{"id":"https://openalex.org/W2020060489","doi":"https://doi.org/10.1109/acc.2010.5530920","title":"On the connection between balanced proper orthogonal decomposition, balanced truncation, and metric complexity theory for infinite dimensional systems","display_name":"On the connection between balanced proper orthogonal decomposition, balanced truncation, and metric complexity theory for infinite dimensional systems","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2020060489","doi":"https://doi.org/10.1109/acc.2010.5530920","mag":"2020060489"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2010.5530920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2010.5530920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 American Control Conference","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/A5107210257","display_name":"Seddik M. Djouadi","orcid":"https://orcid.org/0000-0003-4925-723X"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Seddik M Djouadi","raw_affiliation_strings":["The Electrical Engineering & Computer Science Department, University of Tennessee, Knoxville, TN, USA","Electrical Engineering & Computer Science Department, University of Tennessee, Knoxville, 37996-2100, USA"],"affiliations":[{"raw_affiliation_string":"The Electrical Engineering & Computer Science Department, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Electrical Engineering & Computer Science Department, University of Tennessee, Knoxville, 37996-2100, USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5107210257"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.6935,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.70535391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"4911","last_page":"4916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9968000054359436,"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"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/mathematics","display_name":"Mathematics","score":0.7743133306503296},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6688284873962402},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5756494998931885},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5209746956825256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5160881876945496},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.49235713481903076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36871153116226196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7743133306503296},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6688284873962402},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5756494998931885},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5209746956825256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5160881876945496},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.49235713481903076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36871153116226196},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2010.5530920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2010.5530920","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1262779486","https://openalex.org/W1538686203","https://openalex.org/W1868559974","https://openalex.org/W1994251552","https://openalex.org/W2004485838","https://openalex.org/W2009012799","https://openalex.org/W2059316647","https://openalex.org/W2062393840","https://openalex.org/W2064733273","https://openalex.org/W2071861954","https://openalex.org/W2098077093","https://openalex.org/W2145586686","https://openalex.org/W2213818323","https://openalex.org/W2334269637","https://openalex.org/W2562824137","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1974935850","https://openalex.org/W2074350688","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W2042589464","https://openalex.org/W3158981924","https://openalex.org/W2078650164","https://openalex.org/W184455116","https://openalex.org/W4252883813"],"abstract_inverted_index":{"In":[0,26,91],"this":[1],"paper,":[2],"the":[3,36,48,70,106],"connection":[4],"between":[5],"two":[6],"important":[7],"model":[8],"reduction":[9],"techniques,":[10],"namely":[11],"balanced":[12,18,28,52,62,80],"proper":[13],"orthogonal":[14],"decomposition":[15],"(POD)":[16],"and":[17,79,110,117,125],"truncation":[19,53,81],"is":[20,30,54],"investigated":[21],"for":[22,64,68],"infinite":[23,65],"dimensional":[24,66],"systems.":[25],"particular,":[27],"POD":[29,63,78],"shown":[31,55,95],"to":[32,56,84,96,121],"be":[33,57],"optimal":[34],"in":[35,41],"sense":[37],"of":[38,44,61,87,100,123,127],"distance":[39],"minimization":[40],"a":[42,58],"space":[43],"integral":[45],"operators":[46],"under":[47],"Hilbert-Schmidt":[49],"norm.":[50],"Whereas":[51],"particular":[59,92],"case":[60],"systems":[67],"which":[69],"impulse":[71],"response":[72],"satisfies":[73],"certain":[74,85],"finite":[75],"energy":[76],"constraints.":[77],"are":[82,94],"related":[83],"notions":[86],"metric":[88],"complexity":[89],"theory.":[90],"both":[93],"minimize":[97],"different":[98],"n-widths":[99,114],"partial":[101],"differential":[102],"equation":[103],"solutions":[104],"including":[105],"Kolmogorov,":[107],"Gelfand,":[108],"linear":[109],"Bernstein":[111],"n-widths.":[112],"The":[113],"quantify":[115],"inherent":[116],"representation":[118],"errors":[119],"due":[120],"lack":[122],"data":[124],"loss":[126],"information.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
