[14,26,117,122,136,148,196,218,223],"a":[15,57,110,115,162,190,219],"nonsingular":[16],"M\u2010matrix":[17,22,89],"or":[18,100],"an":[19,86],"irreducible":[20,87],"singular":[21,88],"M.":[23],"The":[24,119],"solution":[25,49,96,121,135,147,180,195,208,217],"practical":[27],"interest":[28],"is":[29,66,85,97,152,171,174,200],"minimal":[31,63,95,120,133,146,179,194,207,216],"nonnegative":[32,134],"solution.":[33],"show":[35,155,203],"that":[36,156],"Newton\u2019s":[37],"method":[38],"with":[39,90,161],"zero":[40,91],"initial":[41],"guess":[42],"can":[43,106,126,209],"be":[44,107,128,210],"used":[45],"to":[46,176],"find":[47,177],"this":[48],"without":[50,189],"any":[51],"further":[52],"assumptions.":[53],"also":[55],"present":[56],"qualitative":[58],"perturbation":[59],"analysis":[60],"for":[61,71],"solution,":[64],"which":[65,83],"instructive":[67],"in":[68,82],"designing":[69],"algorithms":[70],"finding":[72],"more":[73,181,184],"accurate":[74],"approximations.":[75],"For":[76],"most":[78],"practically":[79],"important":[80],"case,":[81],"M":[84],"row":[92],"sums,":[93],"either":[98],"stochastic":[99,215],"substochastic":[101,206],"and":[102,169,173,183],"transformed":[108],"into":[109],"unilateral":[111,138],"matrix":[112],"by":[114,130,166,212],"procedure":[116],"Ramaswami.":[118],"then":[127],"found":[129,211],"computing":[131,213],"using":[140],"Latouche\u2013Ramaswami":[142,158],"algorithm.":[143],"When":[144,192],"stochastic,":[153],"we":[154,202],"algorithm,":[159],"combined":[160],"shift":[163],"technique":[164],"suggested":[165],"He,":[167],"Meini,":[168],"Rhee,":[170],"breakdown\u2010free":[172],"able":[175],"efficiently":[182],"accurately":[185],"than":[186],"algorithm":[188],"shift.":[191],"substochastic,":[201],"how":[204],"related":[220],"same":[225],"type.":[226]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-27T08:22:11.395708","created_date":"2025-10-10T00:00:00"}