{"id":"https://openalex.org/W2946715986","doi":"https://doi.org/10.1109/icoin.2019.8718134","title":"On a Posteriori Error Bounds of Trapezoidal Rule","display_name":"On a Posteriori Error Bounds of Trapezoidal Rule","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2946715986","doi":"https://doi.org/10.1109/icoin.2019.8718134","mag":"2946715986"},"language":"en","primary_location":{"id":"doi:10.1109/icoin.2019.8718134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icoin.2019.8718134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 International Conference on Information Networking (ICOIN)","raw_type":"proceedings-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/A5080652552","display_name":"Bum II Hong","orcid":null},"institutions":[{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Bum II Hong","raw_affiliation_strings":["Dept. of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin-si, Korea"],"affiliations":[{"raw_affiliation_string":"Dept. of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin-si, Korea","institution_ids":["https://openalex.org/I35928602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007473162","display_name":"Intae Ryoo","orcid":"https://orcid.org/0000-0001-6630-1189"},"institutions":[{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Intae Ryoo","raw_affiliation_strings":["Dept. of Computer Engineering, Kyung Hee University, Yongin-si, Korea"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Engineering, Kyung Hee University, Yongin-si, Korea","institution_ids":["https://openalex.org/I35928602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079188570","display_name":"Gon Khang","orcid":"https://orcid.org/0000-0001-7811-0208"},"institutions":[{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Gon Khang","raw_affiliation_strings":["Dept. of Biomedical Engineering, Kyung Hee University, Yongin-si, Korea"],"affiliations":[{"raw_affiliation_string":"Dept. of Biomedical Engineering, Kyung Hee University, Yongin-si, Korea","institution_ids":["https://openalex.org/I35928602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080652552"],"corresponding_institution_ids":["https://openalex.org/I35928602"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07704445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"342","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9995999932289124,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7698062062263489},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.7436261177062988},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5974851846694946},{"id":"https://openalex.org/keywords/trapezoidal-rule","display_name":"Trapezoidal rule","score":0.5841975212097168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5710339546203613},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.553389310836792},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.522354006767273},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4516262114048004},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4508202373981476},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4379042387008667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3904431462287903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.325117826461792},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.226087749004364},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20016971230506897},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16905257105827332},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1604117453098297},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08027830719947815}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7698062062263489},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.7436261177062988},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5974851846694946},{"id":"https://openalex.org/C78727","wikidata":"https://www.wikidata.org/wiki/Q833293","display_name":"Trapezoidal rule","level":3,"score":0.5841975212097168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5710339546203613},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.553389310836792},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.522354006767273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4516262114048004},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4508202373981476},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4379042387008667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3904431462287903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.325117826461792},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.226087749004364},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20016971230506897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16905257105827332},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1604117453098297},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08027830719947815},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icoin.2019.8718134","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icoin.2019.8718134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 International Conference on Information Networking (ICOIN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W626794699","https://openalex.org/W1554388601","https://openalex.org/W1992199208","https://openalex.org/W2093517458","https://openalex.org/W3021898623"],"related_works":["https://openalex.org/W2019605203","https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W62490179","https://openalex.org/W2954004777","https://openalex.org/W1586572182"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,51],"discuss":[4],"the":[5,10,19,34,40,57],"average":[6],"case":[7],"setting":[8,12],"and":[9],"probabilistic":[11,64],"of":[13,21,33,44,59,66],"composite":[14],"Trapezoidal":[15,60],"rule":[16,61],"assuming":[17],"that":[18,80],"class":[20],"integrand":[22],"on":[23,39,56],"an":[24],"interval":[25],"[0],":[26],"[1]":[27],"is":[28,75,81],"equipped":[29],"with":[30],"a":[31,41,53,63,69,71,78],"variant":[32],"r-fold":[35],"wiener":[36],"measure":[37],"based":[38],"finite":[42],"number":[43],"function":[45],"values":[46],"for":[47],"numerical":[48],"integration.":[49],"Moreover,":[50],"compute":[52],"posteriori":[54,72],"bounds":[55],"error":[58,73],"from":[62],"point":[65],"view.":[67],"This":[68],"new":[70],"bound":[74,79],"better":[76],"than":[77],"commonly":[82],"used":[83],"in":[84],"practice.":[85]},"counts_by_year":[],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
