{"id":"https://openalex.org/W4385492392","doi":"https://doi.org/10.1090/mcom/3896","title":"On the reconstruction of functions from values at subsampled quadrature points","display_name":"On the reconstruction of functions from values at subsampled quadrature points","publication_year":2023,"publication_date":"2023-08-02","ids":{"openalex":"https://openalex.org/W4385492392","doi":"https://doi.org/10.1090/mcom/3896"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3896","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3896","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062725379","display_name":"Felix Bartel","orcid":"https://orcid.org/0000-0003-3061-4647"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Felix Bartel","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052412980","display_name":"Lutz K\u00e4mmerer","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz K\u00e4mmerer","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020926962","display_name":"Daniel Potts","orcid":"https://orcid.org/0000-0003-3651-4364"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Potts","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010819277","display_name":"Tino Ullrich","orcid":"https://orcid.org/0000-0002-0055-0542"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tino Ullrich","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062725379"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":null,"apc_paid":null,"fwci":3.5328,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.93116395,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"93","issue":"346","first_page":"785","last_page":"809"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998000264167786,"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":0.9998000264167786,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11949","display_name":"Nuclear Physics and Applications","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6465661525726318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5106237530708313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4005514979362488},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3428173065185547}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6465661525726318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5106237530708313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4005514979362488},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3428173065185547}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3896","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3896","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W253307310","https://openalex.org/W1565176583","https://openalex.org/W1714077815","https://openalex.org/W1867316708","https://openalex.org/W1967374108","https://openalex.org/W1972952296","https://openalex.org/W1973312654","https://openalex.org/W1976544585","https://openalex.org/W1978501336","https://openalex.org/W1981867435","https://openalex.org/W1996806998","https://openalex.org/W2015368696","https://openalex.org/W2026679679","https://openalex.org/W2029386867","https://openalex.org/W2040013301","https://openalex.org/W2064936877","https://openalex.org/W2107411554","https://openalex.org/W2300951034","https://openalex.org/W2419092805","https://openalex.org/W2498858925","https://openalex.org/W2599366207","https://openalex.org/W2914578694","https://openalex.org/W2949924726","https://openalex.org/W2963103105","https://openalex.org/W2963814522","https://openalex.org/W2964011010","https://openalex.org/W2966832657","https://openalex.org/W3039624492","https://openalex.org/W3040771581","https://openalex.org/W3088796800","https://openalex.org/W3108275699","https://openalex.org/W3110811957","https://openalex.org/W3114241195","https://openalex.org/W3114633602","https://openalex.org/W3114928620","https://openalex.org/W3154542836","https://openalex.org/W3155724638","https://openalex.org/W3157488464","https://openalex.org/W3158733253","https://openalex.org/W3194792970","https://openalex.org/W3194844506","https://openalex.org/W3216151625","https://openalex.org/W3216643960","https://openalex.org/W4205624883","https://openalex.org/W4213390110","https://openalex.org/W4214612440","https://openalex.org/W4221144327","https://openalex.org/W4247705294","https://openalex.org/W4286758941","https://openalex.org/W4311465473","https://openalex.org/W4322621393","https://openalex.org/W4385605328","https://openalex.org/W6667175207"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,145,148,186],"concerned":[3],"with":[4,21,60,65],"function":[5],"reconstruction":[6,87],"from":[7,134],"samples.":[8],"The":[9,89],"sampling":[10],"points":[11,19,27,51,64,110,117,224],"used":[12],"in":[13,52,200,237,245],"several":[14,246],"approaches":[15,44],"are":[16,225],"(1)":[17],"structured":[18,50],"connected":[20],"fast":[22,231],"algorithms":[23,236],"or":[24],"(2)":[25],"unstructured":[26],"coming":[28],"from,":[29],"e.g.,":[30],"an":[31,37,53],"initial":[32,156],"random":[33,97],"draw":[34],"to":[35,104,120,180,210,239],"achieve":[36],"improved":[38],"information":[39],"complexity.":[40],"We":[41,159],"connect":[42],"both":[43],"and":[45,68,132,147,232],"propose":[46],"a":[47,94,101,121],"subsampling":[48,90],"of":[49,93,109,126,138,197,202,205,221],"offline":[54],"step.":[55],"In":[56,115,208],"particular,":[57],"we":[58,153,229],"start":[59],"quasi-Monte":[61],"Carlo":[62],"(QMC)":[63],"inherent":[66],"structure":[67],"stable":[69],"<inline-formula":[70,166],"content-type=\"math/mathml\">":[71,167],"<mml:math":[72,168],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[73,169],"alttext=\"upper":[74],"L":[75],"2\">":[76],"<mml:semantics>":[77,171],"<mml:msub>":[78],"<mml:mi>L</mml:mi>":[79],"<mml:mn>2</mml:mn>":[80],"</mml:msub>":[81],"<mml:annotation":[82,173],"encoding=\"application/x-tex\">L_2</mml:annotation>":[83],"</mml:semantics>":[84,175],"</mml:math>":[85,176],"</inline-formula>":[86,177],"properties.":[88],"procedure":[91,103],"consists":[92],"computationally":[95],"inexpensive":[96],"step":[98],"followed":[99],"by":[100],"deterministic":[102],"further":[105],"reduce":[106],"the":[107,139,165,194,203,206,216,222,241],"number":[108],"while":[111],"keeping":[112],"its":[113],"information.":[114],"these":[116],"functions":[118],"(belonging":[119],"reproducing":[122],"kernel":[123],"Hilbert":[124],"space":[125],"bounded":[127],"functions)":[128],"will":[129],"be":[130],"sampled":[131],"reconstructed":[133],"whilst":[135],"achieving":[136],"state":[137],"art":[140],"error":[141],"decay.":[142],"Our":[143],"method":[144],"dimension-independent":[146],"applicable":[149],"as":[150,152],"soon":[151],"know":[154],"some":[155],"quadrature":[157],"points.":[158],"apply":[160],"our":[161,212,249],"general":[162],"findings":[163],"on":[164],"alttext=\"d\">":[170],"<mml:mi>d</mml:mi>":[172],"encoding=\"application/x-tex\">d</mml:annotation>":[174],"-dimensional":[178],"torus":[179],"subsample":[181],"rank-1":[182,190],"lattices,":[183],"where":[184],"it":[185],"known":[187],"that":[188],"full":[189],"lattices":[191],"lose":[192],"half":[193],"optimal":[195,217],"order":[196,238],"convergence":[198],"(expressed":[199],"terms":[201],"size":[204],"lattice).":[207],"contrast":[209],"that,":[211],"subsampled":[213],"version":[214],"regains":[215],"rate":[218],"since":[219],"many":[220],"lattice":[223],"not":[226],"needed.":[227],"Moreover,":[228],"utilize":[230],"memory":[233],"efficient":[234],"Fourier":[235],"compute":[240],"approximation.":[242],"Numerical":[243],"experiments":[244],"dimensions":[247],"support":[248],"findings.":[250]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
