{"id":"https://openalex.org/W2123353249","doi":"https://doi.org/10.23919/ecc.2013.6669383","title":"Iterative solution of operator Lyapunov equations arising in heat transfer","display_name":"Iterative solution of operator Lyapunov equations arising in heat transfer","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2123353249","doi":"https://doi.org/10.23919/ecc.2013.6669383","mag":"2123353249"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2013.6669383","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","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/A5027602749","display_name":"Timo Reis","orcid":"https://orcid.org/0000-0003-0721-8494"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Timo Reis","raw_affiliation_strings":["Department of Mathematics, University of Hamburg, Hamburg, Germany","Dept. of Math., Univ. of Hamburg, Hamburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054920423","display_name":"Winnifried Wollner","orcid":"https://orcid.org/0000-0002-6571-8043"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Winnifried Wollner","raw_affiliation_strings":["Department of Mathematics, University of Hamburg, Hamburg, Germany","Dept. of Math., Univ. of Hamburg, Hamburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027602749"],"corresponding_institution_ids":["https://openalex.org/I159176309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16192653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"41","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9986000061035156,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7086039781570435},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.6881279945373535},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.546714723110199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5063668489456177},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.49424126744270325},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47509491443634033},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4741774797439575},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4726996421813965},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46190008521080017},{"id":"https://openalex.org/keywords/gramian-matrix","display_name":"Gramian matrix","score":0.4165076017379761},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19499292969703674},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.17750489711761475},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08927851915359497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07404494285583496},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07186955213546753}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7086039781570435},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.6881279945373535},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.546714723110199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5063668489456177},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.49424126744270325},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47509491443634033},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4741774797439575},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4726996421813965},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46190008521080017},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.4165076017379761},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19499292969703674},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.17750489711761475},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08927851915359497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07404494285583496},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07186955213546753},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2013.6669383","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W203646022","https://openalex.org/W376531882","https://openalex.org/W1538686203","https://openalex.org/W1551480811","https://openalex.org/W1565627164","https://openalex.org/W1603924973","https://openalex.org/W1969626918","https://openalex.org/W1978115611","https://openalex.org/W1995258411","https://openalex.org/W1995404822","https://openalex.org/W2036191408","https://openalex.org/W2037025184","https://openalex.org/W2045988646","https://openalex.org/W2053449213","https://openalex.org/W2066059560","https://openalex.org/W2088748973","https://openalex.org/W2091634205","https://openalex.org/W2092273264","https://openalex.org/W2097660079","https://openalex.org/W2133627030","https://openalex.org/W2149811200","https://openalex.org/W2161344567","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2063018656","https://openalex.org/W3048970523","https://openalex.org/W2305582521","https://openalex.org/W2594663892","https://openalex.org/W2092273264","https://openalex.org/W2133143430","https://openalex.org/W2587874700","https://openalex.org/W3147831616","https://openalex.org/W1999658804","https://openalex.org/W2973060773"],"abstract_inverted_index":{"We":[0],"consider":[1],"an":[2,18],"iterative":[3],"method":[4,44,59],"for":[5],"the":[6,23,35,49,54,72],"numerical":[7],"solution":[8,36],"of":[9,12,37,48,62],"Lyapunov":[10,39],"equations":[11],"infinite-dimensional":[13],"control":[14],"systems":[15],"governed":[16],"by":[17,22],"heat":[19,55],"equation.":[20],"Inspired":[21],"`alternating":[24],"direction":[25],"implicit":[26],"(ADI)'":[27],"iteration,":[28],"which":[29],"has":[30],"been":[31],"successfully":[32],"applied":[33],"to":[34,45,53,68],"matrix":[38],"equations,":[40],"we":[41],"present":[42],"a":[43],"determine":[46],"approximations":[47,61],"Gramian":[50],"operator":[51],"corresponding":[52],"equation":[56],"system.":[57],"This":[58],"provides":[60],"finite":[63],"rank":[64],"and":[65],"is":[66],"shown":[67],"be":[69],"convergent":[70],"in":[71],"nuclear":[73],"norm.":[74]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}