{"id":"https://openalex.org/W2170005034","doi":"https://doi.org/10.1137/060660837","title":"On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation","display_name":"On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation","publication_year":2007,"publication_date":"2007-11-10","ids":{"openalex":"https://openalex.org/W2170005034","doi":"https://doi.org/10.1137/060660837","mag":"2170005034"},"language":"en","primary_location":{"id":"doi:10.1137/060660837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660837","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chun-Hua Guo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036085823","display_name":"Bruno Iannazzo","orcid":"https://orcid.org/0000-0002-3098-3824"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruno Iannazzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000363133","display_name":"Beatrice Meini","orcid":"https://orcid.org/0000-0003-3139-2513"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beatrice Meini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100956974"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3646,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.96853933,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"4","first_page":"1083","last_page":"1100"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9926999807357788,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9869999885559082,"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.9056070446968079},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8797875642776489},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8253445625305176},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6784948706626892},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5634689927101135},{"id":"https://openalex.org/keywords/matrix-difference-equation","display_name":"Matrix difference equation","score":0.4939272999763489},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42723381519317627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3874838948249817},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3396969139575958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28987637162208557},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1164715588092804}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.9056070446968079},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8797875642776489},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8253445625305176},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6784948706626892},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5634689927101135},{"id":"https://openalex.org/C47285271","wikidata":"https://www.wikidata.org/wiki/Q6787869","display_name":"Matrix difference equation","level":4,"score":0.4939272999763489},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42723381519317627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3874838948249817},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3396969139575958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28987637162208557},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1164715588092804},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060660837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660837","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:CiteSeerX.psu:10.1.1.331.9618","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.9618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uregina.ca/~chguo/gim06.pdf","raw_type":"text"},{"id":"pmh:oai:arpi.unipi.it:11568/114034","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/114034","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1500921805","https://openalex.org/W1569509623","https://openalex.org/W1983184346","https://openalex.org/W2013108889","https://openalex.org/W2017636104","https://openalex.org/W2022067462","https://openalex.org/W2023471726","https://openalex.org/W2035684733","https://openalex.org/W2039532495","https://openalex.org/W2042624802","https://openalex.org/W2052323297","https://openalex.org/W2056589646","https://openalex.org/W2059100658","https://openalex.org/W2082890155","https://openalex.org/W2102352719","https://openalex.org/W2103349730","https://openalex.org/W2114188988","https://openalex.org/W2114349947","https://openalex.org/W2167493384","https://openalex.org/W2171106345","https://openalex.org/W2183011164","https://openalex.org/W2798909945","https://openalex.org/W4230055331"],"related_works":["https://openalex.org/W1977270049","https://openalex.org/W2084401098","https://openalex.org/W1493657407","https://openalex.org/W2792258377","https://openalex.org/W4250220125","https://openalex.org/W2135311228","https://openalex.org/W2023919855","https://openalex.org/W2949824413","https://openalex.org/W2150766149","https://openalex.org/W1561579480"],"abstract_inverted_index":{"Nonsymmetric":[0],"algebraic":[1],"Riccati":[2,80,85,112],"equations":[3],"for":[4,43,62,87],"which":[5,30,88],"the":[6,21,33,45,49,63,78,89,100,110],"four":[7,90],"coefficient":[8,91],"matrices":[9,92],"form":[10,93],"an":[11,26],"irreducible":[12,27],"M-matrix":[13],"M":[14,24,66],"are":[15],"considered.":[16],"The":[17,38,54,97],"emphasis":[18],"is":[19,25,41,67,74,103,107],"on":[20],"case":[22,64],"where":[23,65],"singular":[28],"M-matrix,":[29],"arises":[31],"in":[32],"study":[34],"of":[35,51,99],"Markov":[36],"models.":[37],"doubling":[39,101],"algorithm":[40,55,102],"considered":[42],"finding":[44],"minimal":[46],"nonnegative":[47],"solution,":[48],"one":[50],"practical":[52],"interest.":[53],"has":[56],"been":[57],"recently":[58],"studied":[59],"by":[60],"others":[61],"a":[68,83,94],"nonsingular":[69,95],"M-matrix.":[70],"A":[71],"shift":[72],"technique":[73],"proposed":[75],"to":[76,109],"transform":[77],"original":[79],"equation":[81,86],"into":[82],"new":[84],"matrix.":[96],"convergence":[98],"accelerated":[104],"when":[105],"it":[106],"applied":[108],"shifted":[111],"equation.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-27T08:22:11.395708","created_date":"2025-10-10T00:00:00"}
