{"id":"https://openalex.org/W4283723875","doi":"https://doi.org/10.1137/20m1338137","title":"Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification","display_name":"Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification","publication_year":2022,"publication_date":"2022-06-29","ids":{"openalex":"https://openalex.org/W4283723875","doi":"https://doi.org/10.1137/20m1338137"},"language":"en","primary_location":{"id":"doi:10.1137/20m1338137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338137","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","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/A5004856556","display_name":"Josef Dick","orcid":"https://orcid.org/0000-0003-0142-6022"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia ()","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102738039","display_name":"Marcello Longo","orcid":"https://orcid.org/0000-0002-1211-107X"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210111868","display_name":"Zurich University of Teacher Education","ror":"https://ror.org/01awgk221","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210111868"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Marcello Longo","raw_affiliation_strings":["Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich 8092, Switzerland (, )"],"raw_orcid":"https://orcid.org/0000-0002-1211-107X","affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich 8092, Switzerland (, )","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110448103","display_name":"Christoph Schwab","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210111868","display_name":"Zurich University of Teacher Education","ror":"https://ror.org/01awgk221","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210111868"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Christoph Schwab","raw_affiliation_strings":["Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich 8092, Switzerland (, )"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, ETH Z\u00fcrich, Z\u00fcrich 8092, Switzerland (, )","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9611,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69973059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"10","issue":"2","first_page":"651","last_page":"686"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9743000268936157,"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/mathematics","display_name":"Mathematics","score":0.7295986413955688},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.6194452047348022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5496240854263306},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.45892930030822754},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.41531309485435486},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.414222776889801},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33326923847198486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26266247034072876},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.14152005314826965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09813335537910461},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.09506100416183472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7295986413955688},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.6194452047348022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5496240854263306},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45892930030822754},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.41531309485435486},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.414222776889801},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33326923847198486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26266247034072876},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.14152005314826965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09813335537910461},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.09506100416183472},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1338137","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338137","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5403198076","display_name":"Novel mathematics and numerical methods for ferromagnetic problems","funder_award_id":"DP190101197","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1472566082","https://openalex.org/W1504916371","https://openalex.org/W1630018803","https://openalex.org/W1689157804","https://openalex.org/W1936872399","https://openalex.org/W1978501336","https://openalex.org/W2006047654","https://openalex.org/W2042083287","https://openalex.org/W2049222546","https://openalex.org/W2051344283","https://openalex.org/W2062993069","https://openalex.org/W2124413011","https://openalex.org/W2126980197","https://openalex.org/W2129114523","https://openalex.org/W2133041109","https://openalex.org/W2146736312","https://openalex.org/W2152162686","https://openalex.org/W2191360394","https://openalex.org/W2266019243","https://openalex.org/W2559327389","https://openalex.org/W2685500084","https://openalex.org/W2734717932","https://openalex.org/W2735105826","https://openalex.org/W2782466637","https://openalex.org/W2792017407","https://openalex.org/W2803351718","https://openalex.org/W2810479569","https://openalex.org/W2885538759","https://openalex.org/W2943717311","https://openalex.org/W2964177332","https://openalex.org/W2964207585","https://openalex.org/W3099856523","https://openalex.org/W4240395309"],"related_works":["https://openalex.org/W2378736565","https://openalex.org/W1945408838","https://openalex.org/W2226133288","https://openalex.org/W4254660938","https://openalex.org/W2105196846","https://openalex.org/W4243249212","https://openalex.org/W4377005030","https://openalex.org/W2061025635","https://openalex.org/W4253135066","https://openalex.org/W4387847482"],"abstract_inverted_index":{".We":[0],"present":[1,233],"an":[2,66,302],"extension":[3],"of":[4,35,65,69,79,83,102,131,152,162,172,175,220,242,256,274,286,314],"the":[5,63,70,81,100,103,113,120,129,144,163,173,176,238,254,257,268,275,294],"convergence":[6,136],"analysis":[7],"for":[8,29,62,92,99,149,217,309],"Richardson-extrapolated":[9],"polynomial":[10],"lattice":[11],"rules":[12,46],"from":[13,128,186,237],"[J.":[14,187],"Dick,":[15,188],"T.":[16,19,193],"Goda,":[17],"and":[18,41,51,169,179,232,266,307],"Yoshiki,":[20],"SIAM":[21,198],"J.":[22,199],"Numer.":[23],"Anal.,":[24],"57":[25],"(2019),":[26],"pp.":[27,204],"44\u201369]":[28],"high-dimensional,":[30],"numerical":[31,160,234,272],"integration":[32,45,72,85,114,123,177,213,298],"to":[33,76,112,139,208],"classes":[34,151,219],"integrand":[36,154,222],"functions":[37,155,223],"with":[38,47,74,107,110,167,224,262,283],"quantified":[39,225],"smoothness":[40],"quasi\u2013Monte":[42],"Carlo":[43],"(QMC)":[44],"so-called":[48],"smoothness-driven,":[49],"product":[50],"order":[52],"dependent":[53],"(SPOD)":[54],"weights.":[55],"We":[56,87,117,228,251,279],"establish":[57],"in":[58,281],"particular":[59],"sufficient":[60],"conditions":[61,142],"existence":[64],"asymptotic":[67],"expansion":[68],"QMC":[71,84,104,122,145,164,264,276,297,315],"error":[73,299,321],"respect":[75,111],"suitable":[77,140],"powers":[78],"N,":[80],"number":[82,312],"nodes.":[86],"derive":[88],"a":[89,93,156,243,270,310],"dimension-separated":[90],"criterion":[91],"fast":[94,258],"component-by-component":[95],"(CBC)":[96],"construction":[97,260],"algorithm":[98,261],"computation":[101],"generating":[105],"vector":[106],"quadratic":[108],"scaling":[109,255],"dimension":[115,174,287],"s.":[116],"prove":[118],"that":[119,293],"proposed":[121],"strategies":[124],"(a)":[125],"are":[126,215],"free":[127],"curse":[130],"dimensionality,":[132],"(b)":[133],"afford":[134],"higher-order":[135],"rates":[137],"subject":[138],"summability":[141],"on":[143],"weights,":[146],"(c)":[147],"allow":[148],"certain":[150],"high-dimensional":[153],"computable,":[157],"asymptotically":[158],"exact":[159],"estimate":[161],"quadrature":[165,277],"error,":[166],"reliability":[168],"efficiency":[170,303],"independent":[171],"domain,":[178],"(d)":[180],"accommodate":[181],"fast,":[182],"FFT-based":[183],"matrix-vector":[184],"multiplication":[185],"F.":[189],"Y.":[190],"Kuo,":[191],"Q.":[192],"Le":[194],"Gia,":[195],"C.":[196],"Schwab,":[197],"Sci.":[200],"Comput.,":[201],"37":[202],"(2015),":[203],"A1436\u2013A1450]":[205],"when":[206],"applied":[207],"parametric":[209,226,246],"operator":[210],"equations.":[211],"The":[212],"methods":[214],"applicable":[216],"large":[218],"many-parametric":[221],"smoothness.":[227],"verify":[229,252],"all":[230],"hypotheses":[231],"examples":[235,282],"arising":[236],"Galerkin":[239],"finite-element":[240],"discretization":[241],"model":[244],"linear":[245],"elliptic":[247],"PDE":[248],"illustrating":[249],"(a)\u2013(d).":[250],"computationally":[253],"CBC":[259],"SPOD":[263],"weights":[265],"examine":[267],"extrapolation-based":[269],"posteriori":[271,320],"estimation":[273],"error.":[278],"find":[280],"parameter":[284],"spaces":[285],"s":[288],"=":[289],"10,":[290],"\u2026,":[291],"128":[292],"extrapolation-based,":[295],"computable":[296],"indicator":[300],"has":[301],"index":[304],"between":[305],"0.9":[306],"1.1":[308],"moderate":[311],"N":[313],"points.Keywordshigh-dimensional":[316],"quadraturequasi\u2013Monte":[317],"CarloRichardson":[318],"extrapolationa":[319],"estimationMSC":[322],"codes65C0565N3035J25":[323]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
