{"id":"https://openalex.org/W2026282191","doi":"https://doi.org/10.1137/120861679","title":"A Deflation Approach for Large-Scale Lur'e Equations","display_name":"A Deflation Approach for Large-Scale Lur'e Equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2026282191","doi":"https://doi.org/10.1137/120861679","mag":"2026282191"},"language":"en","primary_location":{"id":"doi:10.1137/120861679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120861679","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/A5031634329","display_name":"Federico Poloni","orcid":"https://orcid.org/0000-0003-2291-990X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Federico Poloni","raw_affiliation_strings":["Technical University of Berlin,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Berlin,","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027602749","display_name":"Timo Reis","orcid":"https://orcid.org/0000-0003-0721-8494"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Timo Reis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8968,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.854811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"4","first_page":"1339","last_page":"1368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983999729156494,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9952999949455261,"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":0.9891999959945679,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.8044641017913818},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7878892421722412},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6515934467315674},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.5473943948745728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5213547945022583},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5195103883743286},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5000150203704834},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4548214077949524},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4521035850048065},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.43207603693008423},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.41552454233169556},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.25677284598350525},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24957779049873352},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24724087119102478},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1798974573612213},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09845402836799622}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.8044641017913818},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7878892421722412},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6515934467315674},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.5473943948745728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5213547945022583},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5195103883743286},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5000150203704834},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4548214077949524},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4521035850048065},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.43207603693008423},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.41552454233169556},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25677284598350525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24957779049873352},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24724087119102478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1798974573612213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09845402836799622},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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:10.1137/120861679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120861679","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W574171861","https://openalex.org/W623515006","https://openalex.org/W1511445895","https://openalex.org/W1579118835","https://openalex.org/W1582492107","https://openalex.org/W1595932937","https://openalex.org/W1600349401","https://openalex.org/W1839782818","https://openalex.org/W1969513875","https://openalex.org/W1978115611","https://openalex.org/W1982724184","https://openalex.org/W1984577430","https://openalex.org/W1997264772","https://openalex.org/W2002357820","https://openalex.org/W2002533862","https://openalex.org/W2013348732","https://openalex.org/W2014905826","https://openalex.org/W2025362408","https://openalex.org/W2028938161","https://openalex.org/W2037025184","https://openalex.org/W2037253724","https://openalex.org/W2037579718","https://openalex.org/W2042106612","https://openalex.org/W2053679404","https://openalex.org/W2056997350","https://openalex.org/W2059654224","https://openalex.org/W2062287526","https://openalex.org/W2065399374","https://openalex.org/W2072913271","https://openalex.org/W2073801507","https://openalex.org/W2073941158","https://openalex.org/W2074210163","https://openalex.org/W2076154074","https://openalex.org/W2085406578","https://openalex.org/W2088872157","https://openalex.org/W2097327029","https://openalex.org/W2104744926","https://openalex.org/W2119836152","https://openalex.org/W2134582887","https://openalex.org/W2138688253","https://openalex.org/W2142621163","https://openalex.org/W2144677171","https://openalex.org/W2148480360","https://openalex.org/W2151030225","https://openalex.org/W2154407829","https://openalex.org/W2163490587","https://openalex.org/W2290256616","https://openalex.org/W2531455017","https://openalex.org/W3216747129","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2798286561","https://openalex.org/W3161880765","https://openalex.org/W1537831955","https://openalex.org/W1980381208","https://openalex.org/W2106635645","https://openalex.org/W2942315554","https://openalex.org/W2153179908","https://openalex.org/W3134028852","https://openalex.org/W2137297956","https://openalex.org/W2323113259"],"abstract_inverted_index":{"We":[0,15],"present":[1],"an":[2,26,95],"approach":[3],"to":[4,32,52,55,67,73,91],"the":[5,8,18,41,60,64,87,99,115,142],"determination":[6],"of":[7,11,20,25,81,109,141],"stabilizing":[9],"solution":[10],"Lur'e":[12,33,44,48,135],"matrix":[13,28,143],"equations.":[14,119],"show":[16],"that":[17,78],"knowledge":[19],"a":[21,74,106],"certain":[22],"deflating":[23,61,88],"subspace":[24,62,65,89],"even":[27],"pencil":[29],"may":[30],"lead":[31],"equations":[34,49,136],"which":[35,104],"are":[36,50],"defined":[37],"on":[38,98],"some":[39],"subspace,":[40],"so-called":[42,100],"\u201cprojected":[43],"equations.\u201d":[45],"These":[46],"projected":[47,56,117],"shown":[51],"be":[53],"equivalent":[54],"Riccati":[57,118],"equations,":[58],"if":[59],"contains":[63],"corresponding":[66,90],"infinite":[68,92],"eigenvalues.":[69],"This":[70],"result":[71],"leads":[72],"novel":[75],"numerical":[76],"algorithm":[77,96],"basically":[79],"consists":[80],"two":[82],"steps.":[83],"First":[84],"we":[85,113],"determine":[86],"eigenvalues":[93],"using":[94],"based":[97],"\u201cneutral":[101],"Wong":[102],"sequences,\u201d":[103],"requires":[105],"moderate":[107],"number":[108],"kernel":[110],"computations;":[111],"then":[112],"solve":[114],"resulting":[116],"Altogether":[120],"this":[121],"method":[122],"can":[123],"deliver":[124],"solutions":[125],"in":[126],"low-rank":[127],"factored":[128],"form,":[129],"it":[130],"is":[131],"applicable":[132],"for":[133],"large-scale":[134],"and":[137],"exploits":[138],"possible":[139],"sparsity":[140],"coefficients.":[144]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
