{"id":"https://openalex.org/W2040396531","doi":"https://doi.org/10.1090/s0025-5718-98-00894-1","title":"A generalized discrepancy and quadrature error bound","display_name":"A generalized discrepancy and quadrature error bound","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2040396531","doi":"https://doi.org/10.1090/s0025-5718-98-00894-1","mag":"2040396531"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00894-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00894-1","pdf_url":"https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049806335","display_name":"Fred J. Hickernell","orcid":"https://orcid.org/0000-0001-6677-1324"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Fred Hickernell","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong","Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong","institution_ids":["https://openalex.org/I141568987"]},{"raw_affiliation_string":"Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049806335"],"corresponding_institution_ids":["https://openalex.org/I141568987"],"apc_list":null,"apc_paid":null,"fwci":17.7043,"has_fulltext":true,"cited_by_count":713,"citation_normalized_percentile":{"value":0.99384345,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"67","issue":"221","first_page":"299","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9991999864578247,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9991999864578247,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9918000102043152,"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"}},{"id":"https://openalex.org/T12299","display_name":"Radiation Shielding Materials Analysis","score":0.9574999809265137,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9012047052383423},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6804327368736267},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46375754475593567},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4281645119190216},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3379497528076172},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3377613425254822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9012047052383423},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6804327368736267},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46375754475593567},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4281645119190216},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3379497528076172},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3377613425254822},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-98-00894-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00894-1","pdf_url":"https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.100.2225","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.2225","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4700","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4700","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.7649","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.7649","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://math.hkbu.edu.hk/pub/techreport/math111.ps.Z","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00894-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00894-1","pdf_url":"https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00894-1/S0025-5718-98-00894-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2040396531.pdf","grobid_xml":"https://content.openalex.org/works/W2040396531.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W97112242","https://openalex.org/W1512171754","https://openalex.org/W1533955387","https://openalex.org/W1976544585","https://openalex.org/W2000834181","https://openalex.org/W2043419861","https://openalex.org/W2073732659","https://openalex.org/W2098269688","https://openalex.org/W2106149169","https://openalex.org/W2155817197","https://openalex.org/W2190966787","https://openalex.org/W2313299119","https://openalex.org/W2314359380","https://openalex.org/W2331011396","https://openalex.org/W2801179766","https://openalex.org/W4235195661","https://openalex.org/W4237938407","https://openalex.org/W4238205818","https://openalex.org/W4285719527","https://openalex.org/W4300580367","https://openalex.org/W6980679104"],"related_works":["https://openalex.org/W2035232447","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2144321310","https://openalex.org/W2001419904","https://openalex.org/W1982234448","https://openalex.org/W2560252838","https://openalex.org/W2024733137","https://openalex.org/W3158760621","https://openalex.org/W2138451012"],"abstract_inverted_index":{"An":[0],"error":[1,18],"bound":[2,19],"for":[3,67],"multidimensional":[4],"quadrature":[5,51,68],"is":[6,37,53,62],"derived":[7],"that":[8,127],"includes":[9,71],"the":[10,21,35,50,75,130],"Koksma-Hlawka":[11],"inequality":[12],"as":[13,39,55,72],"a":[14,24,40,56,63],"special":[15,73],"case.":[16],"This":[17],"takes":[20],"form":[22],"of":[23,26,65,132],"product":[25],"two":[27],"terms.":[28],"One":[29],"term,":[30,45],"which":[31,46],"depends":[32,47],"only":[33,48],"on":[34,49],"integrand,":[36],"defined":[38,54],"generalized":[41,57,60],"variation.":[42],"The":[43,59],"other":[44],"rule,":[52],"discrepancy.":[58],"discrepancy":[61,105],"figure":[64],"merit":[66],"rules":[69],"and":[70,106],"cases":[74],"<inline-formula":[76,107],"content-type=\"math/mathml\">":[77,108],"<mml:math":[78,109],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[79,110],"alttext=\"script":[80],"upper":[81],"L":[82],"Superscript":[83],"p\">":[84],"<mml:semantics>":[85,115],"<mml:msup>":[86],"<mml:mrow":[87,89],"class=\"MJX-TeXAtom-ORD\">":[88,90],"<mml:mi":[91],"class=\"MJX-tex-caligraphic\"":[92],"mathvariant=\"script\">L</mml:mi>":[93],"</mml:mrow>":[94,95],"<mml:mi>p</mml:mi>":[96],"</mml:msup>":[97],"<mml:annotation":[98,122],"encoding=\"application/x-tex\">{\\mathcal":[99],"L}^p</mml:annotation>":[100],"</mml:semantics>":[101,124],"</mml:math>":[102,125],"</inline-formula>":[103,126],"-star":[104],"alttext=\"upper":[111],"P":[112],"Subscript":[113],"alpha\">":[114],"<mml:msub>":[116],"<mml:mi>P</mml:mi>":[117],"<mml:mi>":[118],"\u03b1":[119],"</mml:mi>":[120],"</mml:msub>":[121],"encoding=\"application/x-tex\">P_\\alpha</mml:annotation>":[123],"arises":[128],"in":[129],"study":[131],"lattice":[133],"rules.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":30},{"year":2023,"cited_by_count":27},{"year":2022,"cited_by_count":29},{"year":2021,"cited_by_count":43},{"year":2020,"cited_by_count":32},{"year":2019,"cited_by_count":24},{"year":2018,"cited_by_count":38},{"year":2017,"cited_by_count":29},{"year":2016,"cited_by_count":32},{"year":2015,"cited_by_count":27},{"year":2014,"cited_by_count":35},{"year":2013,"cited_by_count":29},{"year":2012,"cited_by_count":29}],"updated_date":"2026-05-08T15:41:06.802602","created_date":"2025-10-10T00:00:00"}