{"id":"https://openalex.org/W2023471726","doi":"https://doi.org/10.1137/s0895479897318253","title":"Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices","display_name":"Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2023471726","doi":"https://doi.org/10.1137/s0895479897318253","mag":"2023471726"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479897318253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897318253","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/A5041798346","display_name":"Jonq Juang","orcid":"https://orcid.org/0000-0001-9563-8143"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jonq Juang","raw_affiliation_strings":["National Chiao-Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Chiao-Tung University","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101337552","display_name":"Wen\u2010Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["National Tsing Hua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Tsing Hua University","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4655,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.81574523,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"1","first_page":"228","last_page":"243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9990000128746033,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.9047936797142029},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.8342312574386597},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.7375373244285583},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5298758745193481},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49448275566101074},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.47910168766975403},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46765226125717163},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.4380171597003937},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.41775667667388916},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4123914837837219},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.4108751714229584},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3827209770679474},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36348956823349},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3417131304740906},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18896564841270447},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.15508559346199036},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.11917871236801147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11811530590057373},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.10280948877334595}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9047936797142029},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.8342312574386597},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7375373244285583},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5298758745193481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49448275566101074},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.47910168766975403},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46765226125717163},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.4380171597003937},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.41775667667388916},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4123914837837219},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.4108751714229584},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3827209770679474},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36348956823349},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3417131304740906},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18896564841270447},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.15508559346199036},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.11917871236801147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11811530590057373},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.10280948877334595},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479897318253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897318253","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W96651244","https://openalex.org/W133145907","https://openalex.org/W169946747","https://openalex.org/W1971947347","https://openalex.org/W1974781983","https://openalex.org/W2000547016","https://openalex.org/W2002781546","https://openalex.org/W2010464263","https://openalex.org/W2014042806","https://openalex.org/W2052178147","https://openalex.org/W2052323297","https://openalex.org/W2054188927","https://openalex.org/W2060854423","https://openalex.org/W2063973166","https://openalex.org/W2066687638","https://openalex.org/W2072403669","https://openalex.org/W2073190968","https://openalex.org/W2090963365","https://openalex.org/W2100405628","https://openalex.org/W2105433369","https://openalex.org/W2149614645","https://openalex.org/W2478091498","https://openalex.org/W2617854063","https://openalex.org/W3135227555"],"related_works":["https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2005019312","https://openalex.org/W2003686272","https://openalex.org/W1969667742","https://openalex.org/W2144429983"],"abstract_inverted_index":{"We":[0,38],"consider":[1],"a":[2,27,41],"nonsymmetric":[3],"algebraic":[4],"matrix":[5],"Riccati":[6],"equation":[7,17],"arising":[8],"from":[9],"transport":[10],"theory.":[11],"The":[12],"nonnegative":[13,46],"solutions":[14],"of":[15,26,44],"the":[16,23,45],"can":[18],"be":[19],"explicitly":[20],"constructed":[21],"via":[22],"inversion":[24],"formula":[25],"Cauchy":[28],"matrix.":[29],"An":[30],"error":[31],"analysis":[32],"and":[33],"numerical":[34],"results":[35],"are":[36],"given.":[37],"also":[39],"show":[40],"comparison":[42],"theorem":[43],"solutions.":[47]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":6}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}