{"id":"https://openalex.org/W2066539772","doi":"https://doi.org/10.1137/s0895479894272712","title":"On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils","display_name":"On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils","publication_year":1997,"publication_date":"1997-07-01","ids":{"openalex":"https://openalex.org/W2066539772","doi":"https://doi.org/10.1137/s0895479894272712","mag":"2066539772"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894272712","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894272712","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/A5101337552","display_name":"Wen\u2010Wei Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["Department of Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020331323","display_name":"Chern-Shuh Wang","orcid":null},"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":"Chern-Shuh Wang","raw_affiliation_strings":["National Yang Ming Chiao Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5114,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.66252073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"18","issue":"3","first_page":"590","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unimodular-matrix","display_name":"Unimodular matrix","score":0.8439702391624451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.794092059135437},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7730985879898071},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.7070162296295166},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6951127052307129},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.64280766248703},{"id":"https://openalex.org/keywords/hamiltonian-matrix","display_name":"Hamiltonian matrix","score":0.536927342414856},{"id":"https://openalex.org/keywords/symplectic-matrix","display_name":"Symplectic matrix","score":0.5127159357070923},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5090391039848328},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4930984675884247},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.4698582887649536},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4285052418708801},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4193653166294098},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37744566798210144},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3521513342857361},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34779495000839233},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3015229403972626},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.2959769368171692},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.20190295577049255},{"id":"https://openalex.org/keywords/symplectic-representation","display_name":"Symplectic representation","score":0.19012859463691711},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.14506250619888306}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.8439702391624451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.794092059135437},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7730985879898071},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.7070162296295166},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6951127052307129},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.64280766248703},{"id":"https://openalex.org/C135715101","wikidata":"https://www.wikidata.org/wiki/Q3299275","display_name":"Hamiltonian matrix","level":4,"score":0.536927342414856},{"id":"https://openalex.org/C185535465","wikidata":"https://www.wikidata.org/wiki/Q2705070","display_name":"Symplectic matrix","level":5,"score":0.5127159357070923},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5090391039848328},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4930984675884247},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.4698582887649536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4285052418708801},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4193653166294098},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37744566798210144},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3521513342857361},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34779495000839233},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3015229403972626},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.2959769368171692},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.20190295577049255},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.19012859463691711},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.14506250619888306},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479894272712","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894272712","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":27,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W96651244","https://openalex.org/W658559791","https://openalex.org/W1570330619","https://openalex.org/W1984452258","https://openalex.org/W2002357820","https://openalex.org/W2005943884","https://openalex.org/W2006031755","https://openalex.org/W2008205484","https://openalex.org/W2014064802","https://openalex.org/W2017059700","https://openalex.org/W2057110415","https://openalex.org/W2059226396","https://openalex.org/W2060003923","https://openalex.org/W2072913271","https://openalex.org/W2074672395","https://openalex.org/W2082496628","https://openalex.org/W2084380046","https://openalex.org/W2085578956","https://openalex.org/W2102575629","https://openalex.org/W2114992358","https://openalex.org/W2132116266","https://openalex.org/W2163334725","https://openalex.org/W2167097337","https://openalex.org/W2171285986","https://openalex.org/W2328218167","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2016337889","https://openalex.org/W1988291467","https://openalex.org/W2036919507","https://openalex.org/W2130462565","https://openalex.org/W2803930678","https://openalex.org/W1967573410","https://openalex.org/W2369167645","https://openalex.org/W4297926996","https://openalex.org/W2023180382","https://openalex.org/W2066539772"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"algorithms":[3,47,81],"for":[4],"computing":[5],"stable":[6],"Lagrangian":[7],"invariant":[8],"subspaces":[9],"of":[10,45,67,70,76],"a":[11,15],"Hamiltonian":[12,72],"matrix":[13,73],"and":[14,22,38,84,88],"symplectic":[16,78],"pencil,":[17],"respectively,":[18],"having":[19],"purely":[20,57],"imaginary":[21,58],"unimodular":[23],"eigenvalues.":[24],"The":[25,42,80],"problems":[26],"often":[27],"arise":[28],"in":[29,90,97],"solving":[30],"continuous-":[31],"or":[32],"discrete-time":[33],"$H^{\\infty}$-optimal":[34],"control,":[35],"linear-quadratic":[36],"control":[37],"filtering":[39],"theory,":[40],"etc.":[41],"main":[43],"approach":[44],"our":[46],"is":[48],"to":[49,56],"determine":[50],"an":[51],"isotropic":[52],"Jordan":[53,65],"subbasis":[54],"corresponding":[55],"(unimodular)":[59],"eigenvalues":[60],"by":[61],"using":[62],"the":[63,68,71,77,98],"associated":[64],"basis":[66],"square":[69],"(the":[74],"$S+S^{-1}$-transformation":[75],"pencil).":[79],"preserve":[82],"structures":[83],"are":[85],"numerically":[86],"efficient":[87],"reliable":[89],"that":[91],"they":[92],"employ":[93],"only":[94],"orthogonal":[95],"transformations":[96],"continuous":[99],"case.":[100]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
