{"id":"https://openalex.org/W1517593560","doi":"https://doi.org/10.1109/acc.2015.7171025","title":"A unified view of Balanced Truncation and Singular Perturbation Approximations","display_name":"A unified view of Balanced Truncation and Singular Perturbation Approximations","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1517593560","doi":"https://doi.org/10.1109/acc.2015.7171025","mag":"1517593560"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7171025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","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/A5085597072","display_name":"Philip E. Par\u00e9","orcid":"https://orcid.org/0000-0002-4095-7320"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philip E. Pare","raw_affiliation_strings":["University of Illinois at Urbana-Champaign","University of Illinois at Urbana\u2013Champaign, USA"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana\u2013Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083482204","display_name":"Alma T. Wilson","orcid":"https://orcid.org/0000-0001-5844-7516"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alma T. Wilson","raw_affiliation_strings":["Brigham Young University, Provo, Utah","Brigham Young University, Provo, Utah, USA;"],"affiliations":[{"raw_affiliation_string":"Brigham Young University, Provo, Utah","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"Brigham Young University, Provo, Utah, USA;","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048733359","display_name":"Mark K. Transtrum","orcid":"https://orcid.org/0000-0001-9529-9399"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark K. Transtrum","raw_affiliation_strings":["Brigham Young University, Provo, Utah","Brigham Young University, Provo, Utah, USA;"],"affiliations":[{"raw_affiliation_string":"Brigham Young University, Provo, Utah","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"Brigham Young University, Provo, Utah, USA;","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010055271","display_name":"Sean Warnick","orcid":"https://orcid.org/0000-0001-5485-1909"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sean C. Warnick","raw_affiliation_strings":["Brigham Young University, Provo, Utah","Brigham Young University, Provo, Utah, USA;"],"affiliations":[{"raw_affiliation_string":"Brigham Young University, Provo, Utah","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"Brigham Young University, Provo, Utah, USA;","institution_ids":["https://openalex.org/I100005738"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085597072"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.2386,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53841391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"41","issue":null,"first_page":"1989","last_page":"1994"},"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/T12810","display_name":"Real-time simulation and control systems","score":0.9957000017166138,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.690483033657074},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.6236705780029297},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5909348130226135},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5888949036598206},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.5844826698303223},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.560533881187439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5378981828689575},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5335557460784912},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4717574715614319},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4712947607040405},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3690676689147949},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36130842566490173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3454168140888214},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3252701759338379},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10034406185150146}],"concepts":[{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.690483033657074},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.6236705780029297},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5909348130226135},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5888949036598206},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.5844826698303223},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.560533881187439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5378981828689575},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5335557460784912},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4717574715614319},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4712947607040405},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3690676689147949},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36130842566490173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3454168140888214},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3252701759338379},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10034406185150146},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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:10.1109/acc.2015.7171025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W756936897","https://openalex.org/W1542938076","https://openalex.org/W1575147392","https://openalex.org/W1587069887","https://openalex.org/W1644749979","https://openalex.org/W1757084193","https://openalex.org/W1763790326","https://openalex.org/W1783235837","https://openalex.org/W1869042642","https://openalex.org/W1984714339","https://openalex.org/W1985691328","https://openalex.org/W1987919189","https://openalex.org/W1988376519","https://openalex.org/W2039401467","https://openalex.org/W2047564874","https://openalex.org/W2053874495","https://openalex.org/W2062361291","https://openalex.org/W2064733273","https://openalex.org/W2067070250","https://openalex.org/W2080484947","https://openalex.org/W2111326967","https://openalex.org/W2116813424","https://openalex.org/W2128834174","https://openalex.org/W2130989225","https://openalex.org/W2138190945","https://openalex.org/W2144326820","https://openalex.org/W2164412965","https://openalex.org/W2164727176","https://openalex.org/W2175110005","https://openalex.org/W2177625303","https://openalex.org/W2227319605","https://openalex.org/W2315083496","https://openalex.org/W2492791808","https://openalex.org/W4243369158","https://openalex.org/W4253629962","https://openalex.org/W6638212432","https://openalex.org/W6647351063","https://openalex.org/W6662108087","https://openalex.org/W6689130471","https://openalex.org/W7009171728"],"related_works":["https://openalex.org/W2053005959","https://openalex.org/W2299538996","https://openalex.org/W2027136373","https://openalex.org/W2144143333","https://openalex.org/W2086160648","https://openalex.org/W4386631510","https://openalex.org/W2276636510","https://openalex.org/W2105658174","https://openalex.org/W3163145068","https://openalex.org/W1990421243"],"abstract_inverted_index":{"This":[0,60],"paper":[1],"demonstrates":[2],"that":[3,37,78],"both":[4],"Balanced":[5,8],"Truncation":[6],"and":[7,40,103],"Singular":[9],"Perturbation":[10],"Approximations":[11],"can":[12,71],"be":[13],"viewed":[14],"as":[15],"limiting":[16],"approximations":[17],"of":[18,22,34,63,100,110],"the":[19,46,90,97],"same":[20],"parameterization":[21,33,102],"Linear":[23],"Time":[24],"Invariant":[25],"(LTI)":[26],"systems.":[27],"First,":[28],"we":[29,44],"introduce":[30],"a":[31,83,88,107],"specific":[32,98],"LTI":[35],"systems":[36],"distinguishes":[38],"dynamic":[39],"structural":[41],"parameters.":[42],"Next,":[43],"apply":[45],"Model":[47],"Boundary":[48],"Approximation":[49],"Method":[50],"(MBAM)":[51],"[1]":[52],"to":[53,56,82],"particular":[54,84],"parameters":[55],"achieve":[57],"different":[58,75],"approximations.":[59],"unified":[61],"view":[62],"these":[64],"popular":[65],"model":[66,101],"reduction":[67],"techniques,":[68],"which":[69,93],"themselves":[70],"result":[72],"in":[73,106],"quite":[74],"approximations,":[76],"illustrates":[77],"each":[79],"approximation":[80],"corresponds":[81],"boundary":[85],"element":[86],"on":[87],"manifold,":[89],"\u201cmodel":[91],"manifold,\u201d":[92],"is":[94,104],"associated":[95],"with":[96],"choice":[99],"embedded":[105],"sample":[108],"space":[109],"measured":[111],"outputs.":[112]},"counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}