{"id":"https://openalex.org/W2036823075","doi":"https://doi.org/10.1137/040621776","title":"Strong Tractability of Quasi\u2010Monte Carlo Quadrature Using Nets for Certain Banach Spaces","display_name":"Strong Tractability of Quasi\u2010Monte Carlo Quadrature Using Nets for Certain Banach Spaces","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2036823075","doi":"https://doi.org/10.1137/040621776","mag":"2036823075"},"language":"en","primary_location":{"id":"doi:10.1137/040621776","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040621776","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/A5004998206","display_name":"Rong\u2010Xian Yue","orcid":"https://orcid.org/0000-0001-6899-4636"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rong\u2010Xian Yue","raw_affiliation_strings":["Shanghai Normal University"],"affiliations":[{"raw_affiliation_string":"Shanghai Normal University","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049806335","display_name":"Fred J. Hickernell","orcid":"https://orcid.org/0000-0001-6677-1324"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Fred J. Hickernell","raw_affiliation_strings":["Hong Kong Baptist University"],"affiliations":[{"raw_affiliation_string":"Hong Kong Baptist University","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004998206"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":null,"apc_paid":null,"fwci":0.4533,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6339035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"6","first_page":"2559","last_page":"2583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9609000086784363,"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/T12299","display_name":"Radiation Shielding Materials Analysis","score":0.9121999740600586,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8252478837966919},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7886221408843994},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7621966600418091},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6872752904891968},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5955364108085632},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5607694983482361},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.5295295119285583},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.45716962218284607},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4546549320220947},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36331790685653687},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3572922348976135},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28479257225990295},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1272875964641571},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.07080316543579102},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05106407403945923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252478837966919},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7886221408843994},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7621966600418091},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6872752904891968},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5955364108085632},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5607694983482361},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.5295295119285583},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.45716962218284607},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4546549320220947},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36331790685653687},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3572922348976135},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28479257225990295},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1272875964641571},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.07080316543579102},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05106407403945923},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040621776","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040621776","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W89288252","https://openalex.org/W152683667","https://openalex.org/W156963131","https://openalex.org/W1533955387","https://openalex.org/W1620981000","https://openalex.org/W1981743146","https://openalex.org/W1992727072","https://openalex.org/W2005221237","https://openalex.org/W2009741189","https://openalex.org/W2012922531","https://openalex.org/W2017001763","https://openalex.org/W2021578090","https://openalex.org/W2023711160","https://openalex.org/W2024626809","https://openalex.org/W2028393137","https://openalex.org/W2039119321","https://openalex.org/W2043419861","https://openalex.org/W2043466875","https://openalex.org/W2049874077","https://openalex.org/W2065960076","https://openalex.org/W2076350013","https://openalex.org/W2092549287","https://openalex.org/W2093205073","https://openalex.org/W2093213122","https://openalex.org/W2145169372","https://openalex.org/W2232448246","https://openalex.org/W2331011396","https://openalex.org/W4243972486"],"related_works":["https://openalex.org/W2035232447","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2144321310","https://openalex.org/W2001419904","https://openalex.org/W2060217354","https://openalex.org/W1982234448","https://openalex.org/W2560252838","https://openalex.org/W2024733137","https://openalex.org/W3158760621"],"abstract_inverted_index":{"We":[0],"consider":[1],"multivariate":[2,84],"integration":[3,29,85],"in":[4,15,59,75,89,108],"the":[5,19,50,53,64,67,90,100],"weighted":[6,20],"spaces":[7,102],"of":[8,103],"functions":[9],"with":[10],"mixed":[11],"first":[12],"derivatives":[13],"bounded":[14,33],"$L_p$":[16],"norms":[17],"and":[18,39,62,92,112],"coefficients":[21],"introduced":[22],"via":[23],"$\\ell_q$":[24],"norms,":[25],"where":[26],"$p,q\\in[1,\\infty]$.":[27],"The":[28,36],"domain":[30],"may":[31],"be":[32],"or":[34],"unbounded.":[35],"worst\u2010case":[37,51,91],"error":[38,41],"randomized":[40,65,93],"are":[42,80],"investigated":[43],"for":[44,63,99],"quasi\u2010Monte":[45],"Carlo":[46],"quadrature":[47,54,68],"rules.":[48],"For":[49],"setting":[52,66],"rule":[55,69],"uses":[56,70],"deterministic":[57],"$((T_u),s)$\u2010sequences":[58],"base":[60,76],"b,":[61],"randomly":[71],"scrambled":[72],"digital":[73],"$((T_u),m,s)$\u2010nets":[74],"b.":[77],"Sufficient":[78],"conditions":[79],"found":[81,116],"under":[82],"which":[83],"is":[86],"strongly":[87],"tractable":[88],"settings,":[94],"respectively.":[95],"Similar":[96],"results":[97],"hold":[98],"Banach":[101],"finite\u2010order":[104],"weights.":[105],"Results":[106],"presented":[107],"this":[109],"article":[110],"extend":[111],"improve":[113],"upon":[114],"those":[115],"previously.":[117]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
