{"id":"https://openalex.org/W1587462544","doi":"https://doi.org/10.1137/15m1010774","title":"Vector Fitting for Matrix-valued Rational Approximation","display_name":"Vector Fitting for Matrix-valued Rational Approximation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1587462544","doi":"https://doi.org/10.1137/15m1010774","mag":"1587462544"},"language":"en","primary_location":{"id":"doi:10.1137/15m1010774","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010774","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.00411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Z. Drma\u010d","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Z. Drma\u010d","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"S. Gugercin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Gugercin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"C. Beattie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Beattie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3917,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.80428207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"5","first_page":"A2346","last_page":"A2379"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.5450000166893005,"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":0.5450000166893005,"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":0.08460000157356262,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.04910000041127205,"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/scalar","display_name":"Scalar (mathematics)","score":0.642300009727478},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5716000199317932},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5339000225067139},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5205000042915344},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5127000212669373},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4821999967098236},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.3856000006198883},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.384799987077713},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.38420000672340393}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6990000009536743},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.642300009727478},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5716000199317932},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5442000031471252},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5339000225067139},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5205000042915344},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40779998898506165},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.37860000133514404},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C2778153524","wikidata":"https://www.wikidata.org/wiki/Q4241335","display_name":"Optimality criterion","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1010774","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010774","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.00411","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.00411","pdf_url":"https://arxiv.org/pdf/1503.00411","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.00411","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1503.00411","pdf_url":"https://arxiv.org/pdf/1503.00411","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":[],"awards":[{"id":"https://openalex.org/G5030675371","display_name":"Collaborative Research: Innovative Integrative Strategies for Nonlinear Parametric Inversion","funder_award_id":"1217156","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6993146038","display_name":null,"funder_award_id":"HRZZ-9345","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G983044456","display_name":null,"funder_award_id":"DMS-1217156","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322674","display_name":"Hrvatska Zaklada za Znanost","ror":"https://ror.org/03n51vw80"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1561849568","https://openalex.org/W1631445900","https://openalex.org/W1966992674","https://openalex.org/W1974090249","https://openalex.org/W1982886044","https://openalex.org/W1983997964","https://openalex.org/W2007161305","https://openalex.org/W2020828929","https://openalex.org/W2042498709","https://openalex.org/W2043307446","https://openalex.org/W2045266717","https://openalex.org/W2054260755","https://openalex.org/W2054643050","https://openalex.org/W2060335779","https://openalex.org/W2064733273","https://openalex.org/W2069966077","https://openalex.org/W2072293315","https://openalex.org/W2078675418","https://openalex.org/W2087142053","https://openalex.org/W2099995889","https://openalex.org/W2106322182","https://openalex.org/W2108545706","https://openalex.org/W2108660268","https://openalex.org/W2114458102","https://openalex.org/W2125201600","https://openalex.org/W2137765946","https://openalex.org/W2151141567","https://openalex.org/W2155154046","https://openalex.org/W2155305403","https://openalex.org/W2156722294","https://openalex.org/W2161972857","https://openalex.org/W2171353752","https://openalex.org/W4233692749"],"related_works":[],"abstract_inverted_index":{"Vector":[0],"Fitting":[1],"VF)":[2],"is":[3,156],"a":[4,13,37,64,119,235],"popular":[5],"method":[6],"of":[7,29,57,89,100,116,122,159,163,178,192,249],"constructing":[8],"rational":[9,33,59,166],"approximants":[10],"that":[11,70,91,125,144,151],"provides":[12],"least":[14],"squares":[15],"fit":[16],"to":[17,53,61,102,113,244,267],"frequency":[18],"response":[19],"measurements.":[20],"In":[21],"an":[22,27,134],"earlier":[23,215],"work,":[24],"we":[25,92,233],"provided":[26],"analysis":[28,121,135],"VF":[30,101,147,220,250],"for":[31,146,187,228],"scalar-valued":[32],"functions":[34,79,90,104,150],"and":[35,48,105,202,241,272],"established":[36],"connection":[38,236],"with":[39,81,237,254],"optimal":[40,230,238],"${\\mathcal{H}}_2$":[41],"approximation.":[42],"We":[43,131,182,262],"build":[44],"on":[45,148,198,205,217],"this":[46],"work":[47,216],"extend":[49],"the":[50,55,75,87,114,157,160,164,168,176,189,193,218,247,269],"previous":[51],"framework":[52],"include":[54],"construction":[56],"effective":[58],"approximations":[60],"matrix-valued":[62,103,149],"functions,":[63],"problem":[65,221],"which":[66],"presents":[67],"significant":[68],"challenges":[69],"do":[71],"not":[72,128],"appear":[73],"in":[74,175,211,258],"scalar":[76,219],"case.":[77],"Transfer":[78],"associated":[80],"multi-input/multioutput":[82],"(MIMO)":[83],"dynamical":[84],"systems":[85],"typify":[86],"class":[88],"consider":[93],"here.":[94,140],"Others":[95],"have":[96],"also":[97],"considered":[98],"extensions":[99],"related":[106],"numerical":[107,123,252,265],"implementations":[108],"are":[109,242],"readily":[110],"available.":[111],"However,":[112],"best":[115],"our":[117,214],"knowledge,":[118],"detailed":[120],"issues":[124],"arise":[126],"does":[127],"yet":[129],"exist.":[130],"offer":[132],"such":[133],"including":[136],"critical":[137],"implementation":[138],"details":[139],"One":[141],"important":[142],"issue":[143],"arises":[145],"has":[152],"remained":[153],"largely":[154],"unaddressed":[155],"control":[158],"McMillan":[161,169,190],"degree":[162,170,191],"resulting":[165],"approximant;":[167],"can":[171],"grow":[172],"very":[173],"high":[174],"case":[177],"large":[179],"input/output":[180],"dimensions.":[181],"introduce":[183],"two":[184],"new":[185],"mechanisms":[186],"controlling":[188],"final":[194],"approximant,":[195],"one":[196,203],"based":[197,204],"alternating":[199],"least-squares":[200],"minimization":[201],"ancillary":[206],"system-theoretic":[207],"reduction":[208],"methods.":[209],"Motivated":[210],"part":[212],"by":[213,225],"as":[222,224],"well":[223],"recent":[226],"innovations":[227],"computing":[229],"$\\mathcal{H}_2$":[231,239],"approximation,":[232,240],"establish":[234],"able":[243],"improve":[245],"significantly":[246],"fidelity":[248],"through":[251],"quadrature,":[253],"virtually":[255],"no":[256],"increase":[257],"cost":[259],"or":[260],"complexity.":[261],"provide":[263],"several":[264],"examples":[266],"support":[268],"theoretical":[270],"discussion":[271],"proposed":[273],"algorithms.":[274]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}