{"id":"https://openalex.org/W2808579259","doi":"https://doi.org/10.1137/18m1221138","title":"A Numerical Method for Oscillatory Integrals with Coalescing Saddle Points","display_name":"A Numerical Method for Oscillatory Integrals with Coalescing Saddle Points","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2808579259","doi":"https://doi.org/10.1137/18m1221138","mag":"2808579259"},"language":"en","primary_location":{"id":"doi:10.1137/18m1221138","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1221138","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.06549","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":true,"raw_author_name":"Daan Huybrechs","raw_affiliation_strings":["Katholieke Universiteit Leuven"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044081911","display_name":"Arno B. J. Kuijlaars","orcid":"https://orcid.org/0000-0001-6835-0945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arno Kuijlaars","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056140184","display_name":"Nele Lejon","orcid":null},"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":"Nele Lejon","raw_affiliation_strings":["Katholieke Universiteit Leuven"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022994939"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.3324,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.47204506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"57","issue":"6","first_page":"2707","last_page":"2729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9951000213623047,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8409335613250732},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.6401517987251282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6368464231491089},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6070709228515625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5511882901191711},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5459917187690735},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5443236231803894},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4786604344844818},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.22105085849761963},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19450107216835022},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1730310022830963},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.14559268951416016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1101456880569458}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8409335613250732},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.6401517987251282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6368464231491089},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6070709228515625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5511882901191711},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5459917187690735},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5443236231803894},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4786604344844818},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.22105085849761963},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19450107216835022},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1730310022830963},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.14559268951416016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1101456880569458},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/18m1221138","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1221138","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:1806.06549","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.06549","pdf_url":"https://arxiv.org/pdf/1806.06549","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},{"id":"mag:2808579259","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.06549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/626596","is_oa":true,"landing_page_url":"http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW685.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. TW685","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/643883","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/643883/2/lejon2019cubic.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Siam Journal On Numerical Analysis, vol. 57 (6), Art.No. 6, (2707-2729)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1806.06549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.06549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.06549","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.06549","pdf_url":"https://arxiv.org/pdf/1806.06549","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"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/W2808579259.pdf","grobid_xml":"https://content.openalex.org/works/W2808579259.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W590791627","https://openalex.org/W1532438862","https://openalex.org/W1541633373","https://openalex.org/W1549451790","https://openalex.org/W1593505867","https://openalex.org/W1599623497","https://openalex.org/W1860794187","https://openalex.org/W1963586124","https://openalex.org/W1975416173","https://openalex.org/W1990037199","https://openalex.org/W2013194938","https://openalex.org/W2013381930","https://openalex.org/W2020328455","https://openalex.org/W2026614141","https://openalex.org/W2032425536","https://openalex.org/W2044380739","https://openalex.org/W2044745523","https://openalex.org/W2047274778","https://openalex.org/W2057817591","https://openalex.org/W2062938539","https://openalex.org/W2081814612","https://openalex.org/W2087575936","https://openalex.org/W2090733519","https://openalex.org/W2102591969","https://openalex.org/W2105757357","https://openalex.org/W2147983461","https://openalex.org/W2169806412","https://openalex.org/W2237454605","https://openalex.org/W2322932418","https://openalex.org/W2333132544","https://openalex.org/W2505040439","https://openalex.org/W2520754780","https://openalex.org/W2610857016","https://openalex.org/W2775906316","https://openalex.org/W3098428870","https://openalex.org/W3124193524"],"related_works":["https://openalex.org/W3145711066","https://openalex.org/W2948584902","https://openalex.org/W2595830453","https://openalex.org/W2088052391","https://openalex.org/W1964731411","https://openalex.org/W3173893198","https://openalex.org/W3016864069","https://openalex.org/W1893234143","https://openalex.org/W1994237606","https://openalex.org/W2013922716","https://openalex.org/W2070506509","https://openalex.org/W3102786515","https://openalex.org/W2076657383","https://openalex.org/W3126208451","https://openalex.org/W2944307608","https://openalex.org/W2950859730","https://openalex.org/W2140091078","https://openalex.org/W2013320272","https://openalex.org/W2626897650","https://openalex.org/W1987706000"],"abstract_inverted_index":{"The":[0],"value":[1],"of":[2,14,21,28,40,43,46,95,148],"a":[3,18,79],"highly":[4,57],"oscillatory":[5,58,149],"integral":[6],"is":[7,51],"typically":[8],"determined":[9],"asymptotically":[10],"by":[11],"the":[12,15,26,29,33,41,44,47,49,70,96,124,146],"behavior":[13],"integrand":[16,50],"near":[17],"small":[19],"number":[20],"critical":[22],"points.":[23,154],"These":[24,116],"include":[25],"endpoints":[27],"integration":[30],"domain":[31],"and":[32,137,141],"so-called":[34],"stationary":[35],"points":[36,67,77,114],"or":[37],"saddle":[38,66,76,113,153],"points---roots":[39],"derivative":[42],"phase":[45],"integrand---where":[48],"locally":[52],"nonoscillatory.":[53],"Modern":[54],"methods":[55],"for":[56,134,145],"quadrature":[59,105],"exhibit":[60],"numerical":[61,143],"issues":[62],"when":[63,111],"two":[64,112],"such":[65],"coalesce.":[68,115],"On":[69],"other":[71],"hand,":[72],"integrals":[73,150],"with":[74,151],"coalescing":[75,152],"are":[78,118],"classical":[80],"topic":[81],"in":[82,93,123],"asymptotic":[83,91],"analysis,":[84],"where":[85],"they":[86],"give":[87],"rise":[88],"to":[89],"uniform":[90],"expansions":[92],"terms":[94],"Airy":[97],"function.":[98],"In":[99],"this":[100],"paper":[101],"we":[102],"construct":[103],"Gaussian":[104],"rules":[106,117],"that":[107],"remain":[108],"uniformly":[109],"accurate":[110,140],"based":[119],"on":[120],"orthogonal":[121],"polynomials":[122],"complex":[125],"plane.":[126],"We":[127],"analyze":[128],"these":[129],"polynomials,":[130],"prove":[131],"their":[132],"existence":[133],"even":[135],"degrees,":[136],"describe":[138],"an":[139],"efficient":[142],"scheme":[144],"evaluation":[147]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}