{"id":"https://openalex.org/W2606283473","doi":"https://doi.org/10.1137/17m1123079","title":"Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)","display_name":"Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2606283473","doi":"https://doi.org/10.1137/17m1123079","mag":"2606283473"},"language":"en","primary_location":{"id":"doi:10.1137/17m1123079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1123079","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":"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/A5084624008","display_name":"Oliver G. Ernst","orcid":"https://orcid.org/0000-0002-0176-7321"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Oliver G. Ernst","raw_affiliation_strings":["Department of Mathematics, TU Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, TU Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049132140","display_name":"Bj\u00f6rn Sprungk","orcid":"https://orcid.org/0000-0001-8359-6863"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bj\u00f6rn Sprungk","raw_affiliation_strings":["Department of Mathematics, TU Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, TU Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083408859","display_name":"Lorenzo Tamellini","orcid":"https://orcid.org/0000-0002-8008-0359"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lorenzo Tamellini","raw_affiliation_strings":["Istituto di Matematica Applicata e Tecnologie Informatiche \"E. Magenes\" del CNR, Pavia, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto di Matematica Applicata e Tecnologie Informatiche \"E. Magenes\" del CNR, Pavia, Italy","institution_ids":["https://openalex.org/I4210137033"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084624008"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":null,"apc_paid":null,"fwci":3.0183,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92011641,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"56","issue":"2","first_page":"877","last_page":"905"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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":0.9997000098228455,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9976999759674072,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8769657015800476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5746838450431824},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5414505004882812},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5235211849212646},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.46882766485214233},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.4648982584476471},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4447908401489258},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41041794419288635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3438418209552765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3281342685222626}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8769657015800476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5746838450431824},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5414505004882812},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5235211849212646},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.46882766485214233},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4648982584476471},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4447908401489258},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41041794419288635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3438418209552765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3281342685222626},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1123079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1123079","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W333648068","https://openalex.org/W1955320167","https://openalex.org/W1966606705","https://openalex.org/W1970476229","https://openalex.org/W1982421072","https://openalex.org/W1982944750","https://openalex.org/W2005606401","https://openalex.org/W2008058003","https://openalex.org/W2008640483","https://openalex.org/W2034055889","https://openalex.org/W2041509689","https://openalex.org/W2045116180","https://openalex.org/W2049222546","https://openalex.org/W2060528584","https://openalex.org/W2067610138","https://openalex.org/W2072282162","https://openalex.org/W2080348404","https://openalex.org/W2083754610","https://openalex.org/W2083845086","https://openalex.org/W2092333401","https://openalex.org/W2092478820","https://openalex.org/W2109012275","https://openalex.org/W2143591652","https://openalex.org/W2168170318","https://openalex.org/W2962840746","https://openalex.org/W2963062618","https://openalex.org/W2963798430","https://openalex.org/W3021293439","https://openalex.org/W4210729607"],"related_works":["https://openalex.org/W2963368994","https://openalex.org/W2948840354","https://openalex.org/W2908321071","https://openalex.org/W4312080235","https://openalex.org/W4288336360","https://openalex.org/W2984528840","https://openalex.org/W2953159110","https://openalex.org/W2019082066","https://openalex.org/W2400968058","https://openalex.org/W1972533195"],"abstract_inverted_index":{"We":[0,33,95],"give":[1],"a":[2,35,78],"convergence":[3,71,109,128],"proof":[4],"for":[5,73,82,98,120],"the":[6,83,88,113,126],"approximation":[7],"by":[8,43],"sparse":[9,117],"collocation":[10],"of":[11,26,87,116],"Hilbert-space-valued":[12],"functions":[13,22,76],"depending":[14],"on":[15,40],"countably":[16],"many":[17],"Gaussian":[18],"random":[19],"variables.":[20],"Such":[21],"appear":[23],"as":[24],"solutions":[25],"elliptic":[27],"PDEs":[28],"with":[29,110],"lognormal":[30],"diffusion":[31],"coefficients.":[32],"outline":[34],"general":[36],"$L^2$-convergence":[37],"theory":[38],"based":[39],"previous":[41],"work":[42],"Bachmayr":[44],"et":[45],"al.":[46],"[ESAIM":[47,58],"Math.":[48,59],"Model.":[49,60],"Numer.":[50,61],"Anal.,":[51,62],"51":[52],"(2017),":[53],"pp.":[54],"341--363]":[55],"and":[56,67,105],"Chen":[57],"in":[63],"press,":[64],"2018,":[65],"https://doi.org/10.1051/m2an/2018012]":[66],"establish":[68],"an":[69],"algebraic":[70,108],"rate":[72],"sufficiently":[74],"smooth":[75],"assuming":[77],"mild":[79],"growth":[80],"bound":[81],"univariate":[84],"hierarchical":[85],"surpluses":[86],"interpolation":[89],"scheme":[90],"applied":[91],"to":[92,112],"Hermite":[93],"polynomials.":[94],"specifically":[96],"verify":[97],"Gauss--Hermite":[99],"nodes":[100],"that":[101],"this":[102,121],"assumption":[103],"holds":[104],"also":[106],"show":[107],"respect":[111],"resulting":[114],"number":[115],"grid":[118],"points":[119],"case.":[122],"Numerical":[123],"experiments":[124],"illustrate":[125],"dimension-independent":[127],"rate.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
