{"id":"https://openalex.org/W3196926354","doi":"https://doi.org/10.1007/s00211-023-01358-8","title":"Fast hyperbolic wavelet regression meets ANOVA","display_name":"Fast hyperbolic wavelet regression meets ANOVA","publication_year":2023,"publication_date":"2023-06-01","ids":{"openalex":"https://openalex.org/W3196926354","doi":"https://doi.org/10.1007/s00211-023-01358-8","mag":"3196926354"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01358-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01358-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01358-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01358-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112949797","display_name":"Laura Lippert","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":true,"raw_author_name":"Laura Lippert","raw_affiliation_strings":["Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, 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":["Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, 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":["Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112949797"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":3.2793,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.91885779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"154","issue":"1-2","first_page":"155","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9988999962806702,"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":0.9988999962806702,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9962000250816345,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8340849876403809},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7687591314315796},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6054844856262207},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5255188941955566},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5064908266067505},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.48911958932876587},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.47051921486854553},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4408385455608368},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.43357765674591064},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4092088043689728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29947540163993835},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17947602272033691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07076838612556458}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8340849876403809},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7687591314315796},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6054844856262207},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5255188941955566},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5064908266067505},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.48911958932876587},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.47051921486854553},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4408385455608368},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43357765674591064},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4092088043689728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29947540163993835},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17947602272033691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07076838612556458},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-023-01358-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01358-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01358-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01358-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01358-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01358-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4707445492","display_name":"SFB 1410: Hybride Gesellschaften: Menschen in Interaktion mit verk\u00f6rperten Technologien","funder_award_id":"416228727","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7697924455","display_name":null,"funder_award_id":"Ul-403/2-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8263299036","display_name":null,"funder_award_id":"DFG Ul-403/2-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8875356249","display_name":null,"funder_award_id":"SFB 1410","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320311034","display_name":"Technische Universit\u00e4t Chemnitz","ror":"https://ror.org/00a208s56"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3196926354.pdf","grobid_xml":"https://content.openalex.org/works/W3196926354.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W39759813","https://openalex.org/W262738176","https://openalex.org/W602313805","https://openalex.org/W616738372","https://openalex.org/W637625958","https://openalex.org/W1489213177","https://openalex.org/W1542323827","https://openalex.org/W1546004968","https://openalex.org/W1561839199","https://openalex.org/W1698155719","https://openalex.org/W1820164671","https://openalex.org/W1984435106","https://openalex.org/W1998160729","https://openalex.org/W2020990401","https://openalex.org/W2024419927","https://openalex.org/W2026679679","https://openalex.org/W2042587009","https://openalex.org/W2062024414","https://openalex.org/W2065021724","https://openalex.org/W2067393519","https://openalex.org/W2086684904","https://openalex.org/W2091465347","https://openalex.org/W2100179204","https://openalex.org/W2101589741","https://openalex.org/W2107411554","https://openalex.org/W2135512293","https://openalex.org/W2136128169","https://openalex.org/W2300951034","https://openalex.org/W2497677836","https://openalex.org/W2738534281","https://openalex.org/W2795480199","https://openalex.org/W2798679239","https://openalex.org/W2809388168","https://openalex.org/W2914578694","https://openalex.org/W2963103105","https://openalex.org/W3098045837","https://openalex.org/W3119524009","https://openalex.org/W3137438615","https://openalex.org/W3139118318","https://openalex.org/W3178042296","https://openalex.org/W3194792970","https://openalex.org/W3197753951","https://openalex.org/W3199698735","https://openalex.org/W3216135771","https://openalex.org/W4234721591","https://openalex.org/W4255272544","https://openalex.org/W4255975175","https://openalex.org/W4256555983","https://openalex.org/W4385430012"],"related_works":["https://openalex.org/W2393022482","https://openalex.org/W2377346130","https://openalex.org/W2361092061","https://openalex.org/W34817178","https://openalex.org/W4299978068","https://openalex.org/W2319775965","https://openalex.org/W2357314690","https://openalex.org/W4288323582","https://openalex.org/W2951617381","https://openalex.org/W2160065307"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"use":[2],"hyperbolic":[3,29,72],"wavelet":[4,30,58],"regression":[5],"for":[6,26,80,188],"the":[7,27,54,61,77,81,94,98,107,120,139,145,160,178,189,194,197],"fast":[8],"reconstruction":[9],"of":[10,41,53,56,76,97,106,113,154,196],"high-dimensional":[11],"functions":[12],"having":[13],"only":[14,128,152],"low":[15,148,168],"dimensional":[16],"variable":[17,161],"interactions.":[18],"Compactly":[19],"supported":[20],"periodic":[21],"Chui\u2013Wang":[22],"wavelets":[23],"are":[24],"used":[25],"tensorized":[28],"basis.":[31],"In":[32,60,111,142],"a":[33,38,71,103,171],"first":[34],"step":[35,173],"we":[36,64,116,157],"give":[37],"self-contained":[39],"characterization":[40],"tensor":[42],"product":[43],"Sobolev\u2013Besov":[44],"spaces":[45],"on":[46],"thed-torus":[47],"with":[48,123,167],"arbitrary":[49],"smoothness":[50],"in":[51,170,174],"terms":[52,166],"decay":[55],"such":[57],"coefficients.":[59],"second":[62,172],"part":[63],"perform":[65],"and":[66,163],"analyze":[67],"scattered-data":[68],"approximation":[69,121],"using":[70],"cross":[73],"type":[74],"truncation":[75],"basis":[78],"expansion":[79],"associated":[82],"least":[83],"squares":[84],"method.":[85,199],"The":[86],"corresponding":[87],"system":[88],"matrix":[89,108],"is":[90],"sparse":[91],"due":[92],"to":[93,102,138,176,183],"compact":[95],"support":[96],"wavelets,":[99],"which":[100],"leads":[101],"significant":[104],"acceleration":[105],"vector":[109],"multiplication.":[110],"case":[112],"i.i.d.":[114],"samples":[115],"can":[117],"even":[118],"bound":[119],"error":[122],"high":[124],"probability":[125],"by":[126],"loosing":[127],"$$\\log":[129],"$$":[130],"log":[131],"-terms":[132],"that":[133],"do":[134],"not":[135],"depend":[136],"ondcompared":[137],"best":[140],"approximation.":[141,190],"addition,":[143],"if":[144],"function":[146],"has":[147],"effective":[149],"dimension":[150],"(i.e.":[151],"interactions":[153,162],"few":[155],"variables),":[156],"qualitatively":[158],"determine":[159],"omit":[164],"ANOVA":[165],"variance":[169],"order":[175],"increase":[177],"accuracy.":[179],"This":[180],"allows":[181],"us":[182],"suggest":[184],"an":[185],"adapted":[186],"model":[187],"Numerical":[191],"results":[192],"show":[193],"efficiency":[195],"proposed":[198]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}