{"id":"https://openalex.org/W2734717932","doi":"https://doi.org/10.1137/17m1138601","title":"Richardson Extrapolation of Polynomial Lattice Rules","display_name":"Richardson Extrapolation of Polynomial Lattice Rules","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2734717932","doi":"https://doi.org/10.1137/17m1138601","mag":"2734717932"},"language":"en","primary_location":{"id":"doi:10.1137/17m1138601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138601","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.03989","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":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078138886","display_name":"Takashi Goda","orcid":"https://orcid.org/0000-0001-6055-8055"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takashi Goda","raw_affiliation_strings":["Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006620820","display_name":"Takehito Yoshiki","orcid":"https://orcid.org/0000-0002-1136-6732"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takehito Yoshiki","raw_affiliation_strings":["Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8561, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8561, Japan","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0423,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84705569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"1","first_page":"44","last_page":"69"},"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":0.992900013923645,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9707000255584717,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8429639339447021},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6649060845375061},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6200540065765381},{"id":"https://openalex.org/keywords/unit-cube","display_name":"Unit cube","score":0.6184154748916626},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5560123324394226},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5228081941604614},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.49808406829833984},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48584410548210144},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.4371940493583679},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4298635721206665},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.37697136402130127},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37658554315567017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29069429636001587},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.08258706331253052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8429639339447021},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6649060845375061},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6200540065765381},{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.6184154748916626},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5560123324394226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5228081941604614},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.49808406829833984},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48584410548210144},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.4371940493583679},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4298635721206665},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.37697136402130127},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37658554315567017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29069429636001587},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.08258706331253052},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1138601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1138601","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:1707.03989","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1707.03989","pdf_url":"https://arxiv.org/pdf/1707.03989","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.03989","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1707.03989","pdf_url":"https://arxiv.org/pdf/1707.03989","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/G3260032310","display_name":"Construction of quasi-Monte Carlo rules achieving high-order convergence with applications","funder_award_id":"15K20964","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"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/G7018608808","display_name":"\u60c5\u5831\u793e\u4f1a\u306b\u304a\u3051\u308b\u6e96\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306b\u3088\u308b\u65b0\u305f\u306a\u5fdc\u7528","funder_award_id":"17J02651","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1472566082","https://openalex.org/W1504916371","https://openalex.org/W1630018803","https://openalex.org/W1978501336","https://openalex.org/W1980498334","https://openalex.org/W1981743146","https://openalex.org/W2010177608","https://openalex.org/W2014551121","https://openalex.org/W2014853427","https://openalex.org/W2038461951","https://openalex.org/W2042083287","https://openalex.org/W2045845634","https://openalex.org/W2111894258","https://openalex.org/W2132042164","https://openalex.org/W2152162686","https://openalex.org/W2191360394","https://openalex.org/W2266019243","https://openalex.org/W2952469530","https://openalex.org/W2963757024","https://openalex.org/W2964207585","https://openalex.org/W3098528625","https://openalex.org/W3125426943"],"related_works":["https://openalex.org/W2613329859","https://openalex.org/W2962723479","https://openalex.org/W2952962955","https://openalex.org/W4221144311","https://openalex.org/W1998105223","https://openalex.org/W2165477600","https://openalex.org/W2999151175","https://openalex.org/W4293692913","https://openalex.org/W2000121903","https://openalex.org/W2963354045"],"abstract_inverted_index":{"We":[0,24,95,179],"study":[1,181],"multivariate":[2],"numerical":[3],"integration":[4],"of":[5,45,58,69,76,82,86,99,110,112,156,174,184,195,224],"smooth":[6],"functions":[7],"in":[8,53,116,215],"weighted":[9],"Sobolev":[10,117],"spaces":[11,118],"with":[12,65,119],"dominating":[13],"mixed":[14],"smoothness":[15],"$\\alpha\\geq":[16],"2$":[17],"defined":[18],"over":[19,63],"the":[20,34,41,87,97,106,113,141,162,167,182,185,190,206,221],"$s$-dimensional":[21],"unit":[22],"cube.":[23],"propose":[25],"a":[26,80,146,227],"new":[27],"quasi-Monte":[28],"Carlo":[29],"(QMC)-based":[30],"quadrature":[31],"rule,":[32,38,171],"named":[33],"extrapolated":[35,101,133],"polynomial":[36,48,60,92,102,134,169,201],"lattice":[37,49,61,93,103,135,170,202],"which":[39,160,172],"achieves":[40],"almost":[42,107],"optimal":[43,108],"rate":[44,223],"convergence.":[46,225],"Extrapolated":[47],"rules":[50,62,104,136,203],"are":[51],"constructed":[52,139],"two":[54],"steps:":[55],"(i)":[56],"construction":[57,153],"classical":[59],"$\\Bbb{F}_b$":[64],"$\\alpha$":[66,83],"consecutive":[67,91],"sizes":[68],"nodes,":[70],"$b^{m-\\alpha+1},\\ldots,b^{m}$,":[71],"and":[72],"(ii)":[73],"recursive":[74],"application":[75],"Richardson":[77],"extrapolation":[78],"to":[79,125,199],"chain":[81],"approximate":[84],"values":[85],"integral":[88],"obtained":[89],"by":[90,123,140],"rules.":[94],"prove":[96],"existence":[98],"good":[100,132],"achieving":[105,220],"order":[109,157,175],"convergence":[111],"worst-case":[114,186],"error":[115,187],"general":[120],"weights.":[121],"Then,":[122],"restricting":[124],"product":[126],"weights,":[127],"we":[128],"show":[129],"that":[130,205],"such":[131],"can":[137,212],"be":[138,213],"fast":[142,207],"component-by-component":[143],"algorithm":[144],"under":[145],"computable":[147],"quality":[148],"criterion.":[149],"The":[150],"required":[151],"total":[152],"cost":[154],"is":[155,173,204],"$(s+\\alpha)N\\log":[158],"N$,":[159],"improves":[161],"currently":[163],"known":[164],"result":[165],"for":[166,235],"interlaced":[168,200],"$s\\alpha":[176],"N\\log":[177],"N$.":[178],"also":[180],"dependence":[183],"bound":[188],"on":[189],"dimension.":[191],"A":[192],"big":[193],"advantage":[194],"our":[196,239],"method":[197,211,228],"compared":[198],"QMC":[208],"matrix":[209],"vector":[210],"used":[214],"this":[216],"setting,":[217],"while":[218],"still":[219],"same":[222],"Such":[226],"was":[229],"previously":[230],"not":[231],"known.":[232],"Numerical":[233],"experiments":[234],"test":[236],"integrands":[237],"support":[238],"theoretical":[240],"result.":[241]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}