{"id":"https://openalex.org/W1979951317","doi":"https://doi.org/10.1145/2513109.2513117","title":"Algorithm 934","display_name":"Algorithm 934","publication_year":2013,"publication_date":"2013-09-01","ids":{"openalex":"https://openalex.org/W1979951317","doi":"https://doi.org/10.1145/2513109.2513117","mag":"1979951317"},"language":"en","primary_location":{"id":"doi:10.1145/2513109.2513117","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2513109.2513117","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Transactions on Mathematical Software","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/A5021402401","display_name":"Danilo Erricolo","orcid":"https://orcid.org/0000-0001-6352-9567"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Danilo Erricolo","raw_affiliation_strings":["University of Illinois at Chicago, IL","University of Illinois at Chicago, IL,"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, IL","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois at Chicago, IL,","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081713041","display_name":"Giuseppe Carluccio","orcid":"https://orcid.org/0000-0001-5376-3843"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giuseppe Carluccio","raw_affiliation_strings":["University of Illinois at Chicago, IL","University of Illinois at Chicago, IL,"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, IL","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois at Chicago, IL,","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021402401"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":2.4666,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.87432847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"1","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9934999942779541,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.979200005531311,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.785625696182251},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.719697117805481},{"id":"https://openalex.org/keywords/mathieu-function","display_name":"Mathieu function","score":0.681940495967865},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6642555594444275},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6556392312049866},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5368341207504272},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.44371435046195984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40654096007347107},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36402082443237305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3396156430244446},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.27651843428611755},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.15439453721046448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1483798325061798}],"concepts":[{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.785625696182251},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.719697117805481},{"id":"https://openalex.org/C157097347","wikidata":"https://www.wikidata.org/wiki/Q1908689","display_name":"Mathieu function","level":2,"score":0.681940495967865},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6642555594444275},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6556392312049866},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5368341207504272},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.44371435046195984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40654096007347107},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36402082443237305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3396156430244446},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.27651843428611755},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.15439453721046448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1483798325061798}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2513109.2513117","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2513109.2513117","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1442574200","display_name":null,"funder_award_id":"FA9550-05-1-0443","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3568544722","display_name":null,"funder_award_id":"FA9550-12-1-0174","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1500342720","https://openalex.org/W1514025487","https://openalex.org/W1524551886","https://openalex.org/W1524573041","https://openalex.org/W1571784310","https://openalex.org/W1573761753","https://openalex.org/W1578004187","https://openalex.org/W1814912747","https://openalex.org/W1963751882","https://openalex.org/W1964028571","https://openalex.org/W1966179442","https://openalex.org/W1967764205","https://openalex.org/W1983553929","https://openalex.org/W2015078016","https://openalex.org/W2028837575","https://openalex.org/W2029175883","https://openalex.org/W2032535811","https://openalex.org/W2035558515","https://openalex.org/W2039532314","https://openalex.org/W2046849008","https://openalex.org/W2055037898","https://openalex.org/W2062023542","https://openalex.org/W2076644324","https://openalex.org/W2078278595","https://openalex.org/W2096929121","https://openalex.org/W2096936951","https://openalex.org/W2098257663","https://openalex.org/W2106648987","https://openalex.org/W2120303160","https://openalex.org/W2122477263","https://openalex.org/W2128357137","https://openalex.org/W2131433368","https://openalex.org/W2138008062","https://openalex.org/W2138014828","https://openalex.org/W2141952369","https://openalex.org/W2145915949","https://openalex.org/W2148760827","https://openalex.org/W2158748300","https://openalex.org/W2159429887","https://openalex.org/W2163537153","https://openalex.org/W2170825483","https://openalex.org/W2335872485","https://openalex.org/W2477829615","https://openalex.org/W2805738490","https://openalex.org/W3010782316","https://openalex.org/W3012322763","https://openalex.org/W3016843226","https://openalex.org/W4239835997"],"related_works":["https://openalex.org/W136575323","https://openalex.org/W3150993086","https://openalex.org/W1516043520","https://openalex.org/W3150762485","https://openalex.org/W767506823","https://openalex.org/W3125463300","https://openalex.org/W3124022197","https://openalex.org/W2218209960","https://openalex.org/W246887380","https://openalex.org/W1508156279"],"abstract_inverted_index":{"Software":[0],"to":[1,47],"compute":[2,48],"angular":[3],"and":[4,21,34,40,52],"radial":[5],"Mathieu":[6,38],"functions":[7,39],"is":[8,17,26,60],"provided":[9],"in":[10],"the":[11,14,22,32,35],"case":[12],"that":[13],"parameter":[15],"q":[16],"a":[18],"complex":[19],"variable":[20,24],"independent":[23],"x":[25],"real.":[27],"After":[28],"an":[29],"introduction":[30],"on":[31],"notation":[33],"definitions":[36],"of":[37],"their":[41],"related":[42],"properties,":[43],"Fortran":[44],"90":[45],"subroutines":[46],"them":[49],"are":[50],"described":[51],"validated":[53],"with":[54],"some":[55],"comparisons.":[56],"A":[57],"sample":[58],"application":[59],"also":[61],"provided.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2016-06-24T00:00:00"}
