{"id":"https://openalex.org/W2021578090","doi":"https://doi.org/10.1090/s0025-5718-01-01377-1","title":"The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension","display_name":"The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension","publication_year":2001,"publication_date":"2001-08-02","ids":{"openalex":"https://openalex.org/W2021578090","doi":"https://doi.org/10.1090/s0025-5718-01-01377-1","mag":"2021578090"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01377-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01377-1","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Fred Hickernell","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033309103","display_name":"Xiaoqun Wang","orcid":"https://orcid.org/0000-0002-5438-9635"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqun Wang","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University - Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049806335"],"corresponding_institution_ids":["https://openalex.org/I141568987"],"apc_list":null,"apc_paid":null,"fwci":5.3314,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.95586726,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"71","issue":"240","first_page":"1641","last_page":"1661"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9767000079154968,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9280999898910522,"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":0.8322943449020386},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6003993153572083},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5704806447029114},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5637398958206177},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5142190456390381},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4889603853225708},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4815978705883026},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.47312110662460327},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4469534158706665},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.4461452066898346},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.444757878780365},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4234324097633362},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4120178818702698},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4033529460430145},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35918962955474854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3314914107322693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23349925875663757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21802857518196106},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.13688376545906067}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8322943449020386},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6003993153572083},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5704806447029114},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5637398958206177},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5142190456390381},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4889603853225708},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4815978705883026},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.47312110662460327},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4469534158706665},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.4461452066898346},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.444757878780365},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4234324097633362},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4120178818702698},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4033529460430145},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35918962955474854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3314914107322693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23349925875663757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21802857518196106},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.13688376545906067},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-01-01377-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01377-1","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3767","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.2244","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.2244","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://math.hkbu.edu.hk/pub/techreport/math273.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.97.5905","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.97.5905","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01377-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01377-1","pdf_url":"https://www.ams.org/mcom/2002-71-240/S0025-5718-01-01377-1/S0025-5718-01-01377-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021578090.pdf","grobid_xml":"https://content.openalex.org/works/W2021578090.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W39759813","https://openalex.org/W87334110","https://openalex.org/W91227773","https://openalex.org/W152683667","https://openalex.org/W225736130","https://openalex.org/W1563229119","https://openalex.org/W1579063588","https://openalex.org/W1590281894","https://openalex.org/W1976544585","https://openalex.org/W1981743146","https://openalex.org/W1984812257","https://openalex.org/W1986280275","https://openalex.org/W2017001763","https://openalex.org/W2040396531","https://openalex.org/W2043419861","https://openalex.org/W2054312661","https://openalex.org/W2073732659","https://openalex.org/W2079884250","https://openalex.org/W2098269688","https://openalex.org/W2098612888","https://openalex.org/W2106149169","https://openalex.org/W2146766088","https://openalex.org/W2151582349","https://openalex.org/W2259546388","https://openalex.org/W2314359380","https://openalex.org/W2320585129","https://openalex.org/W2331011396","https://openalex.org/W2767905780","https://openalex.org/W4254884888","https://openalex.org/W4299112371","https://openalex.org/W4300580367"],"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/W1982234448","https://openalex.org/W2560252838","https://openalex.org/W2024733137","https://openalex.org/W3158760621","https://openalex.org/W2358506996"],"abstract_inverted_index":{"Dimensionally":[0],"unbounded":[1],"problems":[2,20,24],"are":[3],"frequently":[4],"encountered":[5],"in":[6,10,15,22,44,281],"practice,":[7],"such":[8],"as":[9,79,249],"simulations":[11],"of":[12,25,38,40,48,63,83,86,93,98,102,117,133,245,253,318,333,362],"stochastic":[13],"processes,":[14],"particle":[16],"and":[17,21,123,211,328],"light":[18],"transport":[19],"the":[23,46,80,115,120,124,130,139,250,293,326,334,342,346],"mathematical":[26],"finance.":[27],"This":[28],"paper":[29],"considers":[30],"quasi-Monte":[31],"Carlo":[32,290],"integration":[33,141,371],"algorithms":[34],"for":[35,196,314,329],"weighted":[36,316],"classes":[37,317],"functions":[39,49,92],"infinitely":[41],"many":[42],"variables,":[43],"which":[45,113,366],"dependence":[47,57],"on":[50,325],"successive":[51],"variables":[52],"is":[53,58,105,114,160,247,285,309,338,364,372],"increasingly":[54],"limited.":[55],"The":[56,65,100,229],"modeled":[59],"by":[60,143,162,287],"a":[61,84,95,109,144,321,330],"sequence":[62,344],"weights.":[64],"integrands":[66],"belong":[67],"to":[68,107,137],"rather":[69],"general":[70],"reproducing":[71,103,335],"kernel":[72,336],"Hilbert":[73],"spaces":[74],"that":[75,129,292,345,368],"can":[76],"be":[77],"decomposed":[78],"direct":[81],"sum":[82],"series":[85],"their":[87],"subspaces,":[88],"each":[89],"subspace":[90],"containing":[91],"only":[94],"finite":[96],"number":[97,132],"variables.":[99],"theory":[101],"kernels":[104],"used":[106],"derive":[108],"quadrature":[110,291],"error":[111,142],"bound,":[112],"product":[116],"two":[118],"terms:":[119],"generalized":[121,125],"discrepancy":[122],"variation.":[126],"Tractability":[127],"means":[128],"minimal":[131],"function":[134],"evaluations":[135],"needed":[136],"reduce":[138],"initial":[140],"factor":[145],"<inline-formula":[146,163,199,215,230,254,294,347],"content-type=\"math/mathml\">":[147,164,200,216,231,255,295,348],"<mml:math":[148,165,201,217,232,256,296,349],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[149,166,202,218,233,257,297,350],"alttext=\"epsilon\">":[150,234,298,351],"<mml:semantics>":[151,173,204,221,235,262,299,352],"<mml:mi>":[152,177,236,264,300,353],"\u03b5":[153,178,237,265,301,354],"</mml:mi>":[154,179,238,266,302,355],"<mml:annotation":[155,189,206,223,239,275,303,356],"encoding=\"application/x-tex\">\\varepsilon</mml:annotation>":[156,240,304,357],"</mml:semantics>":[157,193,208,225,241,278,305,358],"</mml:math>":[158,194,209,226,242,279,306,359],"</inline-formula>":[159,195,210,227,243,280,307,360],"bounded":[161],"alttext=\"upper":[167,219],"C":[168],"epsilon":[169],"Superscript":[170,259],"negative":[171,260],"p\">":[172],"<mml:mrow>":[174],"<mml:mi>C</mml:mi>":[175,222],"<mml:msup>":[176,263],"<mml:mrow":[180,267],"class=\"MJX-TeXAtom-ORD\">":[181,268],"<mml:mo>":[182,269],"\u2212":[183,270],"</mml:mo>":[184,271],"<mml:mi>p</mml:mi>":[185,205],"</mml:mrow>":[186,188,273],"</mml:msup>":[187,274],"encoding=\"application/x-tex\">C":[190],"\\varepsilon":[191],"^{-p}</mml:annotation>":[192],"some":[197,212],"exponent":[198],"alttext=\"p\">":[203],"encoding=\"application/x-tex\">p</mml:annotation>":[207],"positive":[213],"constant":[214],"C\">":[220],"encoding=\"application/x-tex\">C</mml:annotation>":[224],".":[228],"-exponent":[244,308,361],"tractability":[246,363],"defined":[248],"smallest":[251],"power":[252],"alttext=\"epsilon":[258],"1\">":[261],"<mml:mn>1</mml:mn>":[272],"encoding=\"application/x-tex\">\\varepsilon":[276],"^{-1}</mml:annotation>":[277],"these":[282,315],"bounds.":[283],"It":[284],"shown":[286,339],"using":[288,341],"Monte":[289],"no":[310,373],"greater":[311],"than":[312,375],"2":[313],"integrands.":[319],"Under":[320],"somewhat":[322],"stronger":[323],"assumption":[324],"weights":[327],"popular":[331],"choice":[332],"it":[337],"constructively":[340],"Halton":[343],"1,":[365],"implies":[367],"infinite":[369],"dimensional":[370],"harder":[374],"one-dimensional":[376],"integration.":[377]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}