{"id":"https://openalex.org/W2283917733","doi":"https://doi.org/10.1137/15m1052184","title":"Transformations and Hardy--Krause Variation","display_name":"Transformations and Hardy--Krause Variation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2283917733","doi":"https://doi.org/10.1137/15m1052184","mag":"2283917733"},"language":"en","primary_location":{"id":"doi:10.1137/15m1052184","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1052184","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1512.02713","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078166693","display_name":"Kinjal Basu","orcid":"https://orcid.org/0000-0002-4091-0119"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kinjal Basu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035543011","display_name":"Art B. Owen","orcid":"https://orcid.org/0000-0001-5860-3945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Art B. Owen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078166693"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01807592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"3","first_page":"1946","last_page":"1966"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9975000023841858,"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/T11166","display_name":"Analytic Number Theory Research","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/bounded-function","display_name":"Bounded function","score":0.7098066806793213},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.6203280687332153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6003057360649109},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.578453779220581},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5676143169403076},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.5612084865570068},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5257374048233032},{"id":"https://openalex.org/keywords/hardy-space","display_name":"Hardy space","score":0.4669925272464752},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3233957588672638},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22025859355926514},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06792643666267395}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7098066806793213},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.6203280687332153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6003057360649109},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.578453779220581},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5676143169403076},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.5612084865570068},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5257374048233032},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.4669925272464752},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3233957588672638},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22025859355926514},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06792643666267395},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1052184","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1052184","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1512.02713","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.02713","pdf_url":"https://arxiv.org/pdf/1512.02713","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":"","raw_type":"text"},{"id":"mag:2283917733","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1512.02713","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1011.4089","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1011.4089","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://statweb.stanford.edu/%7Eowen/reports/varfalpos.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1512.02713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.02713","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1512.02713","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.02713","pdf_url":"https://arxiv.org/pdf/1512.02713","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5411398610","display_name":"Monte Carlo and Quasi-Monte Carlo Methods for Statistics","funder_award_id":"1407397","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G884165620","display_name":null,"funder_award_id":"DMS-1407397","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2283917733.pdf","grobid_xml":"https://content.openalex.org/works/W2283917733.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W137498958","https://openalex.org/W1518816409","https://openalex.org/W1532908400","https://openalex.org/W1533955387","https://openalex.org/W1862031973","https://openalex.org/W1993553799","https://openalex.org/W1995565517","https://openalex.org/W2057487175","https://openalex.org/W2057565703","https://openalex.org/W2073870969","https://openalex.org/W2079637049","https://openalex.org/W2103459249","https://openalex.org/W2111524489","https://openalex.org/W2112459735","https://openalex.org/W2165477600","https://openalex.org/W2806087731","https://openalex.org/W2952674597","https://openalex.org/W2963308814","https://openalex.org/W2964085736"],"related_works":["https://openalex.org/W1520230059","https://openalex.org/W3150966873","https://openalex.org/W2952750102","https://openalex.org/W2985064468","https://openalex.org/W2741595416","https://openalex.org/W2963599089","https://openalex.org/W3106298863","https://openalex.org/W2781781482","https://openalex.org/W942957578","https://openalex.org/W2004445558","https://openalex.org/W3092904518","https://openalex.org/W3145018940","https://openalex.org/W1965194910","https://openalex.org/W1976337900","https://openalex.org/W2032646515","https://openalex.org/W2060340463","https://openalex.org/W2676785966","https://openalex.org/W2949796173","https://openalex.org/W2990406751"],"abstract_inverted_index":{"Using":[0],"a":[1,18,126],"multivariable":[2],"Faa":[3],"di":[4],"Bruno":[5],"formula":[6],"we":[7],"give":[8,45],"conditions":[9,47,135],"on":[10],"transformations":[11,65,79,106],"$\\tau:[0,1]^m\\to{\\cal":[12],"X}$":[13,16],"where":[14],"${\\cal":[15],"is":[17,28],"closed":[19],"and":[20,37,69,83,141,155],"bounded":[21,30,148],"subset":[22],"of":[23,29,35,128,147,153],"${\\mathbb{R}}^d$":[24],"such":[25],"that":[26,110],"$f\\circ\\tau$":[27,49,112],"variation":[31,149],"in":[32,125,139,150],"the":[33,67,97,101,108,151],"sense":[34,152],"Hardy":[36,154],"Krause":[38],"for":[39,48,54,107,122,136,142],"all":[40,123],"$f\\in":[41],"C^m({\\cal":[42],"X})$.":[43],"We":[44,104,131],"similar":[46],"to":[50,58,66,73,81,115,145],"be":[51,146],"smooth":[52,113],"enough":[53,114],"scrambled":[55,119],"net":[56,120],"sampling":[57,121,144],"attain":[59],"$O(n^{-3/2+\\epsilon})$":[60],"accuracy.":[61],"Some":[62,77],"popular":[63],"symmetric":[64],"simplex":[68,109],"sphere":[70],"are":[71],"shown":[72],"satisfy":[74,96],"neither":[75],"condition.":[76,103],"other":[78],"due":[80],"Fang":[82],"Wang":[84],"(Monogr.":[85],"Statist.":[86],"Appl.":[87],"Probab.":[88],"51,":[89],"CRC":[90],"Press,":[91],"Boca":[92],"Raton,":[93],"FL,":[94],"1993)":[95],"first":[98],"but":[99],"not":[100],"second":[102],"provide":[105],"makes":[111],"fully":[116],"benefit":[117],"from":[118],"$f$":[124],"class":[127],"generalized":[129],"polynomials.":[130],"also":[132],"find":[133],"sufficient":[134],"conditional":[137],"inversion":[138],"${\\mathbb{R}}^2$":[140],"importance":[143],"Krause.":[156]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
