{"id":"https://openalex.org/W2042083287","doi":"https://doi.org/10.1090/s0025-5718-06-01785-6","title":"Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces","display_name":"Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces","publication_year":2006,"publication_date":"2006-01-04","ids":{"openalex":"https://openalex.org/W2042083287","doi":"https://doi.org/10.1090/s0025-5718-06-01785-6","mag":"2042083287"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01785-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01785-6","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-06-01785-6/S0025-5718-06-01785-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-06-01785-6/S0025-5718-06-01785-6.pdf","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":false,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium","Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan, 200A, B-3001 Heverlee, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan, 200A, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012279560","display_name":"Ronald Cools","orcid":"https://orcid.org/0000-0002-5567-5836"},"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":false,"raw_author_name":"Ronald Cools","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium","Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan, 200A, B-3001 Heverlee, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan, 200A, B-3001 Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.3215,"has_fulltext":true,"cited_by_count":257,"citation_normalized_percentile":{"value":0.99676214,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"75","issue":"254","first_page":"903","last_page":"920"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9994999766349792,"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":0.9994999766349792,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.7582012414932251},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4700644910335541},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.418204665184021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.347240686416626}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7582012414932251},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4700644910335541},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.418204665184021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.347240686416626}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01785-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01785-6","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-06-01785-6/S0025-5718-06-01785-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.100.4010","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.4010","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/2006-75-254/S0025-5718-06-01785-6/S0025-5718-06-01785-6.pdf","raw_type":"text"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/131930","is_oa":true,"landing_page_url":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW392.abs.html","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"TW Reports, Report No. TW392","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01785-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01785-6","pdf_url":"https://www.ams.org/mcom/2006-75-254/S0025-5718-06-01785-6/S0025-5718-06-01785-6.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2042083287.pdf","grobid_xml":"https://content.openalex.org/works/W2042083287.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W5439749","https://openalex.org/W1543280314","https://openalex.org/W1966904279","https://openalex.org/W1981745143","https://openalex.org/W1989439787","https://openalex.org/W2011200438","https://openalex.org/W2059141990","https://openalex.org/W2079366547","https://openalex.org/W2086574596","https://openalex.org/W2096070062","https://openalex.org/W2134572726","https://openalex.org/W2313299119","https://openalex.org/W2798909945","https://openalex.org/W2801179766","https://openalex.org/W6600221534"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0],"reformulate":[1],"the":[2,94,146,163,183,187],"original":[3,95,188],"component-by-component":[4],"algorithm":[5,96,180,192],"for":[6],"rank-":[7],"<inline-formula":[8,49,101,133,151],"content-type=\"math/mathml\">":[9,50,102,134,152],"<mml:math":[10,51,103,135,153],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,52,104,136,154],"alttext=\"1\">":[12],"<mml:semantics>":[13,63,112,138,156],"<mml:mn>1</mml:mn>":[14],"<mml:annotation":[15,82,125,140,158],"encoding=\"application/x-tex\">1</mml:annotation>":[16],"</mml:semantics>":[17,87,128,142,160],"</mml:math>":[18,88,129,143,161],"</inline-formula>":[19,89,130,144,162],"lattices":[20],"in":[21,91,203],"a":[22,37,43],"matrix-vector":[23],"notation":[24],"so":[25],"as":[26,186],"to":[27,36,171,174,197],"highlight":[28],"its":[29],"structural":[30],"properties.":[31],"For":[32],"function":[33],"spaces":[34],"similar":[35],"weighted":[38,204],"Korobov":[39],"space,":[40],"we":[41],"derive":[42],"technique":[44],"which":[45,97],"has":[46,98],"construction":[47,99],"cost":[48,100],"alttext=\"upper":[53,105],"O":[54,106],"left-parenthesis":[55,59,107],"s":[56,108],"n":[57,60,84,109],"log":[58],"right-parenthesis":[61],"right-parenthesis\">":[62,111],"<mml:mrow>":[64,113],"<mml:mi>O</mml:mi>":[65,114],"<mml:mo":[66,74,77,79,115,122],"stretchy=\"false\">(</mml:mo>":[67,75,116],"<mml:mi>s</mml:mi>":[68,117,139],"<mml:mi>n</mml:mi>":[69,76,119,157],"<mml:mi>log</mml:mi>":[70],"<mml:mo>":[71],"\u2061":[72],"</mml:mo>":[73],"stretchy=\"false\">)</mml:mo>":[78,80,123],"</mml:mrow>":[81,124],"encoding=\"application/x-tex\">O(s":[83,126],"\\log":[85],"(n))</mml:annotation>":[86],",":[90],"contrast":[92,170],"with":[93],"squared":[110],"<mml:msup>":[118],"<mml:mn>2</mml:mn>":[120],"</mml:msup>":[121],"n^2)</mml:annotation>":[127],".":[131],"Herein":[132],"alttext=\"s\">":[137],"encoding=\"application/x-tex\">s</mml:annotation>":[141],"is":[145],"number":[147,164],"of":[148,165],"dimensions":[149],"and":[150],"alttext=\"n\">":[155],"encoding=\"application/x-tex\">n</mml:annotation>":[159],"points":[166],"(taken":[167],"prime).":[168],"In":[169],"other":[172],"approaches":[173],"speed":[175],"up":[176],"construction,":[177],"our":[178],"fast":[179],"computes":[181],"exactly":[182],"same":[184],"quantity":[185],"algorithm.":[189],"The":[190],"presented":[191],"can":[193],"also":[194],"be":[195],"used":[196],"construct":[198],"randomly":[199],"shifted":[200],"lattice":[201],"rules":[202],"Sobolev":[205],"spaces.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":14}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}