{"id":"https://openalex.org/W2069178210","doi":"https://doi.org/10.1090/s0025-5718-00-01231-x","title":"Fast convergence of quasi-Monte Carlo for a class of isotropic integrals","display_name":"Fast convergence of quasi-Monte Carlo for a class of isotropic integrals","publication_year":2000,"publication_date":"2000-02-23","ids":{"openalex":"https://openalex.org/W2069178210","doi":"https://doi.org/10.1090/s0025-5718-00-01231-x","mag":"2069178210"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01231-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01231-x","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.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/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004068464","display_name":"Anargyros Papageorgiou","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Papageorgiou","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, NY 10027","Department of Computer Science; Columbia University; New York NY 10027"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, NY 10027","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Department of Computer Science; Columbia University; New York NY 10027","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004068464"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":3.6928,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93854352,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"70","issue":"233","first_page":"297","last_page":"306"},"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":0.97079998254776,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9520999789237976,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7082098126411438},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4227392077445984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3890928328037262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3720189332962036}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7082098126411438},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4227392077445984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3890928328037262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3720189332962036}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-00-01231-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01231-x","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.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:10.1.1.207.2701","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.2701","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/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.2888","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.2888","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.columbia.edu/~ap/html/QMCIsotr.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.98.8918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.8918","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/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01231-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01231-x","pdf_url":"https://www.ams.org/mcom/2001-70-233/S0025-5718-00-01231-X/S0025-5718-00-01231-X.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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069178210.pdf","grobid_xml":"https://content.openalex.org/works/W2069178210.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W645185567","https://openalex.org/W1564001778","https://openalex.org/W1579063588","https://openalex.org/W1981743146","https://openalex.org/W1998213879","https://openalex.org/W2001322270","https://openalex.org/W2009741189","https://openalex.org/W2030307575","https://openalex.org/W2034638017","https://openalex.org/W2043419861","https://openalex.org/W2046645122","https://openalex.org/W2065195078","https://openalex.org/W2106149169","https://openalex.org/W2146261346","https://openalex.org/W2163417850","https://openalex.org/W2476762106","https://openalex.org/W3135037104","https://openalex.org/W3143261911","https://openalex.org/W4206021986","https://openalex.org/W4212933304","https://openalex.org/W4300580367","https://openalex.org/W6634846813"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W1974891317","https://openalex.org/W2007980826","https://openalex.org/W3107474891","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506"],"abstract_inverted_index":{"We":[0,24,45],"consider":[1],"the":[2,48,55,112,164,179],"approximation":[3,56],"of":[4,20,51,57,159,166,172,227],"<inline-formula":[5,31,61,116,183],"content-type=\"math/mathml\">":[6,32,62,117,184],"<mml:math":[7,33,63,118,185],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8,34,64,119,186],"alttext=\"d\">":[9,35],"<mml:semantics>":[10,36,75,131,198],"<mml:mi>d</mml:mi>":[11,37,205],"<mml:annotation":[12,38,95,154,219],"encoding=\"application/x-tex\">d</mml:annotation>":[13,39],"</mml:semantics>":[14,40,99,156,223],"</mml:math>":[15,41,100,157,224],"</inline-formula>":[16,42,101,158,225],"-dimensional":[17],"weighted":[18],"integrals":[19,59],"certain":[21],"isotropic":[22],"functions.":[23],"are":[25],"mainly":[26],"interested":[27],"in":[28],"cases":[29],"where":[30],"is":[43,60,105,175],"large.":[44],"show":[46],"that":[47],"convergence":[49,114],"rate":[50,115],"quasi-Monte":[52,167,228],"Carlo":[53,168],"for":[54,169],"these":[58],"alttext=\"upper":[65,120,187],"O":[66,121,188],"left-parenthesis":[67,122,189],"StartRoot":[68],"log":[69,190],"n":[70,73,123,194,196],"EndRoot":[71],"slash":[72,127,195],"right-parenthesis\">":[74,130,197],"<mml:mrow>":[76,132,199],"<mml:mi>O</mml:mi>":[77,133,200],"<mml:mo":[78,92,134,151,201,216],"stretchy=\"false\">(</mml:mo>":[79,135,202],"<mml:msqrt>":[80],"<mml:mi>log</mml:mi>":[81,204],"<mml:mo>":[82,140,207],"\u2061":[83,208],"</mml:mo>":[84,142,209],"<mml:mi>n</mml:mi>":[85,91,137,210,215],"</mml:msqrt>":[86],"<mml:mrow":[87,138,144,211],"class=\"MJX-TeXAtom-ORD\">":[88,139,145,212],"<mml:mo>/</mml:mo>":[89,146,213],"</mml:mrow>":[90,94,147,149,153,214,218],"stretchy=\"false\">)</mml:mo>":[93,152,217],"encoding=\"application/x-tex\">O(\\sqrt":[96],"{\\log":[97],"n}/n)</mml:annotation>":[98],".":[102],"Since":[103],"this":[104,170],"a":[106],"worst":[107,180],"case":[108,181],"result,":[109],"compared":[110],"to":[111],"expected":[113],"Superscript":[124,191],"negative":[125],"1":[126],"2":[128],"Baseline":[129,193],"<mml:msup>":[136,203],"\u2212":[141],"<mml:mn>1</mml:mn>":[143],"<mml:mn>2</mml:mn>":[148],"</mml:msup>":[150,206],"encoding=\"application/x-tex\">O(n^{-1/2})</mml:annotation>":[155],"Monte":[160],"Carlo,":[161],"it":[162],"shows":[163],"superiority":[165],"type":[171],"integral.":[173],"This":[174],"much":[176],"faster":[177],"than":[178],"convergence,":[182],"d":[192],"encoding=\"application/x-tex\">O(\\log":[220],"^d":[221],"n/n)</mml:annotation>":[222],",":[226],"Carlo.":[229]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}