{"id":"https://openalex.org/W1963565023","doi":"https://doi.org/10.1109/cdc.2012.6426344","title":"Realization-independent &amp;#x210C;&lt;inf&gt;2&lt;/inf&gt;-approximation","display_name":"Realization-independent &amp;#x210C;&lt;inf&gt;2&lt;/inf&gt;-approximation","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W1963565023","doi":"https://doi.org/10.1109/cdc.2012.6426344","mag":"1963565023"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2012.6426344","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","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/A5084513956","display_name":"Christopher Beattie","orcid":"https://orcid.org/0000-0003-3302-4845"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Beattie","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA, USA","Department of Mathematics, Virginia Tech., Blacksburg, 24061-0123, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Department of Mathematics, Virginia Tech., Blacksburg, 24061-0123, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028332862","display_name":"Serkan Gugercin","orcid":"https://orcid.org/0000-0003-4564-5999"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Serkan Gugercin","raw_affiliation_strings":["Department of Mathematics, Virginia Tech, Blacksburg, VA, USA","Department of Mathematics, Virginia Tech., Blacksburg, 24061-0123, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Department of Mathematics, Virginia Tech., Blacksburg, 24061-0123, USA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":1.2143,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.77499477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"4953","last_page":"4958"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9983000159263611,"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/T10787","display_name":"Lightning and Electromagnetic Phenomena","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/realization","display_name":"Realization (probability)","score":0.7747548818588257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.463374525308609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30561354756355286},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0902881920337677}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.7747548818588257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.463374525308609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30561354756355286},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0902881920337677}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2012.6426344","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","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":17,"referenced_works":["https://openalex.org/W49128507","https://openalex.org/W1539600348","https://openalex.org/W1966255369","https://openalex.org/W1966992674","https://openalex.org/W2043307446","https://openalex.org/W2064610948","https://openalex.org/W2069970858","https://openalex.org/W2073813183","https://openalex.org/W2076742685","https://openalex.org/W2085724310","https://openalex.org/W2098158506","https://openalex.org/W2106654677","https://openalex.org/W2118958734","https://openalex.org/W2120676102","https://openalex.org/W2136195193","https://openalex.org/W2159122878","https://openalex.org/W2171353752"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2022544890","https://openalex.org/W2142036596"],"abstract_inverted_index":{"The":[0],"Iterative":[1],"Rational":[2],"Krylov":[3],"Algorithm":[4],"(IRKA)":[5],"of":[6,30,36,54,70,78,107,116],"[9]":[7],"is":[8],"an":[9],"effective":[10],"tool":[11],"for":[12,47],"approaching":[13],"the":[14,28,37,98,105,114,117],"H":[15,73,99],"<sub":[16,74,100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,75,101],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[18,76,102],"-optimal":[19],"model":[20],"reduction":[21],"problem.":[22],"However,":[23],"it":[24],"has":[25],"relied":[26],"on":[27],"availability":[29],"a":[31,44,51,85],"standard":[32],"first-order":[33],"state-space":[34],"realization":[35],"model-to-be-reduced.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42],"employ":[43],"Loewner-matrix":[45],"approach":[46],"interpolation,":[48],"and":[49],"develop":[50],"new":[52],"formulation":[53],"IRKA":[55,71,89],"that":[56,90],"only":[57],"uses":[58],"transfer":[59],"function":[60],"evaluations,":[61],"without":[62],"requiring":[63],"any":[64],"particular":[65],"realization.":[66],"This":[67],"allows":[68],"extension":[69],"to":[72,96],"approximation":[77],"irrational,":[79],"infinite-dimensional":[80],"dynamical":[81],"systems.":[82],"We":[83],"incorporate":[84],"residue-correction":[86],"step":[87],"within":[88],"adjusts":[91],"vector":[92],"residues":[93],"so":[94],"as":[95],"minimize":[97],"error":[103],"at":[104],"end":[106],"each":[108],"cycle.":[109],"Two":[110],"numerical":[111],"examples":[112],"illustrate":[113],"effectiveness":[115],"proposed":[118],"methods.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
