{"id":"https://openalex.org/W2887309792","doi":"https://doi.org/10.1080/00207179.2019.1670360","title":"Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction","display_name":"Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction","publication_year":2019,"publication_date":"2019-09-20","ids":{"openalex":"https://openalex.org/W2887309792","doi":"https://doi.org/10.1080/00207179.2019.1670360","mag":"2887309792"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2019.1670360","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1670360","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.04119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022413371","display_name":"Roland Pulch","orcid":"https://orcid.org/0000-0002-6503-3300"},"institutions":[{"id":"https://openalex.org/I36522303","display_name":"Universit\u00e4t Greifswald","ror":"https://ror.org/00r1edq15","country_code":"DE","type":"education","lineage":["https://openalex.org/I36522303"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Roland Pulch","raw_affiliation_strings":["Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany","institution_ids":["https://openalex.org/I36522303"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022413371"],"corresponding_institution_ids":["https://openalex.org/I36522303"],"apc_list":null,"apc_paid":null,"fwci":0.1471,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.41801548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"94","issue":"7","first_page":"1734","last_page":"1750"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9905999898910522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8178083300590515},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5910968780517578},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5782365202903748},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.565470278263092},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5199921727180481},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.4632493257522583},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4412323534488678},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4370354413986206},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40275752544403076},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16724300384521484},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.145000159740448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08818298578262329}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8178083300590515},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5910968780517578},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5782365202903748},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.565470278263092},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5199921727180481},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.4632493257522583},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4412323534488678},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4370354413986206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40275752544403076},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16724300384521484},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.145000159740448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08818298578262329},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00207179.2019.1670360","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2019.1670360","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.04119","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.04119","pdf_url":"https://arxiv.org/pdf/1808.04119","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2887309792","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.04119","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1808.04119","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.04119","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.04119","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.04119","pdf_url":"https://arxiv.org/pdf/1808.04119","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.4000000059604645,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2887309792.pdf","grobid_xml":"https://content.openalex.org/works/W2887309792.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W177822632","https://openalex.org/W297328598","https://openalex.org/W1509923322","https://openalex.org/W1522399516","https://openalex.org/W1526279138","https://openalex.org/W1551480811","https://openalex.org/W1560872612","https://openalex.org/W1601714778","https://openalex.org/W1880751280","https://openalex.org/W1969626918","https://openalex.org/W1971947347","https://openalex.org/W1995504856","https://openalex.org/W2001773339","https://openalex.org/W2009900301","https://openalex.org/W2023763718","https://openalex.org/W2028212620","https://openalex.org/W2052143849","https://openalex.org/W2064180468","https://openalex.org/W2067136705","https://openalex.org/W2088872157","https://openalex.org/W2103142200","https://openalex.org/W2106565812","https://openalex.org/W2152896489","https://openalex.org/W2156707583","https://openalex.org/W2161344224","https://openalex.org/W2162658196","https://openalex.org/W2167759761","https://openalex.org/W2168791566","https://openalex.org/W2172042498","https://openalex.org/W2186595203","https://openalex.org/W2340513506","https://openalex.org/W2480611454","https://openalex.org/W2513379397","https://openalex.org/W2555226553","https://openalex.org/W2561163408","https://openalex.org/W2587609464","https://openalex.org/W2591843631","https://openalex.org/W2644635209","https://openalex.org/W2743025172","https://openalex.org/W2758064830","https://openalex.org/W2962693324","https://openalex.org/W2964307396","https://openalex.org/W3125083050","https://openalex.org/W3134940460","https://openalex.org/W3211399162","https://openalex.org/W4232846525","https://openalex.org/W4300600608","https://openalex.org/W4301866048"],"related_works":["https://openalex.org/W2004140001","https://openalex.org/W1831421551","https://openalex.org/W2937583337","https://openalex.org/W3006847464","https://openalex.org/W2963047046","https://openalex.org/W2310692453","https://openalex.org/W3119860031","https://openalex.org/W1600457729","https://openalex.org/W3018874078","https://openalex.org/W2302459478","https://openalex.org/W1995259299","https://openalex.org/W3049629553","https://openalex.org/W2046731378","https://openalex.org/W2038533035","https://openalex.org/W2893162802","https://openalex.org/W2739796060","https://openalex.org/W2002787207","https://openalex.org/W3169809351","https://openalex.org/W2009133961","https://openalex.org/W2272082705"],"abstract_inverted_index":{"We":[0,37,69],"investigate":[1],"linear":[2,99],"dynamical":[3],"systems":[4,18,100,114],"consisting":[5],"of":[6,19,43,47,64,101,115,128],"ordinary":[7],"differential":[8],"equations":[9,103,117],"with":[10,118],"high":[11],"dimensionality.":[12],"Model":[13],"order":[14,41],"reduction":[15,42],"yields":[16],"alternative":[17],"much":[20],"lower":[21],"dimensions.":[22],"However,":[23],"a":[24,65,74,84,124],"reduced":[25,54],"system":[26,33,50,55],"may":[27],"be":[28,81,106],"unstable,":[29],"although":[30],"the":[31,48,62,88],"original":[32,49],"is":[34,56],"asymptotically":[35,57],"stable.":[36,58],"consider":[38],"projection-based":[39],"model":[40],"Galerkin-type.":[44],"A":[45],"transformation":[46,60],"ensures":[51],"that":[52],"any":[53],"This":[59],"requires":[61],"solution":[63,79],"high-dimensional":[66,134],"Lyapunov":[67,76],"inequality.":[68],"solve":[70],"this":[71,111],"problem":[72],"using":[73],"specific":[75],"equation.":[77],"Its":[78],"can":[80],"represented":[82],"as":[83],"matrix-valued":[85],"integral":[86],"in":[87],"frequency":[89],"domain.Consequently,":[90],"quadrature":[91],"rules":[92],"yield":[93],"numerical":[94,129],"approximations,":[95],"where":[96],"large":[97],"sparse":[98],"algebraic":[102],"have":[104],"to":[105,113],"solved.":[107],"Furthermore,":[108],"we":[109],"extend":[110],"technique":[112],"differential-algebraic":[116],"strictly":[119],"proper":[120],"transfer":[121],"functions":[122],"by":[123],"regularisation.":[125],"Finally,":[126],"results":[127],"computations":[130],"are":[131],"presented":[132],"for":[133],"examples.":[135]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}