{"id":"https://openalex.org/W1976324450","doi":"https://doi.org/10.1109/fskd.2012.6234039","title":"Algebraic method for solving a class of quaternion algebraic Riccati equation","display_name":"Algebraic method for solving a class of quaternion algebraic Riccati equation","publication_year":2012,"publication_date":"2012-05-01","ids":{"openalex":"https://openalex.org/W1976324450","doi":"https://doi.org/10.1109/fskd.2012.6234039","mag":"1976324450"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2012.6234039","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2012.6234039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 9th International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-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/A5058619642","display_name":"Sitao Ling","orcid":"https://orcid.org/0000-0002-0510-6184"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sitao Ling","raw_affiliation_strings":["Department of Mathematics, China University of Mining and Technology, Xuzhou, China","Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China#TAB#","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050221328","display_name":"Tongsong Jiang","orcid":"https://orcid.org/0000-0002-7990-5800"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tongsong Jiang","raw_affiliation_strings":["Department of Mathematics, Linyi University, Linyi, China","Department of Mathematics, Linyi University, 276005, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linyi University, Linyi, China","institution_ids":["https://openalex.org/I15823474"]},{"raw_affiliation_string":"Department of Mathematics, Linyi University, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002674139","display_name":"Xuehan Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I182707071","display_name":"Ludong University","ror":"https://ror.org/028h95t32","country_code":"CN","type":"education","lineage":["https://openalex.org/I182707071"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuehan Cheng","raw_affiliation_strings":["Department of Mathematics and Information, Ludong University, Yantai, China","Department of mathematics and information, LuDong University, Yantai, 264025, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Information, Ludong University, Yantai, China","institution_ids":["https://openalex.org/I182707071"]},{"raw_affiliation_string":"Department of mathematics and information, LuDong University, Yantai, 264025, China","institution_ids":["https://openalex.org/I182707071"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058619642"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0585643,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":null,"first_page":"2339","last_page":"2342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.9024890065193176},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.8384614586830139},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8069154620170593},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.7168388366699219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6888779401779175},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5812065005302429},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5528165102005005},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5295720100402832},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.48451608419418335},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.477884441614151},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.4462878108024597},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.4170484244823456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4121135175228119},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.281228244304657},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1922016739845276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19214308261871338},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16227614879608154},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.12603309750556946},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0967676043510437},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.05462649464607239}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.9024890065193176},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8384614586830139},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8069154620170593},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.7168388366699219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6888779401779175},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5812065005302429},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5528165102005005},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5295720100402832},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.48451608419418335},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.477884441614151},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.4462878108024597},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.4170484244823456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4121135175228119},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.281228244304657},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1922016739845276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19214308261871338},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16227614879608154},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.12603309750556946},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0967676043510437},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.05462649464607239},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fskd.2012.6234039","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2012.6234039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 9th International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1600349401","https://openalex.org/W1981583743","https://openalex.org/W2052323297","https://openalex.org/W2383300817","https://openalex.org/W4252130364","https://openalex.org/W4388319978"],"related_works":["https://openalex.org/W2032847817","https://openalex.org/W2167673968","https://openalex.org/W415152954","https://openalex.org/W1968887028","https://openalex.org/W4298065935","https://openalex.org/W2261407670","https://openalex.org/W1502419693","https://openalex.org/W4240000413","https://openalex.org/W2086775644","https://openalex.org/W2336285457"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"by":[3],"means":[4],"of":[5,25,38],"complex":[6,26],"representation":[7],"and":[8,29],"Jordan":[9],"canonical":[10],"form,":[11],"we":[12],"change":[13],"the":[14],"problem":[15],"for":[16,34],"solving":[17,35],"a":[18,36],"quaternion":[19,39],"algebraic":[20,32,40],"Riccati":[21,41],"equation":[22],"to":[23],"that":[24],"matrix":[27],"equation,":[28],"provide":[30],"an":[31],"method":[33],"class":[37],"equation.":[42]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}