{"id":"https://openalex.org/W2513208677","doi":"https://doi.org/10.1137/16m1087461","title":"On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness","display_name":"On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2513208677","doi":"https://doi.org/10.1137/16m1087461","mag":"2513208677"},"language":"en","primary_location":{"id":"doi:10.1137/16m1087461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1087461","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1608.06061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004856556","display_name":"Josef Dick","orcid":"https://orcid.org/0000-0003-0142-6022"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079858628","display_name":"Christian Irrgeher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Irrgeher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083229856","display_name":"Gunther Leobacher","orcid":"https://orcid.org/0000-0002-7837-784X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gunther Leobacher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052381247","display_name":"Friedrich Pillichshammer","orcid":"https://orcid.org/0000-0001-6952-9218"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Friedrich Pillichshammer","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":0.6409,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61163522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"56","issue":"2","first_page":"684","last_page":"707"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9926000237464905,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unit-cube","display_name":"Unit cube","score":0.8214764595031738},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.7824763059616089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7739835381507874},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7463441491127014},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6187014579772949},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5435696244239807},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5258541703224182},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5053775906562805},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47959935665130615},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4773454964160919},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4738845229148865},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.46862390637397766},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.456132709980011},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.45486918091773987},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4345681667327881},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.42628148198127747},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41774508357048035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4141808748245239},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35503536462783813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3347243070602417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10572227835655212},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07458800077438354}],"concepts":[{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.8214764595031738},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7824763059616089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7739835381507874},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7463441491127014},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6187014579772949},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5435696244239807},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5258541703224182},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5053775906562805},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47959935665130615},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4773454964160919},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4738845229148865},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.46862390637397766},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.456132709980011},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.45486918091773987},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4345681667327881},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.42628148198127747},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41774508357048035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4141808748245239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35503536462783813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3347243070602417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10572227835655212},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07458800077438354},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1087461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1087461","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:1608.06061","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1608.06061","pdf_url":"https://arxiv.org/pdf/1608.06061","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:2513208677","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1608.06061.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"doi:10.48550/arxiv.1608.06061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1608.06061","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1608.06061","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1608.06061","pdf_url":"https://arxiv.org/pdf/1608.06061","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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/G1199718552","display_name":null,"funder_award_id":"F5508-N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G378720623","display_name":null,"funder_award_id":"F5506","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5592139713","display_name":null,"funder_award_id":"F5506-N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5749826759","display_name":null,"funder_award_id":"F5509\u2010N26","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5773529614","display_name":"Quantifying uncertainty: innovations in high dimensional computation","funder_award_id":"DP150101770","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G8550582057","display_name":null,"funder_award_id":"F5509","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2513208677.pdf","grobid_xml":"https://content.openalex.org/works/W2513208677.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W598051755","https://openalex.org/W2014551121","https://openalex.org/W2030404880","https://openalex.org/W2043419861","https://openalex.org/W2052335571","https://openalex.org/W2078197553","https://openalex.org/W2137224975","https://openalex.org/W2314485382","https://openalex.org/W2319072435","https://openalex.org/W2951568738","https://openalex.org/W2963374275","https://openalex.org/W2964330574","https://openalex.org/W3038165843","https://openalex.org/W3102328113","https://openalex.org/W3119524009"],"related_works":["https://openalex.org/W2962718855","https://openalex.org/W3106016933","https://openalex.org/W2904804828","https://openalex.org/W3099386363","https://openalex.org/W2033560593","https://openalex.org/W2014551121","https://openalex.org/W2953326397","https://openalex.org/W1976695998","https://openalex.org/W2338000073","https://openalex.org/W2021186990","https://openalex.org/W2247178600","https://openalex.org/W2111894258","https://openalex.org/W1480851625","https://openalex.org/W116055073","https://openalex.org/W2951237229","https://openalex.org/W2963183893","https://openalex.org/W2396247630","https://openalex.org/W574270000","https://openalex.org/W2256886023","https://openalex.org/W2096086749"],"abstract_inverted_index":{"We":[0,61],"study":[1],"the":[2,12,30,42,46,56,59,68,93,99],"numerical":[3],"approximation":[4],"of":[5,24,29,55,58,75,90,96,98],"integrals":[6],"over":[7],"${R}^s$":[8,76],"with":[9],"respect":[10],"to":[11,71],"standard":[13],"Gaussian":[14],"measure":[15],"for":[16],"integrands":[17],"which":[18,40],"lie":[19],"in":[20],"certain":[21],"Hermite":[22],"spaces":[23],"functions.":[25],"The":[26],"decay":[27],"rate":[28,95],"associated":[31],"sequence":[32],"is":[33],"specified":[34],"by":[35],"a":[36,72,78],"single":[37],"integer":[38],"parameter":[39],"determines":[41],"smoothness":[43],"classes":[44],"and":[45,81],"inner":[47],"product":[48],"can":[49],"be":[50],"expressed":[51],"via":[52,77],"$L_2$":[53],"norms":[54],"derivatives":[57],"function.":[60],"map":[62],"higher":[63],"order":[64],"digital":[65],"nets":[66],"from":[67,88],"unit":[69],"cube":[70],"suitable":[73],"subcube":[74],"linear":[79],"transformation":[80],"show":[82],"that":[83],"such":[84],"rules":[85],"achieve,":[86],"apart":[87],"powers":[89],"$\\log":[91],"N$,":[92],"optimal":[94],"convergence":[97],"integration":[100],"error.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}