{"id":"https://openalex.org/W2919280737","doi":"https://doi.org/10.1007/s10444-019-09695-9","title":"A bilinear \u210b2$\\mathcal {H}_{2}$ model order reduction approach to linear parameter-varying systems","display_name":"A bilinear \u210b2$\\mathcal {H}_{2}$ model order reduction approach to linear parameter-varying systems","publication_year":2019,"publication_date":"2019-04-18","ids":{"openalex":"https://openalex.org/W2919280737","doi":"https://doi.org/10.1007/s10444-019-09695-9","mag":"2919280737"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-019-09695-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-019-09695-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-019-09695-9.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-019-09695-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060985095","display_name":"Peter Benner","orcid":"https://orcid.org/0000-0003-3362-4103"},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Benner","raw_affiliation_strings":["Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086377276","display_name":"Xingang Cao","orcid":"https://orcid.org/0000-0003-1482-4388"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Xingang Cao","raw_affiliation_strings":["Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-1482-4388","affiliations":[{"raw_affiliation_string":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057699287","display_name":"W.H.A. Schilders","orcid":"https://orcid.org/0000-0001-5838-8579"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Wil Schilders","raw_affiliation_strings":["Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060985095"],"corresponding_institution_ids":["https://openalex.org/I4210127568"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.3036,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.88722291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"45","issue":"5-6","first_page":"2241","last_page":"2271"},"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/T11236","display_name":"Control Systems and Identification","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7748386859893799},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.7441903948783875},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.629125714302063},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6204123497009277},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.597150981426239},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.5588322877883911},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.5488172769546509},{"id":"https://openalex.org/keywords/bilinear-transform","display_name":"Bilinear transform","score":0.5487795472145081},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.5429641008377075},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5005872249603271},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.48124194145202637},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.48068079352378845},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4798021614551544},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47013598680496216},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4151037633419037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3041936755180359},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.275765061378479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15659478306770325},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10849884152412415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7748386859893799},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7441903948783875},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.629125714302063},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6204123497009277},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.597150981426239},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.5588322877883911},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.5488172769546509},{"id":"https://openalex.org/C109786386","wikidata":"https://www.wikidata.org/wiki/Q861804","display_name":"Bilinear transform","level":4,"score":0.5487795472145081},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.5429641008377075},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5005872249603271},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.48124194145202637},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.48068079352378845},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4798021614551544},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47013598680496216},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4151037633419037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3041936755180359},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.275765061378479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15659478306770325},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10849884152412415},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10444-019-09695-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-019-09695-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-019-09695-9.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/70e55f69-3e8e-40e2-9ad4-53d74ea54941","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/70e55f69-3e8e-40e2-9ad4-53d74ea54941","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Benner, P, Cao, X & Schilders, W H A 2019, 'A bilinear H2 model order reduction approach to linear parameter-varying systems', Advances in Computational Mathematics, vol. 45, no. 5-6, pp. 2241\u20132271. https://doi.org/10.1007/s10444-019-09695-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/70e55f69-3e8e-40e2-9ad4-53d74ea54941","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/70e55f69-3e8e-40e2-9ad4-53d74ea54941","pdf_url":"https://research.tue.nl/nl/publications/70e55f69-3e8e-40e2-9ad4-53d74ea54941","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Computational Mathematics, 45(5-6). Springer","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_3036320","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0003-4D86-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Computational Mathematics","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10444-019-09695-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-019-09695-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-019-09695-9.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6050058274","display_name":null,"funder_award_id":"TD1307 STSM reference number: 38143","funder_id":"https://openalex.org/F4320320366","funder_display_name":"European Cooperation in Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320366","display_name":"European Cooperation in Science and Technology","ror":"https://ror.org/01bstzn19"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2919280737.pdf","grobid_xml":"https://content.openalex.org/works/W2919280737.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1511438772","https://openalex.org/W1525296983","https://openalex.org/W1804110266","https://openalex.org/W1873968263","https://openalex.org/W1964373008","https://openalex.org/W2002858896","https://openalex.org/W2009180289","https://openalex.org/W2045512849","https://openalex.org/W2069049088","https://openalex.org/W2080925234","https://openalex.org/W2081604815","https://openalex.org/W2083642242","https://openalex.org/W2090696580","https://openalex.org/W2093008604","https://openalex.org/W2135680841","https://openalex.org/W2137874355","https://openalex.org/W2152896489","https://openalex.org/W2255739630","https://openalex.org/W2289544830","https://openalex.org/W2421414037","https://openalex.org/W2429699477","https://openalex.org/W2568036279","https://openalex.org/W2588810965","https://openalex.org/W2745639111","https://openalex.org/W3029645440","https://openalex.org/W3105351150","https://openalex.org/W4205293427","https://openalex.org/W4293775970","https://openalex.org/W6638016432"],"related_works":["https://openalex.org/W2797269282","https://openalex.org/W1974170983","https://openalex.org/W2372940869","https://openalex.org/W4230650749","https://openalex.org/W1838705720","https://openalex.org/W1996402842","https://openalex.org/W1559589769","https://openalex.org/W2041373103","https://openalex.org/W2919280737","https://openalex.org/W2049100639"],"abstract_inverted_index":{"This":[0,16],"paper":[1],"focuses":[2],"on":[3,28,55,59],"the":[4,29,38,43,56,60,66,72,76,86,101],"model":[5,49],"reduction":[6,50],"problem":[7],"for":[8],"a":[9,35,48],"special":[10],"class":[11],"of":[12,18,37,65,85],"linear":[13],"parameter-varying":[14],"systems.":[15,26],"kind":[17],"systems":[19],"can":[20,89],"be":[21,90],"reformulated":[22],"as":[23,92],"bilinear":[24,30],"dynamical":[25],"Based":[27],"system":[31],"theory,":[32],"we":[33],"give":[34],"definition":[36],"$\\mathcal":[39],"{H}_{2}$":[40],"norm":[41],"in":[42],"generalized":[44],"frequency":[45],"domain.":[46],"Then,":[47],"method":[51,67],"is":[52,68,78],"proposed":[53,102],"based":[54],"gradient":[57,73],"descent":[58],"Grassmann":[61],"manifold.":[62],"The":[63],"merit":[64],"that":[69],"by":[70],"utilizing":[71],"flow":[74],"analysis,":[75],"algorithm":[77],"guaranteed":[79],"to":[80,99],"converge,":[81],"and":[82],"further":[83],"speedup":[84],"convergence":[87],"rate":[88],"achieved":[91],"well.":[93],"Two":[94],"numerical":[95],"examples":[96],"are":[97],"tested":[98],"demonstrate":[100],"method.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-03-11T00:00:00"}
