{"id":"https://openalex.org/W1997947089","doi":"https://doi.org/10.1145/9327.9332","title":"An automatic adaptive integration routine in APL","display_name":"An automatic adaptive integration routine in APL","publication_year":1986,"publication_date":"1986-12-01","ids":{"openalex":"https://openalex.org/W1997947089","doi":"https://doi.org/10.1145/9327.9332","mag":"1997947089"},"language":"en","primary_location":{"id":"doi:10.1145/9327.9332","is_oa":true,"landing_page_url":"https://doi.org/10.1145/9327.9332","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/9327.9332","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/9327.9332","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084055139","display_name":"F W Zwan","orcid":null},"institutions":[{"id":"https://openalex.org/I156317336","display_name":"FMC (United States)","ror":"https://ror.org/01h95gp06","country_code":"US","type":"company","lineage":["https://openalex.org/I156317336"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F W Zwan","raw_affiliation_strings":["FMC Corporation, 200 E. Randolph Drive, Chicago, IL"],"affiliations":[{"raw_affiliation_string":"FMC Corporation, 200 E. Randolph Drive, Chicago, IL","institution_ids":["https://openalex.org/I156317336"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084055139"],"corresponding_institution_ids":["https://openalex.org/I156317336"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11470303,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"2","first_page":"21","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T13999","display_name":"Digital Rights Management and Security","score":0.9502999782562256,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/citation","display_name":"Citation","score":0.8003472089767456},{"id":"https://openalex.org/keywords/corporation","display_name":"Corporation","score":0.7132256627082825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5641118288040161},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.478588342666626},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.17665383219718933},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.062235891819000244}],"concepts":[{"id":"https://openalex.org/C2778805511","wikidata":"https://www.wikidata.org/wiki/Q1713","display_name":"Citation","level":2,"score":0.8003472089767456},{"id":"https://openalex.org/C2778348171","wikidata":"https://www.wikidata.org/wiki/Q167037","display_name":"Corporation","level":2,"score":0.7132256627082825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5641118288040161},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.478588342666626},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.17665383219718933},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.062235891819000244}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/9327.9332","is_oa":true,"landing_page_url":"https://doi.org/10.1145/9327.9332","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/9327.9332","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/9327.9332","is_oa":true,"landing_page_url":"https://doi.org/10.1145/9327.9332","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/9327.9332","source":{"id":"https://openalex.org/S4210186172","display_name":"ACM SIGAPL APL Quote Quad","issn_l":"0163-6006","issn":["0163-6006","1558-3392"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGAPL APL Quote Quad","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997947089.pdf","grobid_xml":"https://content.openalex.org/works/W1997947089.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1978805351","https://openalex.org/W1982102936","https://openalex.org/W1986632437","https://openalex.org/W2004345491","https://openalex.org/W2166384105"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2347674884","https://openalex.org/W1995891224","https://openalex.org/W4362520165","https://openalex.org/W2347523850","https://openalex.org/W2376288354","https://openalex.org/W2387973599","https://openalex.org/W2377378201","https://openalex.org/W2392209542"],"abstract_inverted_index":{"In":[0],"many":[1],"scientific":[2],"and":[3,23,70,124,144,148],"engineering":[4],"problems":[5],"the":[6,20,62,81,86,105,112,115,130,141,155],"calculation":[7],"of":[8,30,78,88,98,104,108,114,129,154,157],"a":[9,26,75,126,150],"definite":[10],"integrah":[11],"bis":[12],"involved.This":[13],"has":[14],"lead":[15,73],"to":[16,25,47,55,74,122,135,139],"extensive":[17],"research":[18],"in":[19,117],"past":[21],"years":[22],"also":[24,71],"very":[27],"large":[28,82],"number":[29,83],"publications,":[31],"(gee":[32],"[tl).Also,":[33],"today":[34],"innumerable":[35],"subroutines":[36],"for":[37,80,125],"automatic":[38,109],"integration":[39],"exist,":[40],"estimated":[41],"by":[42],"Rice":[43],"{21":[44],"at":[45],"one":[46],"ten":[48],"million.In":[49],"this":[50,118],"paper":[51],"we":[52,59,120],"will":[53],"add":[54],"that":[56,61],"number,":[57],"because":[58],"think":[60],"functions":[63,146],"are":[64,69,92,160],"interesting":[65],"enough":[66],"as":[67],"they":[68],"may":[72],"new":[76],"clans":[77],"routines":[79,91],"crunchers":[84],"with":[85],"possibility":[87],"vector":[89],"computations.Our":[90],"APL":[93],"Functions,":[94],"which":[95],"make":[96],"use":[97],"parallel":[99],"computing.They":[100],"furthermore":[101],"avoid":[102],"most":[103],"well-known":[106],"pitfalls":[107],"adaptive":[110],"integration.For":[111],"state":[113],"art":[116],"field":[119],"refer":[121],"{3]":[123],"theoretical":[127],"background":[128],"well":[131],"known":[132],"quadrature":[133],"rules":[134,159],"{4].We":[136],"restrict":[137],"ourselves":[138],"describing":[140],"algorithm":[142],"used":[143],"two":[145,152],"DEFIN3":[147],"DEFIN5.As":[149],"base,":[151],"members":[153],"family":[156],"Guassbegendre":[158],"used.If":[161],"(1)":[162],"is":[163],"transformed":[164],"into:":[165]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}
