{"id":"https://openalex.org/W3091850900","doi":"https://doi.org/10.1137/20m1371798","title":"On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition","display_name":"On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3091850900","doi":"https://doi.org/10.1137/20m1371798","mag":"3091850900"},"language":"en","primary_location":{"id":"doi:10.1137/20m1371798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1371798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.03750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009960829","display_name":"Birgul Koc","orcid":"https://orcid.org/0000-0002-1733-4862"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Birgul Koc","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049698923","display_name":"Samuele Rubino","orcid":"https://orcid.org/0000-0002-4571-1936"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samuele Rubino","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011820135","display_name":"Michael Schneier","orcid":"https://orcid.org/0000-0003-1101-4507"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Schneier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065565731","display_name":"John R. Singler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Singler","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063855550","display_name":"Traian Iliescu","orcid":"https://orcid.org/0000-0003-1437-7362"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Traian Iliescu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5009960829"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01567518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"4","first_page":"2163","last_page":"2196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/pointwise","display_name":"Pointwise","score":0.8654524087905884},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7073847651481628},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6584709286689758},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5918066501617432},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.5844323635101318},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.529979944229126},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.42699557542800903},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24506932497024536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1966601312160492},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07611545920372009}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8654524087905884},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7073847651481628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6584709286689758},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5918066501617432},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.5844323635101318},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.529979944229126},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.42699557542800903},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24506932497024536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1966601312160492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07611545920372009}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/20m1371798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1371798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2010.03750","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.03750","pdf_url":"https://arxiv.org/pdf/2010.03750","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"},{"id":"mag:3091850900","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.03750.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-03937022v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03937022","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2021, 59 (4), pp.2163-2196. &#x27E8;10.1137/20m1371798&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2010.03750","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.03750","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.03750","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.03750","pdf_url":"https://arxiv.org/pdf/2010.03750","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/G1284463829","display_name":null,"funder_award_id":"872442 (ARIA)","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G1786514303","display_name":null,"funder_award_id":"DMS-1439786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G195059270","display_name":"Transforming Reduced-Order Models of Fluids with Data Assimilation","funder_award_id":"1953113","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3000645326","display_name":null,"funder_award_id":"2012253","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4662355870","display_name":null,"funder_award_id":"CMMI-1929731","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5812068588","display_name":null,"funder_award_id":"1929731","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5822219397","display_name":null,"funder_award_id":"DMS-1953113","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5954070948","display_name":null,"funder_award_id":"CMMI-","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6182847705","display_name":null,"funder_award_id":"50736","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G6747301150","display_name":null,"funder_award_id":"DMS-2012253","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7527772353","display_name":null,"funder_award_id":"RTI2018-093521-B-C31","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G801081470","display_name":"Accurate Roms for Industrial Applications","funder_award_id":"872442","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W209265777","https://openalex.org/W1579236455","https://openalex.org/W1674659126","https://openalex.org/W1970736911","https://openalex.org/W1975698444","https://openalex.org/W1984617383","https://openalex.org/W1989951672","https://openalex.org/W1998028876","https://openalex.org/W2017745440","https://openalex.org/W2019655926","https://openalex.org/W2035934750","https://openalex.org/W2045627558","https://openalex.org/W2047378168","https://openalex.org/W2047591100","https://openalex.org/W2052690618","https://openalex.org/W2056088366","https://openalex.org/W2059748840","https://openalex.org/W2072136228","https://openalex.org/W2082621526","https://openalex.org/W2093049475","https://openalex.org/W2102273815","https://openalex.org/W2104225554","https://openalex.org/W2108311308","https://openalex.org/W2121569150","https://openalex.org/W2124056301","https://openalex.org/W2124773266","https://openalex.org/W2128953295","https://openalex.org/W2133041109","https://openalex.org/W2135913515","https://openalex.org/W2148105077","https://openalex.org/W2185376543","https://openalex.org/W2276712392","https://openalex.org/W2295099209","https://openalex.org/W2326313759","https://openalex.org/W2492374739","https://openalex.org/W2594340015","https://openalex.org/W2604065733","https://openalex.org/W2616320280","https://openalex.org/W2625397542","https://openalex.org/W2754139061","https://openalex.org/W2782277020","https://openalex.org/W2789354000","https://openalex.org/W2804974381","https://openalex.org/W2900896188","https://openalex.org/W2920954641","https://openalex.org/W2950254180","https://openalex.org/W2963056102","https://openalex.org/W2963192040","https://openalex.org/W2963582054","https://openalex.org/W2964276189","https://openalex.org/W2972464058","https://openalex.org/W2980401910","https://openalex.org/W3004767590","https://openalex.org/W3016478174","https://openalex.org/W3021544678","https://openalex.org/W3048581331"],"related_works":["https://openalex.org/W1979567129","https://openalex.org/W2045318013","https://openalex.org/W2155621154","https://openalex.org/W2186891146","https://openalex.org/W2010206499","https://openalex.org/W2022366221","https://openalex.org/W3211624668","https://openalex.org/W2089942753","https://openalex.org/W2125499703","https://openalex.org/W421650457","https://openalex.org/W2209349286","https://openalex.org/W26707179","https://openalex.org/W1593959000","https://openalex.org/W2024475368","https://openalex.org/W2555420911","https://openalex.org/W2004798810","https://openalex.org/W3147448769","https://openalex.org/W2182940243","https://openalex.org/W2176302550","https://openalex.org/W2178071329"],"abstract_inverted_index":{"In":[0,28],"this":[1],"paper,":[2],"we":[3,30,69,88],"resolve":[4],"several":[5],"long-standing":[6],"issues":[7],"dealing":[8],"with":[9,50],"optimal":[10,49],"pointwise":[11],"in":[12,39],"time":[13,55],"error":[14,45,57,76,80,95,99],"bounds":[15,46],"for":[16,105],"proper":[17],"orthogonal":[18],"decomposition":[19],"(POD)":[20],"reduced":[21,41],"order":[22,42],"modeling":[23],"of":[24],"the":[25,32,54,59,64,73,78,84,92,97,106,110],"heat":[26,107],"equation.":[27],"particular,":[29],"study":[31],"role":[33],"played":[34],"by":[35],"difference":[36],"quotients":[37],"(DQs)":[38],"obtaining":[40],"model":[43],"(ROM)":[44],"that":[47,71,90],"are":[48,66,81,86,100],"respect":[51],"to":[52],"both":[53,72,91],"discretization":[56,61],"and":[58,77,96],"ROM":[60,79,98],"error.":[62],"When":[63,83],"DQs":[65,85],"not":[67],"used,":[68,87],"prove":[70,89],"POD":[74,93],"projection":[75,94],"suboptimal.":[82],"optimal.":[101],"The":[102],"numerical":[103],"results":[104],"equation":[108],"support":[109],"theoretical":[111],"results.":[112]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
