{"id":"https://openalex.org/W2044970181","doi":"https://doi.org/10.1137/140969063","title":"To Be or Not to be Intrusive? The Solution of Parametric and Stochastic Equations---Proper Generalized Decomposition","display_name":"To Be or Not to be Intrusive? The Solution of Parametric and Stochastic Equations---Proper Generalized Decomposition","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2044970181","doi":"https://doi.org/10.1137/140969063","mag":"2044970181"},"language":"en","primary_location":{"id":"doi:10.1137/140969063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969063","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/1405.0875","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002106106","display_name":"Lo\u00efc Giraldi","orcid":"https://orcid.org/0000-0003-4886-5938"},"institutions":[{"id":"https://openalex.org/I4210137520","display_name":"Institut de Recherche en G\u00e9nie Civil et M\u00e9canique","ror":"https://ror.org/03x30hb31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210137520","https://openalex.org/I97188460","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Lo\u00efc Giraldi","raw_affiliation_strings":["GeM - Institut de Recherche en G\u00e9nie Civil et M\u00e9canique (1, rue de la No\u00eb BP92101 44321 Nantes cedex 3 - France)"],"affiliations":[{"raw_affiliation_string":"GeM - Institut de Recherche en G\u00e9nie Civil et M\u00e9canique (1, rue de la No\u00eb BP92101 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I4210137520"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069489614","display_name":"Dishi Liu","orcid":"https://orcid.org/0000-0001-5811-8237"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dishi Liu","raw_affiliation_strings":["DLR Institute of Aerodynamics and Flow Control (Germany)"],"affiliations":[{"raw_affiliation_string":"DLR Institute of Aerodynamics and Flow Control (Germany)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037684251","display_name":"Hermann G. Matthies","orcid":"https://orcid.org/0000-0002-8644-5574"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hermann G. Matthies","raw_affiliation_strings":["WiRe - Institut f\u00fcr Wissenschaftliches Rechnen (Technische Universit\u00e4t Braunschweig D-38092 Braunschweig - Germany)"],"affiliations":[{"raw_affiliation_string":"WiRe - Institut f\u00fcr Wissenschaftliches Rechnen (Technische Universit\u00e4t Braunschweig D-38092 Braunschweig - Germany)","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031143836","display_name":"Anthony Nouy","orcid":"https://orcid.org/0000-0002-2149-2986"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Anthony Nouy","raw_affiliation_strings":["LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","ECN - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)"],"affiliations":[{"raw_affiliation_string":"LMJL - Laboratoire de Math\u00e9matiques Jean Leray (France)","institution_ids":["https://openalex.org/I4210153365"]},{"raw_affiliation_string":"ECN - \u00c9cole Centrale de Nantes (1 rue de la No\u00eb - BP 92101 - 44321 Nantes cedex 3 - France)","institution_ids":["https://openalex.org/I100445878"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002106106"],"corresponding_institution_ids":["https://openalex.org/I4210137520"],"apc_list":null,"apc_paid":null,"fwci":1.0613,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.74344569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"A347","last_page":"A368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9940999746322632,"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":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8664794564247131},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6184390783309937},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5573039650917053},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5394620895385742},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.43409180641174316},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3513793349266052},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33067888021469116},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1793437898159027},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1676894724369049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8664794564247131},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6184390783309937},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5573039650917053},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5394620895385742},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.43409180641174316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3513793349266052},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33067888021469116},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1793437898159027},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1676894724369049},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/140969063","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140969063","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:1405.0875","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.0875","pdf_url":"https://arxiv.org/pdf/1405.0875","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":"pmh:oai:HAL:hal-00987530v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00987530","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":"https://hal.archives-ouvertes.fr/hal-00987530","raw_type":"\\ninfo:eu-repo/semantics/preprint\\n"},{"id":"pmh:oai:HAL:hal-01899842v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01899842","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 2015, 37 (1), pp.A347 - A368. &#x27E8;10.1137/140969063&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1405.0875","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.0875","pdf_url":"https://arxiv.org/pdf/1405.0875","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1504748373","https://openalex.org/W1567457275","https://openalex.org/W1634277530","https://openalex.org/W1853276794","https://openalex.org/W1975206377","https://openalex.org/W1982559793","https://openalex.org/W1984516949","https://openalex.org/W1998444222","https://openalex.org/W2014910287","https://openalex.org/W2024165284","https://openalex.org/W2034801304","https://openalex.org/W2036242000","https://openalex.org/W2053211759","https://openalex.org/W2056404710","https://openalex.org/W2060200773","https://openalex.org/W2060528584","https://openalex.org/W2064332562","https://openalex.org/W2068484625","https://openalex.org/W2082406229","https://openalex.org/W2083299971","https://openalex.org/W2088087394","https://openalex.org/W2092189481","https://openalex.org/W2094085947","https://openalex.org/W2105596596","https://openalex.org/W2110632054","https://openalex.org/W2142918656","https://openalex.org/W2167720109","https://openalex.org/W2403013574","https://openalex.org/W2608505863","https://openalex.org/W2613145724","https://openalex.org/W2798813531","https://openalex.org/W2913975905","https://openalex.org/W2963858059","https://openalex.org/W3103499934","https://openalex.org/W3105645565","https://openalex.org/W3118870036","https://openalex.org/W4211080438","https://openalex.org/W4255975175","https://openalex.org/W4298302794"],"related_works":["https://openalex.org/W2330487432","https://openalex.org/W2153629319","https://openalex.org/W2104316494","https://openalex.org/W239705756","https://openalex.org/W156119379","https://openalex.org/W2082139080","https://openalex.org/W4231015910","https://openalex.org/W2364847091","https://openalex.org/W1547852488","https://openalex.org/W1543223008"],"abstract_inverted_index":{"A":[0],"numerical":[1,97,117],"method":[2,80],"is":[3,90,112],"proposed":[4],"to":[5,11,81,115],"compute":[6],"a":[7,15,21,34,42,78],"low-rank":[8,57],"Galerkin":[9],"approximation":[10],"the":[12,31,56,62,70,72,83,86,94,102],"solution":[13],"of":[14,33,45,64,69,85,96,104],"parametric":[16],"or":[17],"stochastic":[18],"equation":[19],"in":[20],"nonintrusive":[22,92],"fashion.":[23],"The":[24,88,110],"considered":[25],"nonlinear":[26],"problems":[27],"are":[28,74],"associated":[29],"with":[30,61,77],"minimization":[32,52],"parameterized":[35],"differentiable":[36],"convex":[37],"functional.":[38],"We":[39],"first":[40],"introduce":[41],"bilinear":[43],"parameterization":[44],"fixed-rank":[46],"tensors":[47],"and":[48],"employ":[49],"an":[50],"alternating":[51],"scheme":[53],"for":[54],"computing":[55],"approximation.":[58],"In":[59],"keeping":[60],"idea":[63],"nonintrusiveness,":[65],"at":[66,106],"each":[67],"step":[68],"algorithm":[71,89,111],"minimizations":[73],"carried":[75],"out":[76],"quasi-Newton":[79],"avoid":[82],"computation":[84],"Hessian.":[87],"made":[91],"through":[93],"use":[95],"integration.":[98],"It":[99],"only":[100],"requires":[101],"evaluation":[103],"residuals":[105],"specific":[107],"parameter":[108],"values.":[109],"then":[113],"applied":[114],"two":[116],"examples.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2016-06-24T00:00:00"}
