{"id":"https://openalex.org/W1996765007","doi":"https://doi.org/10.1145/1377596.1377601","title":"Algorithm 876","display_name":"Algorithm 876","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W1996765007","doi":"https://doi.org/10.1145/1377596.1377601","mag":"1996765007"},"language":"en","primary_location":{"id":"doi:10.1145/1377596.1377601","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377596.1377601","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/A5066323735","display_name":"Kendall Atkinson","orcid":"https://orcid.org/0000-0002-5727-7030"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kendall E. Atkinson","raw_affiliation_strings":["University of Iowa","University of Iowa, "],"affiliations":[{"raw_affiliation_string":"University of Iowa","institution_ids":["https://openalex.org/I126307644"]},{"raw_affiliation_string":"University of Iowa, ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111466368","display_name":"L. F. Shampine","orcid":null},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lawrence F. Shampine","raw_affiliation_strings":["Southern Methodist University, Dallas","Southern Methodist University, Dallas,"],"affiliations":[{"raw_affiliation_string":"Southern Methodist University, Dallas","institution_ids":["https://openalex.org/I178169726"]},{"raw_affiliation_string":"Southern Methodist University, Dallas,","institution_ids":["https://openalex.org/I178169726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066323735"],"corresponding_institution_ids":["https://openalex.org/I126307644"],"apc_list":null,"apc_paid":null,"fwci":2.5457,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.88961932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"34","issue":"4","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9796000123023987,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9796000123023987,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.970300018787384,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9358000159263611,"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/kernel","display_name":"Kernel (algebra)","score":0.6637283563613892},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6552873253822327},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.61851966381073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5945779085159302},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4682009816169739},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4456965923309326},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.4399562478065491},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4385848939418793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4352213740348816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3423810601234436},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29993921518325806},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2227262258529663},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1653110682964325}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6637283563613892},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6552873253822327},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.61851966381073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5945779085159302},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4682009816169739},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4456965923309326},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.4399562478065491},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4385848939418793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4352213740348816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3423810601234436},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29993921518325806},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2227262258529663},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1653110682964325}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1377596.1377601","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377596.1377601","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W617367799","https://openalex.org/W1963857841","https://openalex.org/W1983335525","https://openalex.org/W1985307809","https://openalex.org/W1995255737","https://openalex.org/W2014208709","https://openalex.org/W2027472325","https://openalex.org/W2027731955","https://openalex.org/W2031364441","https://openalex.org/W2080887426","https://openalex.org/W2084632999","https://openalex.org/W2312940325","https://openalex.org/W2318788438","https://openalex.org/W2330297279","https://openalex.org/W4237795074","https://openalex.org/W4294836170","https://openalex.org/W6987431168"],"related_works":["https://openalex.org/W4293495792","https://openalex.org/W1500488077","https://openalex.org/W2410127010","https://openalex.org/W2078150528","https://openalex.org/W2582934162","https://openalex.org/W2106295220","https://openalex.org/W172868526","https://openalex.org/W4378554534","https://openalex.org/W1937879542","https://openalex.org/W2039502053"],"abstract_inverted_index":{"We":[0],"present":[1],"here":[2],"the":[3,20,62,69,85],"algorithms":[4],"and":[5],"user":[6],"interface":[7],"of":[8,19,82,120],"a":[9,27,32,50,55,80,99,102,106,117],"Matlab":[10],"program,":[11],"Fie,":[12],"that":[13,77,87],"solves":[14,116],"numerically":[15],"Fredholm":[16],"integral":[17,121],"equations":[18,122],"second":[21],"kind":[22],"on":[23,48,128],"an":[24,111],"interval":[25,70],"[":[26,49],",":[28,42,51,56,92],"b":[29,52,57],"]":[30,53,58],"to":[31],"specified,":[33],"modest":[34],"accuracy.":[35],"The":[36],"kernel":[37,75,126],"function":[38,127],"K":[39,89],"(":[40,90],"s":[41,64,91],"t":[43,66,93],")":[44,94],"is":[45,71],"moderately":[46,124],"smooth":[47,125],"\u00d7[":[54],"except":[59],"possibly":[60],"across":[61,84],"diagonal":[63],"=":[65],".":[67],"If":[68],"finite,":[72],"provides":[73],"for":[74],"functions":[76],"behave":[78],"in":[79,101],"variety":[81],"ways":[83],"diagonal,":[86],"is,":[88],"may":[95],"be":[96],"smooth,":[97],"have":[98,105,110],"discontinuity":[100],"low-order":[103],"derivative,":[104],"logarithmic":[107],"singularity,":[108],"or":[109],"algebraic":[112],"singularity.":[113],"Fie":[114],"also":[115],"large":[118],"class":[119],"with":[123],"[0,":[129],"\u221e":[130],").":[131]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}