{"id":"https://openalex.org/W2055081012","doi":"https://doi.org/10.1137/s1064827503427741","title":"Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes","display_name":"Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2055081012","doi":"https://doi.org/10.1137/s1064827503427741","mag":"2055081012"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503427741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503427741","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":["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/A5052112271","display_name":"Bert Debusschere","orcid":"https://orcid.org/0000-0001-7253-7059"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bert J. Debusschere","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075501406","display_name":"Habib N. Najm","orcid":"https://orcid.org/0000-0002-6338-7260"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Habib N. Najm","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090559121","display_name":"Philippe P\u00e9ba\u00ff","orcid":"https://orcid.org/0000-0002-2311-3775"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philippe P. P\u00e9bay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108087933","display_name":"Omar M. Knio","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omar M. Knio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006138292","display_name":"Roger Ghanem","orcid":"https://orcid.org/0000-0002-1890-920X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger G. Ghanem","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012736293","display_name":"Olivier Le Ma\u0131\u0302tre","orcid":"https://orcid.org/0000-0002-3811-7787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivier P. Le Ma\u0131\u2041tre","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":11.9481,"has_fulltext":false,"cited_by_count":455,"citation_normalized_percentile":{"value":0.98693652,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"26","issue":"2","first_page":"698","last_page":"719"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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/T11371","display_name":"Wind and Air Flow Studies","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9588000178337097,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.8133610486984253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7841037511825562},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6263002753257751},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6218459606170654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5825647711753845},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.43051791191101074},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.42657095193862915},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4111138880252838},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38659676909446716},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3610670566558838},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.27005887031555176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16735747456550598},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07975327968597412}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.8133610486984253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7841037511825562},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6263002753257751},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6218459606170654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5825647711753845},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.43051791191101074},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.42657095193862915},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4111138880252838},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38659676909446716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3610670566558838},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.27005887031555176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16735747456550598},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07975327968597412},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":2,"locations":[{"id":"doi:10.1137/s1064827503427741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503427741","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:CiteSeerX.psu:10.1.1.104.393","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.393","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://gmfe16.cemif.univ-evry.fr:8080/pub/DEB04R.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W65928136","https://openalex.org/W73098682","https://openalex.org/W1538934584","https://openalex.org/W1554577510","https://openalex.org/W1634277530","https://openalex.org/W1965847964","https://openalex.org/W1982769461","https://openalex.org/W1986585913","https://openalex.org/W1987043741","https://openalex.org/W2004515370","https://openalex.org/W2014655927","https://openalex.org/W2018159038","https://openalex.org/W2024825926","https://openalex.org/W2034762535","https://openalex.org/W2046076021","https://openalex.org/W2055712310","https://openalex.org/W2067074889","https://openalex.org/W2089770162","https://openalex.org/W2094149917","https://openalex.org/W2103621341","https://openalex.org/W2105596596","https://openalex.org/W2113517083","https://openalex.org/W2167720109","https://openalex.org/W2184045405","https://openalex.org/W2321957512","https://openalex.org/W2332771484","https://openalex.org/W2951262552","https://openalex.org/W4293510232"],"related_works":["https://openalex.org/W2797263970","https://openalex.org/W2891782306","https://openalex.org/W2287391662","https://openalex.org/W339217817","https://openalex.org/W2971126152","https://openalex.org/W2103244625","https://openalex.org/W2142056387","https://openalex.org/W2789381754","https://openalex.org/W4300567873","https://openalex.org/W108297729"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"an":[3],"overview":[4],"of":[5,8,37,68,71,76],"the":[6,69,72,77,90,111],"use":[7],"polynomial":[9,33],"chaos":[10],"(PC)":[11],"expansions":[12],"to":[13],"represent":[14],"stochastic":[15],"processes":[16],"in":[17,110],"numerical":[18],"simulations.":[19],"Several":[20],"methods":[21,44,79],"are":[22],"presented":[23],"for":[24,31,61,80,99],"performing":[25],"arithmetic":[26],"on,":[27],"as":[28,30,53,55],"well":[29,54],"evaluating":[32,100],"and":[34,75,96],"nonpolynomial":[35,62,81,101],"functions":[36],"variables":[38],"represented":[39],"by":[40],"PC":[41,73,112],"expansions.":[42,113],"These":[43],"include":[45],"{Taylor}":[46],"series,":[47],"a":[48,56,94],"newly":[49],"developed":[50],"integration":[51,91],"method,":[52],"sampling-based":[57],"spectral":[58],"projection":[59],"method":[60,92],"function":[63,82],"evaluations.":[64],"A":[65],"detailed":[66],"analysis":[67],"accuracy":[70],"representations,":[74],"different":[78],"evaluations,":[83],"is":[84,87,108],"performed.":[85],"It":[86],"found":[88],"that":[89],"offers":[93],"robust":[95],"accurate":[97],"approach":[98],"functions,":[102],"even":[103],"when":[104],"very":[105],"high-order":[106],"information":[107],"present":[109]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":22},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":32},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":29},{"year":2014,"cited_by_count":21},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":36}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
