{"id":"https://openalex.org/W2098556820","doi":"https://doi.org/10.1090/s0025-5718-07-01937-0","title":"The Construction of cubature rules for multivariate highly oscillatory integrals","display_name":"The Construction of cubature rules for multivariate highly oscillatory integrals","publication_year":2007,"publication_date":"2007-04-27","ids":{"openalex":"https://openalex.org/W2098556820","doi":"https://doi.org/10.1090/s0025-5718-07-01937-0","mag":"2098556820"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-01937-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01937-0","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01937-0/S0025-5718-07-01937-0.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/2007-76-260/S0025-5718-07-01937-0/S0025-5718-07-01937-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022994939","display_name":"Daan Huybrechs","orcid":"https://orcid.org/0000-0002-0536-2647"},"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":"Daan Huybrechs","raw_affiliation_strings":["Scientific Computing, Department of Computer Science, K.U.Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Computing, Department of Computer Science, K.U.Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"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":"Stefan Vandewalle","raw_affiliation_strings":["Scientific Computing, Department of Computer Science, K.U.Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Computing, Department of Computer Science, K.U.Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":6.7566,"has_fulltext":true,"cited_by_count":54,"citation_normalized_percentile":{"value":0.9756515,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"76","issue":"260","first_page":"1955","last_page":"1980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987999796867371,"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":0.9979000091552734,"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/T10514","display_name":"Numerical methods in engineering","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.8437784910202026},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7244564294815063},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6705968976020813},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5242393612861633},{"id":"https://openalex.org/keywords/order-of-integration","display_name":"Order of integration (calculus)","score":0.5093659162521362},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.47709164023399353},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46445512771606445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4438718557357788},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.4128459095954895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38913682103157043},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08208075165748596},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06704598665237427}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8437784910202026},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7244564294815063},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6705968976020813},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5242393612861633},{"id":"https://openalex.org/C38582570","wikidata":"https://www.wikidata.org/wiki/Q3825182","display_name":"Order of integration (calculus)","level":2,"score":0.5093659162521362},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.47709164023399353},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46445512771606445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4438718557357788},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.4128459095954895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38913682103157043},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08208075165748596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06704598665237427},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/s0025-5718-07-01937-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01937-0","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01937-0/S0025-5718-07-01937-0.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:lirias2repo.kuleuven.be:123456789/146651","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/146651","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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. 76 (260), Art.No. 260, (1955-1980)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.3360","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.3360","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/2007-76-260/S0025-5718-07-01937-0/S0025-5718-07-01937-0.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.724.4215","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.724.4215","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.kuleuven.be/%7Edaan.huybrechs/research/mathcomp2007cubature.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.724.6009","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.724.6009","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.kuleuven.be/%7Edaan.huybrechs/research/TW442.pdf","raw_type":"text"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/131695","is_oa":true,"landing_page_url":"http://www.cs.kuleuven.ac.be/publicaties/rapporten/tw/TW442.abs.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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. TW442, (26-26)","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-01937-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01937-0","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01937-0/S0025-5718-07-01937-0.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":[{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2098556820.pdf","grobid_xml":"https://content.openalex.org/works/W2098556820.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1549451790","https://openalex.org/W1584610719","https://openalex.org/W1593505867","https://openalex.org/W1966478028","https://openalex.org/W1981373189","https://openalex.org/W2019984076","https://openalex.org/W2023413246","https://openalex.org/W2044380739","https://openalex.org/W2047274778","https://openalex.org/W2069130437","https://openalex.org/W2073732659","https://openalex.org/W2081814612","https://openalex.org/W2087350936","https://openalex.org/W2143341849","https://openalex.org/W2147983461","https://openalex.org/W2170706425","https://openalex.org/W2314359380","https://openalex.org/W2463002925"],"related_works":["https://openalex.org/W4233593527","https://openalex.org/W4236312217","https://openalex.org/W2042828208","https://openalex.org/W2612980214","https://openalex.org/W4230841224","https://openalex.org/W2124504556","https://openalex.org/W3080337404","https://openalex.org/W3004989866","https://openalex.org/W2226534957","https://openalex.org/W1981203195"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"efficient":[3],"approach":[4],"to":[5,42,47],"evaluate":[6],"multivariate":[7],"highly":[8],"oscillatory":[9],"integrals":[10,91],"on":[11,92,96,105],"piecewise":[12],"analytic":[13],"integration":[14],"domains.":[15],"Cubature":[16],"rules":[17,60],"are":[18,86],"developed":[19],"that":[20],"only":[21],"require":[22],"the":[23,26,49,52,58,66,72,82,97],"evaluation":[24],"of":[25,35,51,57,65,81],"integrand":[27],"and":[28,46,95,100],"its":[29],"derivatives":[30,80],"in":[31],"a":[32,69,93,106],"limited":[33],"set":[34],"points.":[36],"A":[37],"general":[38,103],"method":[39],"is":[40],"presented":[41],"identify":[43],"these":[44],"points":[45],"compute":[48],"weights":[50],"corresponding":[53],"rule.":[54],"The":[55,84],"accuracy":[56,73],"constructed":[59],"increases":[61],"with":[62],"increasing":[63],"frequency":[64],"integrand.":[67,83],"For":[68],"fixed":[70],"frequency,":[71],"can":[74],"be":[75],"improved":[76],"by":[77],"incorporating":[78],"more":[79,102],"results":[85],"illustrated":[87],"numerically":[88],"for":[89,101],"Fourier":[90],"circle":[94],"unit":[98],"ball,":[99],"oscillators":[104],"rectangular":[107],"domain.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
