{"id":"https://openalex.org/W2161352487","doi":"https://doi.org/10.1007/s00211-015-0765-y","title":"Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions","display_name":"Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions","publication_year":2015,"publication_date":"2015-09-18","ids":{"openalex":"https://openalex.org/W2161352487","doi":"https://doi.org/10.1007/s00211-015-0765-y","mag":"2161352487"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-015-0765-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-015-0765-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1501.01800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Aicke Hinrichs","orcid":null},"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":true,"raw_author_name":"Aicke Hinrichs","raw_affiliation_strings":["Institute for Analysis, Johannes Kepler University, 4040, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Institute for Analysis, Johannes Kepler University, 4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lev Markhasin","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lev Markhasin","raw_affiliation_strings":["Institute for Stochastics and Applications, University of Stuttgart, 70569, Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Stochastics and Applications, University of Stuttgart, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jens Oettershagen","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jens Oettershagen","raw_affiliation_strings":["Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":null,"display_name":"Tino Ullrich","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tino Ullrich","raw_affiliation_strings":["Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Numerical Simulation, University of Bonn, 53115, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":5.5669,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.96392667,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"134","issue":"1","first_page":"163","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9976999759674072,"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":0.9976999759674072,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.00019999999494757503,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6753000020980835},{"id":"https://openalex.org/keywords/besov-space","display_name":"Besov space","score":0.6366999745368958},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.607699990272522},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6025999784469604},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5817000269889832},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48919999599456787},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4837999939918518},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.47839999198913574},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.448199987411499}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8442999720573425},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6753000020980835},{"id":"https://openalex.org/C129698243","wikidata":"https://www.wikidata.org/wiki/Q526261","display_name":"Besov space","level":5,"score":0.6366999745368958},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.609499990940094},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.607699990272522},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6025999784469604},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5817000269889832},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4034999907016754},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35109999775886536},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C130231550","wikidata":"https://www.wikidata.org/wiki/Q5189500","display_name":"Real-valued function","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.31119999289512634},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30079999566078186},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C121927907","wikidata":"https://www.wikidata.org/wiki/Q1952516","display_name":"Multiresolution analysis","level":5,"score":0.272599995136261},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.2678999900817871},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-015-0765-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-015-0765-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1501.01800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1501.01800","pdf_url":"https://arxiv.org/pdf/1501.01800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1501.01800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1501.01800","pdf_url":"https://arxiv.org/pdf/1501.01800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W78572047","https://openalex.org/W98388201","https://openalex.org/W123541731","https://openalex.org/W598051755","https://openalex.org/W1263021028","https://openalex.org/W1493969319","https://openalex.org/W1583871618","https://openalex.org/W1602773783","https://openalex.org/W1607069976","https://openalex.org/W1630018803","https://openalex.org/W1839061065","https://openalex.org/W1968287514","https://openalex.org/W1970465045","https://openalex.org/W1975252280","https://openalex.org/W1979730921","https://openalex.org/W1980840110","https://openalex.org/W1986280275","https://openalex.org/W1987192334","https://openalex.org/W2009231757","https://openalex.org/W2011523133","https://openalex.org/W2012922531","https://openalex.org/W2014551121","https://openalex.org/W2016359720","https://openalex.org/W2030404880","https://openalex.org/W2045422729","https://openalex.org/W2053162361","https://openalex.org/W2079573105","https://openalex.org/W2085256544","https://openalex.org/W2110888545","https://openalex.org/W2128770615","https://openalex.org/W2129599384","https://openalex.org/W2140170995","https://openalex.org/W2154735927","https://openalex.org/W2497677836","https://openalex.org/W2963473207","https://openalex.org/W2964073520","https://openalex.org/W3161027129","https://openalex.org/W4249137521"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
