{"id":"https://openalex.org/W4280647373","doi":"https://doi.org/10.1090/mcom/3754","title":"Scaled lattice rules for integration on \u211d^{\ud835\udd55} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces","display_name":"Scaled lattice rules for integration on \u211d^{\ud835\udd55} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces","publication_year":2022,"publication_date":"2022-05-11","ids":{"openalex":"https://openalex.org/W4280647373","doi":"https://doi.org/10.1090/mcom/3754"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/3754","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3754","pdf_url":null,"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":"green","oa_url":"https://lirias.kuleuven.be/handle/20.500.12942/713310","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045125806","display_name":"Dirk Nuyens","orcid":"https://orcid.org/0000-0002-4555-2314"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":["Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004676873","display_name":"Yuya Suzuki","orcid":"https://orcid.org/0000-0002-4988-8106"},"institutions":[{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Yuya Suzuki","raw_affiliation_strings":["Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg II, Alfred Getz\u00e2\u0080\u0099 vei 1, Gl\u00c3\u00b8shaugen, 7034 Trondheim, Norway","Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg II, Alfred Getz' vei 1, Gl\u00f8shaugen, 7034 Trondheim, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg II, Alfred Getz\u00e2\u0080\u0099 vei 1, Gl\u00c3\u00b8shaugen, 7034 Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, Sentralbygg II, Alfred Getz' vei 1, Gl\u00f8shaugen, 7034 Trondheim, Norway","institution_ids":["https://openalex.org/I204778367"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045125806"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":1.9217,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82978202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"92","issue":"339","first_page":"307","last_page":"347"},"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":0.9907000064849854,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.598032534122467},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3970974385738373},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3384208381175995}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.598032534122467},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3970974385738373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3384208381175995}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3754","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3754","pdf_url":null,"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:lirias2repo.kuleuven.be:20.500.12942/713310","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/713310","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Mathematics Of Computation, vol. 92 (339), (307-347)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/713310","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/713310","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Mathematics Of Computation, vol. 92 (339), (307-347)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6165159355","display_name":null,"funder_award_id":"G091920N","funder_id":"https://openalex.org/F4320311040","funder_display_name":"Norges Teknisk-Naturvitenskapelige Universitet"},{"id":"https://openalex.org/G8658790835","display_name":null,"funder_award_id":"81617985","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8958123436","display_name":null,"funder_award_id":"81617985","funder_id":"https://openalex.org/F4320311040","funder_display_name":"Norges Teknisk-Naturvitenskapelige Universitet"},{"id":"https://openalex.org/G955108010","display_name":null,"funder_award_id":"G091920N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320311040","display_name":"Norges Teknisk-Naturvitenskapelige Universitet","ror":"https://ror.org/05xg72x27"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W62263425","https://openalex.org/W415311214","https://openalex.org/W1630018803","https://openalex.org/W1820164671","https://openalex.org/W1976544585","https://openalex.org/W1978501336","https://openalex.org/W1981743146","https://openalex.org/W2033560593","https://openalex.org/W2035455944","https://openalex.org/W2072216330","https://openalex.org/W2079366547","https://openalex.org/W2080288600","https://openalex.org/W2092549287","https://openalex.org/W2109306509","https://openalex.org/W2138020995","https://openalex.org/W2144819966","https://openalex.org/W2392207747","https://openalex.org/W2472038253","https://openalex.org/W2513208677","https://openalex.org/W2620258316","https://openalex.org/W2772165262","https://openalex.org/W2963183893","https://openalex.org/W2963374275","https://openalex.org/W2963592159","https://openalex.org/W2964258076","https://openalex.org/W3089116201","https://openalex.org/W3123947097","https://openalex.org/W3124681825","https://openalex.org/W3176515582","https://openalex.org/W4241992531","https://openalex.org/W4253117982","https://openalex.org/W4300580367","https://openalex.org/W6676274655"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"We":[0,284,314,408],"introduce":[1],"a":[2,169,204,222,233,240,257,281,339],"new":[3,223,318],"method":[4,178,227,290,319,340],"to":[5,114,210,232,235,252,266,325],"approximate":[6],"integrals":[7],"<inline-formula":[8,85,119,156,188],"content-type=\"math/mathml\">":[9,86,120,157,189],"<mml:math":[10,87,121,158,190],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,88,122,159,191],"alttext=\"integral":[12],"Underscript":[13],"double-struck":[14],"upper":[15,124],"R":[16,125],"Superscript":[17,94,126],"d":[18,26],"Endscripts":[19],"f":[20],"left-parenthesis":[21],"bold-italic":[22,27],"x":[23],"right-parenthesis":[24],"normal":[25],"x\">":[28],"<mml:semantics>":[29,96,128,161,193],"<mml:mrow>":[30,97],"<mml:msub>":[31],"<mml:mo>":[32],"\u222b":[33],"</mml:mo>":[34],"<mml:mrow":[35,38,56,130],"class=\"MJX-TeXAtom-ORD\">":[36,39,57,131],"<mml:msup>":[37,103,129],"<mml:mi":[40,50,58,61,132],"mathvariant=\"double-struck\">R</mml:mi>":[41,133],"</mml:mrow>":[42,45,60,63,108,134],"<mml:mi>d</mml:mi>":[43,106,135],"</mml:msup>":[44,107,136],"</mml:msub>":[46],"<mml:mi>f</mml:mi>":[47,162,194],"<mml:mo":[48,52,98,104],"stretchy=\"false\">(</mml:mo>":[49],"mathvariant=\"bold-italic\">x</mml:mi>":[51,62],"stretchy=\"false\">)</mml:mo>":[53],"<mml:mspace":[54],"width=\"thinmathspace\"/>":[55],"mathvariant=\"normal\">d</mml:mi>":[59],"<mml:annotation":[64,109,137,163,195],"encoding=\"application/x-tex\">\\int":[65],"_{\\mathbb":[66],"{R}^d}":[67],"f(\\boldsymbol":[68],"{x})":[69],"\\,\\mathrm":[70],"{d}\\boldsymbol":[71],"{x}</mml:annotation>":[72],"</mml:semantics>":[73,111,140,165,197],"</mml:math>":[74,112,141,166,198],"</inline-formula>":[75,113,142,167,199],"which":[76,278,416],"simply":[77],"scales":[78],"lattice":[79,323,401],"rules":[80,324,402],"from":[81,212,256],"the":[82,150,153,185,208,217,226,248,273,287,345,350,357,366,372,378,385,391],"unit":[83,346],"cube":[84,347],"alttext=\"left-bracket":[89],"0":[90],"comma":[91],"1":[92],"right-bracket":[93],"d\">":[95,127],"stretchy=\"false\">[</mml:mo>":[99],"<mml:mn>0</mml:mn>":[100],"<mml:mo>,</mml:mo>":[101],"<mml:mn>1</mml:mn>":[102],"stretchy=\"false\">]</mml:mo>":[105],"encoding=\"application/x-tex\">[0,1]^d</mml:annotation>":[110],"properly":[115],"sized":[116],"boxes":[117,327,379],"on":[118,239,344,365,405],"alttext=\"double-struck":[123],"encoding=\"application/x-tex\">\\mathbb":[138],"{R}^d</mml:annotation>":[139],",":[143],"hereby":[144],"achieving":[145],"higher-order":[146,396],"convergence":[147,397],"that":[148,181,225,286,316],"matches":[149],"smoothness":[151,265],"of":[152,173,228,262,272,296,308,320,356],"integrand":[154,186,358],"function":[155,187,234],"alttext=\"f\">":[160,192],"encoding=\"application/x-tex\">f</mml:annotation>":[164,196],"in":[168,310,398],"certain":[170,373],"Sobolev":[171,260,270],"space":[172,261,271,368],"dominating":[174,263,275],"mixed":[175,264,276],"smoothness.":[176],"Our":[177],"only":[179,305],"assumes":[180],"we":[182,220,279,304,369,382],"can":[183,328,370,383],"evaluate":[184],"and":[200,301,394],"does":[201],"not":[202,293,342],"assume":[203],"particular":[205],"density":[206],"nor":[207],"ability":[209],"sample":[211],"it.":[213],"In":[214],"particular,":[215],"for":[216,363,403],"theoretical":[218,312,411],"analysis":[219,412],"show":[221,315,395],"result":[224],"adding":[229],"Bernoulli":[230,288],"polynomials":[231],"make":[236,306],"it":[237,309],"\u201cperiodic\u201d":[238],"box":[241,249],"without":[242],"changing":[243],"its":[244,297],"integral":[245],"value":[246],"over":[247],"is":[250,291],"equivalent":[251],"an":[253,267],"orthogonal":[254,332],"projection":[255,336,392],"well":[258,389],"chosen":[259],"associated":[268],"periodic":[269],"same":[274],"smoothness,":[277],"call":[280],"Korobov":[282],"space.":[283,407],"note":[285],"polynomial":[289],"often":[292],"used":[294],"because":[295],"excessive":[298],"computational":[299],"complexity":[300],"also":[302],"here":[303],"use":[307,371],"our":[311,317,410,418],"analysis.":[313],"applying":[321,399],"scaled":[322,400],"increasing":[326],"be":[329,360],"interpreted":[330],"as":[331,388,390],"projections":[333],"with":[334],"decreasing":[335],"error.":[337],"Such":[338],"would":[341,359],"work":[343],"since":[348],"then":[349],"committed":[351],"error":[352,387,393],"caused":[353],"by":[354,413],"non-periodicity":[355],"constant,":[361],"but":[362],"integration":[364,404],"Euclidean":[367,406],"decay":[374],"towards":[375],"zero":[376],"when":[377],"grow.":[380],"Hence":[381],"bound":[384],"truncation":[386],"illustrate":[409],"numerical":[414],"experiments":[415],"confirm":[417],"findings.":[419]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2022-05-22T00:00:00"}