{"id":"https://openalex.org/W1836001610","doi":"https://doi.org/10.1137/15m1019155","title":"Structure-Preserving Flows of Symplectic Matrix Pairs","display_name":"Structure-Preserving Flows of Symplectic Matrix Pairs","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1836001610","doi":"https://doi.org/10.1137/15m1019155","mag":"1836001610"},"language":"en","primary_location":{"id":"doi:10.1137/15m1019155","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019155","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/A5004863623","display_name":"Yueh\u2010Cheng Kuo","orcid":"https://orcid.org/0000-0003-2387-6913"},"institutions":[{"id":"https://openalex.org/I192168892","display_name":"National University of Kaohsiung","ror":"https://ror.org/013zjb662","country_code":"TW","type":"education","lineage":["https://openalex.org/I192168892"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Yueh-Cheng Kuo","raw_affiliation_strings":["National\u00a0University\u00a0of\u00a0Kaohsiung"],"affiliations":[{"raw_affiliation_string":"National\u00a0University\u00a0of\u00a0Kaohsiung","institution_ids":["https://openalex.org/I192168892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110004104","display_name":"Wen-Wei Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["Department of Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113663730","display_name":"Shih-Feng Shieh","orcid":null},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Shih-Feng Shieh","raw_affiliation_strings":["National Taiwan Normal University"],"affiliations":[{"raw_affiliation_string":"National Taiwan Normal University","institution_ids":["https://openalex.org/I134161618"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004863623"],"corresponding_institution_ids":["https://openalex.org/I192168892"],"apc_list":null,"apc_paid":null,"fwci":0.7188,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.73121591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"3","first_page":"976","last_page":"1001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.7871670722961426},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.6958216428756714},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.570974588394165},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5216262936592102},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5195470452308655},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.510244607925415},{"id":"https://openalex.org/keywords/symplectic-matrix","display_name":"Symplectic matrix","score":0.4780505299568176},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44843995571136475},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.3652302622795105},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3025705814361572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24812725186347961},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11362558603286743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7871670722961426},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6958216428756714},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.570974588394165},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5216262936592102},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5195470452308655},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.510244607925415},{"id":"https://openalex.org/C185535465","wikidata":"https://www.wikidata.org/wiki/Q2705070","display_name":"Symplectic matrix","level":5,"score":0.4780505299568176},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44843995571136475},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.3652302622795105},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3025705814361572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24812725186347961},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11362558603286743},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1019155","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019155","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":[{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W80977353","https://openalex.org/W634095343","https://openalex.org/W1483804921","https://openalex.org/W1488435683","https://openalex.org/W1551784909","https://openalex.org/W1600349401","https://openalex.org/W1965452869","https://openalex.org/W1965473151","https://openalex.org/W1965640670","https://openalex.org/W1966533816","https://openalex.org/W1968542615","https://openalex.org/W1969059980","https://openalex.org/W1970459238","https://openalex.org/W1975886185","https://openalex.org/W1977106683","https://openalex.org/W1983470242","https://openalex.org/W1983873190","https://openalex.org/W1988565074","https://openalex.org/W1996967464","https://openalex.org/W2002533862","https://openalex.org/W2005328416","https://openalex.org/W2005999980","https://openalex.org/W2006448940","https://openalex.org/W2007322084","https://openalex.org/W2014858709","https://openalex.org/W2023565465","https://openalex.org/W2025185012","https://openalex.org/W2028362534","https://openalex.org/W2028808207","https://openalex.org/W2029822378","https://openalex.org/W2034169759","https://openalex.org/W2034347866","https://openalex.org/W2043708129","https://openalex.org/W2046824594","https://openalex.org/W2052124277","https://openalex.org/W2052387764","https://openalex.org/W2059909832","https://openalex.org/W2060003923","https://openalex.org/W2060190738","https://openalex.org/W2065832220","https://openalex.org/W2067575573","https://openalex.org/W2068257363","https://openalex.org/W2068330205","https://openalex.org/W2071824735","https://openalex.org/W2072305544","https://openalex.org/W2081157748","https://openalex.org/W2082496628","https://openalex.org/W2085578956","https://openalex.org/W2087958846","https://openalex.org/W2089724807","https://openalex.org/W2091541040","https://openalex.org/W2097156328","https://openalex.org/W2097327029","https://openalex.org/W2120459890","https://openalex.org/W2120794985","https://openalex.org/W2122055952","https://openalex.org/W2122068733","https://openalex.org/W2123505857","https://openalex.org/W2128978199","https://openalex.org/W2138545361","https://openalex.org/W2145933873","https://openalex.org/W2150412237","https://openalex.org/W2163334725","https://openalex.org/W2168022335","https://openalex.org/W2493202208","https://openalex.org/W2809460247"],"related_works":["https://openalex.org/W3123892175","https://openalex.org/W1584493883","https://openalex.org/W4297672998","https://openalex.org/W1541189163","https://openalex.org/W2951114943","https://openalex.org/W1983133745","https://openalex.org/W2520160177","https://openalex.org/W2254056384","https://openalex.org/W1994560279","https://openalex.org/W1966144394"],"abstract_inverted_index":{"We":[0,109],"construct":[1],"a":[2,80,84,91,226,234],"nonlinear":[3,151],"differential":[4,93],"equation":[5,94],"of":[6,18,96,119,165,214,220,243,257],"matrix":[7,20,107,152],"pairs":[8,21],"$(\\mathcal{M}(t),\\mathcal{L}(t))$":[9],"that":[10,184],"are":[11,61,260],"invariant":[12],"(structure-preserving":[13],"property)":[14],"in":[15],"the":[16,74,97,112,117,120,124,132,135,157,175,192,201,215,221,244,258,263],"class":[17],"symplectic":[19,64,166],"$":[22],"\\left\\{":[23],"\\left(\\mathcal{M},\\mathcal{L}\\right)=":[24],"\\scriptstyle\\left.\\left(\\left[":[25],"\\begin{smallmatrix}":[26,38],"X_{12}":[27],"&&":[28,32,40,44],"0":[29,43],"\\\\":[30,34,42,46],"X_{22}":[31],"I":[33,39],"\\end{smallmatrix}":[35,47],"\\right]\\mathcal{S}_2,":[36],"\\left[":[37],"X_{11}":[41],"X_{21}":[45],"\\right]\\mathcal{S}_1\\right)":[48],"\\right|":[49],"\\":[50],"X=[X_{ij}]_{1\\le":[51],"i,j\\le2}\\":[52],"\\textstyle{\\rm":[53],"is\\":[54],"Hermitian}":[55],"\\right\\},$":[56],"where":[57],"$\\mathcal{S}_1$":[58],"and":[59,87,150,169,179,197,203,218,247,265],"$\\mathcal{S}_2$":[60],"two":[62,162],"fixed":[63],"matrices.":[65],"Furthermore,":[66],"its":[67,204],"solution":[68],"also":[69],"preserves":[70],"deflating":[71],"subspaces":[72],"on":[73],"whole":[75,125],"orbit":[76],"(Eigenvector-preserving":[77],"property).":[78],"Such":[79],"flow":[81,86,122,189,207],"is":[82,88,140,182,249],"called":[83],"structure-preserving":[85,121,136,158,206,245],"governed":[89],"by":[90,195,251],"Riccati":[92,148],"(RDE)":[95],"form":[98,238],"$\\dot{W}(t)=[-W(t),I]\\mathscr{H}[I":[99],",W(t)^{\\top}":[100],"]^{\\top}$,":[101],"$W(0)=W_0$,":[102],"for":[103,145],"some":[104,128],"suitable":[105],"Hamiltonian":[106,222,235],"$\\mathscr{H}$.":[108],"then":[110],"utilize":[111],"Grassmann":[113],"manifolds":[114],"to":[115,123,230,233],"extend":[116],"domain":[118],"$\\mathbb{R}$":[126],"except":[127],"isolated":[129],"points.":[130],"On":[131],"other":[133],"hand,":[134],"doubling":[137],"algorithm":[138],"(SDA)":[139],"an":[141],"efficient":[142],"numerical":[143],"method":[144],"solving":[146],"algebraic":[147],"equations":[149],"equations.":[153],"In":[154],"conjunction":[155],"with":[156],"flow,":[159],"we":[160,224],"consider":[161],"special":[163,216],"classes":[164],"pairs:":[167],"$\\mathcal{S}_1=\\mathcal{S}_2=I_{2n}$":[168],"$\\mathcal{S}_1=\\mathcal{J}$,":[170],"$\\mathcal{S}_2=-I_{2n}$":[171],"as":[172,174],"well":[173],"associated":[176],"algorithms":[177],"SDA-1":[178,196],"SDA-2.":[180],"It":[181],"shown":[183],"at":[185],"$t=2^{k-1},k\\in":[186],"\\mathbb{Z}$":[187],"this":[188],"passes":[190],"through":[191],"iterates":[193],"generated":[194],"SDA-2,":[198],"respectively.":[199],"Therefore,":[200],"SDA":[202,259],"corresponding":[205],"have":[208],"identical":[209],"asymptotic":[210,241,255],"behaviors.":[211],"Taking":[212],"advantage":[213],"structure":[217],"properties":[219],"matrix,":[223],"apply":[225],"symplectically":[227],"similarity":[228],"transformation":[229],"reduce":[231],"$\\mathscr{H}$":[232],"Jordan":[236],"canonical":[237],"$\\mathfrak{J}$.":[239],"The":[240],"analysis":[242],"flows":[246],"RDEs":[248],"studied":[250],"using":[252],"$e^{\\mathfrak{J}t}$.":[253],"Some":[254],"dynamics":[256],"investigated,":[261],"including":[262],"linear":[264],"quadratic":[266],"convergence.":[267]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
