{"id":"https://openalex.org/W3045327592","doi":"https://doi.org/10.1007/s11075-020-00963-0","title":"Generalizing the trapezoidal rule in the complex plane","display_name":"Generalizing the trapezoidal rule in the complex plane","publication_year":2020,"publication_date":"2020-07-21","ids":{"openalex":"https://openalex.org/W3045327592","doi":"https://doi.org/10.1007/s11075-020-00963-0","mag":"3045327592"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-020-00963-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00963-0","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5029242127","display_name":"Bengt Fornberg","orcid":"https://orcid.org/0000-0003-0014-6985"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bengt Fornberg","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA"],"raw_orcid":"https://orcid.org/0000-0003-0014-6985","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029242127"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.1886,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77255985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"87","issue":"1","first_page":"187","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.998199999332428,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9952999949455261,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trapezoidal-rule","display_name":"Trapezoidal rule","score":0.7685562968254089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7179132699966431},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.7039667367935181},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7031244039535522},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6091834306716919},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.596981406211853},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5452616214752197},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5093861222267151},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.48102933168411255},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4627167582511902},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.4626883268356323},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.45521846413612366},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.42053940892219543},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4167846143245697},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4145699143409729},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3830653131008148},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.27881738543510437},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25507158041000366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17061200737953186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11468505859375}],"concepts":[{"id":"https://openalex.org/C78727","wikidata":"https://www.wikidata.org/wiki/Q833293","display_name":"Trapezoidal rule","level":3,"score":0.7685562968254089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7179132699966431},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.7039667367935181},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7031244039535522},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6091834306716919},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.596981406211853},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5452616214752197},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5093861222267151},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.48102933168411255},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4627167582511902},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.4626883268356323},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.45521846413612366},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.42053940892219543},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4167846143245697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4145699143409729},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3830653131008148},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.27881738543510437},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25507158041000366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17061200737953186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11468505859375},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-020-00963-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00963-0","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1998527589","https://openalex.org/W2001773004","https://openalex.org/W2022538649","https://openalex.org/W2030762303","https://openalex.org/W2033022456","https://openalex.org/W2318377621","https://openalex.org/W2504492770","https://openalex.org/W2989284669","https://openalex.org/W3015622028","https://openalex.org/W3045215878","https://openalex.org/W3089386356","https://openalex.org/W3129118332"],"related_works":["https://openalex.org/W4299522098","https://openalex.org/W2749095681","https://openalex.org/W2298619543","https://openalex.org/W2109641974","https://openalex.org/W49034894","https://openalex.org/W3127707657","https://openalex.org/W3002581604","https://openalex.org/W2103900747","https://openalex.org/W4287754151","https://openalex.org/W2068547097"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}