{"id":"https://openalex.org/W1981674458","doi":"https://doi.org/10.1137/s0036142903425021","title":"On Korobov Lattice Rules in Weighted Spaces","display_name":"On Korobov Lattice Rules in Weighted Spaces","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1981674458","doi":"https://doi.org/10.1137/s0036142903425021","mag":"1981674458"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903425021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903425021","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/A5033309103","display_name":"Xiaoqun Wang","orcid":"https://orcid.org/0000-0002-5438-9635"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoqun Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075686837","display_name":"Ian H. Sloan","orcid":"https://orcid.org/0000-0003-3769-0538"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ian H. Sloan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004856556","display_name":"Josef Dick","orcid":"https://orcid.org/0000-0003-0142-6022"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9854,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.96363081,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"42","issue":"4","first_page":"1760","last_page":"1779"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9988999962806702,"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":0.9988999962806702,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9685999751091003,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9664999842643738,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8411546945571899},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6790396571159363},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38035833835601807},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3762081265449524}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8411546945571899},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6790396571159363},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38035833835601807},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3762081265449524},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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":1,"locations":[{"id":"doi:10.1137/s0036142903425021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903425021","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":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W39759813","https://openalex.org/W1511560458","https://openalex.org/W1543280314","https://openalex.org/W1590281894","https://openalex.org/W1976544585","https://openalex.org/W1981743146","https://openalex.org/W2004971474","https://openalex.org/W2005221237","https://openalex.org/W2011200438","https://openalex.org/W2021578090","https://openalex.org/W2031141876","https://openalex.org/W2032381682","https://openalex.org/W2040396531","https://openalex.org/W2059141990","https://openalex.org/W2075278791","https://openalex.org/W2079366547","https://openalex.org/W2084898049","https://openalex.org/W2086574596","https://openalex.org/W2092549287","https://openalex.org/W2126004257","https://openalex.org/W2146261346","https://openalex.org/W2190966787","https://openalex.org/W4235903219","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,17,22,33,40,64,69,90,98,106,110,116,119,132,136,143,146,171,179,188,203,207],"error":[4,48,76],"bounds":[5,49],"of":[6,16,78,109,126,134,142,145,158,170,190],"multivariate":[7],"integration":[8],"in":[9,20,54,199],"weighted":[10,55,111,155,208],"function":[11],"spaces":[12,157,209],"using":[13,161],"lattice":[14,52,72,147,166,176,194],"rules":[15,53,177,195],"Korobov":[18,51,56,71,112,165,175,193],"form,":[19],"which":[21,205],"generating":[23],"vector":[24],"for":[25,50,154,174,196],"an":[26,75],"n-point":[27],"rule":[28,73],"with":[29,89,131],"n":[30,122],"prime":[31,129],"has":[32,74],"form":[34],"(1,a,...,ad":[35],"-1":[36],")":[37],"(mod,n).":[38],"With":[39],"parameter":[41,108],"a":[42,124],"chosen":[43],"optimally,":[44],"we":[45,60],"establish":[46],"new":[47],"spaces.":[57,113],"In":[58],"particular,":[59],"prove":[61],"that":[62],"if":[63,202],"weights":[65,204],"decay":[66],"sufficiently":[67],"fast,":[68],"optimal":[70,164,192],"bound":[77],"order":[79],"O(n^{-\\alpha/2":[80],"+\\delta})$":[81],"(for":[82],"arbitrary":[83,127],"$\\delta":[84],"\\,{":[85,102],">":[86,103],"}\\,":[87],"0$),":[88],"implied":[91],"constant":[92],"depending":[93],"at":[94],"worst":[95],"polynomially":[96],"on":[97],"dimension.":[99],"Here":[100],"$\\alpha":[101],"}\\,1$":[104],"is":[105,123,152,183],"smoothness":[107],"We":[114],"generalize":[115],"construction":[117,137],"to":[118],"case":[120],"where":[121],"product":[125],"distinct":[128],"numbers,":[130],"purpose":[133],"reducing":[135],"cost":[138],"without":[139],"sacrificing":[140],"much":[141],"quality":[144],"rules.":[148,167],"A":[149,168],"corresponding":[150],"result":[151],"deduced":[153],"Sobolev":[156],"nonperiodic":[159],"functions,":[160],"randomly":[162],"shifted":[163],"comparison":[169],"worst-case":[172],"errors":[173],"and":[178],"recent":[180],"component-by-component":[181],"constructions":[182],"presented.":[184],"The":[185],"investigation":[186],"establishes":[187],"usefulness":[189],"(shifted)":[191],"integration,":[197],"even":[198],"high":[200],"dimensions,":[201],"characterize":[206],"are":[210],"suitably":[211],"chosen.":[212]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}