{"id":"https://openalex.org/W2138020995","doi":"https://doi.org/10.1007/s11075-011-9482-5","title":"Weighted compound integration rules with higher order convergence for all N","display_name":"Weighted compound integration rules with higher order convergence for all N","publication_year":2011,"publication_date":"2011-07-05","ids":{"openalex":"https://openalex.org/W2138020995","doi":"https://doi.org/10.1007/s11075-011-9482-5","mag":"2138020995"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-011-9482-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-011-9482-5","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":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/250967","any_repository_has_fulltext":true},"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/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fred J. Hickernell","raw_affiliation_strings":["Department of Applied Mathematics, Illinois Institute of Technology, Room E1-208, 10 West 32nd Street, Chicago, IL, 60616, USA","Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA 60616#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Illinois Institute of Technology, Room E1-208, 10 West 32nd Street, Chicago, IL, 60616, USA","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA 60616#TAB#","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038787781","display_name":"Peter Kritzer","orcid":"https://orcid.org/0000-0002-7919-7672"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Peter Kritzer","raw_affiliation_strings":["Department of Financial Mathematics, University of Linz, Altenbergerstr. 69, 4040, Linz, Austria","Department of Financial Mathematics, University of Linz, Linz, Austria 4040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Financial Mathematics, University of Linz, Altenbergerstr. 69, 4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Department of Financial Mathematics, University of Linz, Linz, Austria 4040#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045896084","display_name":"Frances Y. Kuo","orcid":"https://orcid.org/0000-0003-2123-6971"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Frances Y. Kuo","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia","School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052 ("],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052 (","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045125806","display_name":"Dirk Nuyens","orcid":"https://orcid.org/0000-0002-4555-2314"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":["Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium","Department of Computer Science, K.U. Leuven, Heverlee, Belgium 3001"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Computer Science, K.U. Leuven, Heverlee, Belgium 3001","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045125806"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.7528,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.89438589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"59","issue":"2","first_page":"161","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9861999750137329,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9560999870300293,"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/mathematics","display_name":"Mathematics","score":0.7772220373153687},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6617262959480286},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6214132308959961},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5844050645828247},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5660452246665955},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.545555055141449},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5182557106018066},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5165570974349976},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.48198574781417847},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.476493775844574},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4554363191127777},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4392692744731903},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4139312207698822},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3212229013442993},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31716102361679077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21919119358062744},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1774648129940033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11847257614135742}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7772220373153687},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6617262959480286},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6214132308959961},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5844050645828247},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5660452246665955},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.545555055141449},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5182557106018066},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5165570974349976},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.48198574781417847},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.476493775844574},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4554363191127777},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4392692744731903},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4139312207698822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3212229013442993},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31716102361679077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21919119358062744},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1774648129940033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11847257614135742},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-011-9482-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-011-9482-5","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"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/250967","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/250967","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Applied Mathematics Reports","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/332782","is_oa":true,"landing_page_url":"http://www.maths.unsw.edu.au/applied/pubs/apppreprints2009.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Applied Mathematics Reports, vol. 59 (2), Art.No. AMR09/19, (161-183)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/250967","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/250967","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Applied Mathematics Reports","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W59186131","https://openalex.org/W415311214","https://openalex.org/W598051755","https://openalex.org/W1543280314","https://openalex.org/W1607458528","https://openalex.org/W1975819870","https://openalex.org/W1976544585","https://openalex.org/W1985018928","https://openalex.org/W2011200438","https://openalex.org/W2014208555","https://openalex.org/W2014551121","https://openalex.org/W2014959310","https://openalex.org/W2015558767","https://openalex.org/W2035455944","https://openalex.org/W2039696973","https://openalex.org/W2042083287","https://openalex.org/W2043419861","https://openalex.org/W2048305092","https://openalex.org/W2059141990","https://openalex.org/W2059965246","https://openalex.org/W2061750459","https://openalex.org/W2061874121","https://openalex.org/W2069421332","https://openalex.org/W2079347437","https://openalex.org/W2080686387","https://openalex.org/W2084898049","https://openalex.org/W2094438648","https://openalex.org/W2094952117","https://openalex.org/W2111894258","https://openalex.org/W2145169372","https://openalex.org/W2151582349","https://openalex.org/W2152162686","https://openalex.org/W2166634029","https://openalex.org/W2183868163","https://openalex.org/W2801179766","https://openalex.org/W3102328113","https://openalex.org/W4206038828","https://openalex.org/W4238531019","https://openalex.org/W4256263170","https://openalex.org/W4300580367","https://openalex.org/W7000791799"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2052835778","https://openalex.org/W2049003611","https://openalex.org/W2127804977","https://openalex.org/W2108418243","https://openalex.org/W164103134","https://openalex.org/W2787352659","https://openalex.org/W1970611213","https://openalex.org/W1707372784","https://openalex.org/W2755124412"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
