{"id":"https://openalex.org/W2497254580","doi":"https://doi.org/10.1137/16m1071699","title":"Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection","display_name":"Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2497254580","doi":"https://doi.org/10.1137/16m1071699","mag":"2497254580"},"language":"en","primary_location":{"id":"doi:10.1137/16m1071699","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1071699","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1327571","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046509521","display_name":"Guannan Zhang","orcid":"https://orcid.org/0000-0001-7256-150X"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guannan Zhang","raw_affiliation_strings":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Dept. of Computational and Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Dept. of Computational and Applied Mathematics","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009338966","display_name":"Clayton Webster","orcid":"https://orcid.org/0000-0002-1375-0359"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Clayton G. Webster","raw_affiliation_strings":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Dept. of Computational and Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Dept. of Computational and Applied Mathematics","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Max Gunzburger","raw_affiliation_strings":["Florida State Univ., Tallahassee, FL (United States). Dept. of of Scientific Computing"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State Univ., Tallahassee, FL (United States). Dept. of of Scientific Computing","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024090165","display_name":"John Burkardt","orcid":"https://orcid.org/0000-0003-0273-2769"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Burkardt","raw_affiliation_strings":["Florida State Univ., Tallahassee, FL (United States). Dept. of of Scientific Computing"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State Univ., Tallahassee, FL (United States). Dept. of of Scientific Computing","institution_ids":["https://openalex.org/I103163165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3392,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.95048635,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"3","first_page":"517","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9865999817848206,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7997821569442749},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7607403993606567},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5735300779342651},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.550640881061554},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5229561924934387},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.49750760197639465},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4971506893634796},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.49472352862358093},{"id":"https://openalex.org/keywords/moving-least-squares","display_name":"Moving least squares","score":0.4838034510612488},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.480854332447052},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.47160348296165466},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.46930789947509766},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4482625722885132},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4215674102306366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3808295726776123},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3754816949367523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18499213457107544},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1629866659641266},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10895654559135437}],"concepts":[{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7997821569442749},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7607403993606567},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5735300779342651},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.550640881061554},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5229561924934387},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.49750760197639465},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4971506893634796},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.49472352862358093},{"id":"https://openalex.org/C2780580100","wikidata":"https://www.wikidata.org/wiki/Q6927143","display_name":"Moving least squares","level":2,"score":0.4838034510612488},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.480854332447052},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.47160348296165466},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.46930789947509766},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4482625722885132},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4215674102306366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3808295726776123},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3754816949367523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18499213457107544},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1629866659641266},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10895654559135437},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1071699","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1071699","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:osti.gov:1327571","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1327571","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1327571","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1327571","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W155488731","https://openalex.org/W176737369","https://openalex.org/W1597405158","https://openalex.org/W1646309082","https://openalex.org/W1970476229","https://openalex.org/W1982421072","https://openalex.org/W1998213879","https://openalex.org/W1998917464","https://openalex.org/W2002274796","https://openalex.org/W2013576021","https://openalex.org/W2015740317","https://openalex.org/W2020717814","https://openalex.org/W2026679679","https://openalex.org/W2040727702","https://openalex.org/W2055064119","https://openalex.org/W2065120373","https://openalex.org/W2072205359","https://openalex.org/W2073043218","https://openalex.org/W2083845086","https://openalex.org/W2096969866","https://openalex.org/W2100474665","https://openalex.org/W2107359160","https://openalex.org/W2117122565","https://openalex.org/W2126447218","https://openalex.org/W2127689830","https://openalex.org/W2152469101","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2441614350","https://openalex.org/W1968883776","https://openalex.org/W2033586214","https://openalex.org/W4386614394","https://openalex.org/W603561220","https://openalex.org/W2146739464","https://openalex.org/W1986237207","https://openalex.org/W2131833267","https://openalex.org/W1986132361","https://openalex.org/W3036075344"],"abstract_inverted_index":{"This":[0],"work":[1],"proposes":[2],"a":[3,20,53,77],"hyperspherical":[4,45,66,117],"sparse":[5,36,56,121],"approximation":[6],"framework":[7],"for":[8,19,38],"detecting":[9],"jump":[10,94],"discontinuities":[11,95],"in":[12,14,64,115],"functions":[13],"high-dimensional":[15],"spaces.":[16],"The":[17],"need":[18],"novel":[21],"approach":[22,42],"results":[23],"from":[24],"the":[25,44,49,59,65,84,87,89,111,116,146,153,165],"theoretical":[26],"and":[27,123,132],"computational":[28,99],"inefficiencies":[29],"of":[30,48,52,58,86,152,167],"well-known":[31],"approaches,":[32],"such":[33],"as":[34,158],"adaptive":[35,120],"grids,":[37],"discontinuity":[39,50,79,113],"detection.":[40],"Our":[41],"constructs":[43],"coordinate":[46,67],"representation":[47],"surface":[51,114],"function.":[54],"Then":[55],"approximations":[57],"transformed":[60,112],"function":[61,126],"are":[62,107,140,156,159],"built":[63],"system,":[68,118],"with":[69,96],"values":[70],"at":[71],"each":[72],"point":[73],"estimated":[74],"by":[75],"solving":[76],"one-dimensional":[78],"detection":[80],"problem.":[81],"Due":[82],"to":[83,102,109,143],"smoothness":[85],"hypersurface,":[88],"new":[90,154],"technique":[91],"can":[92],"identify":[93],"significantly":[97],"reduced":[98],"cost,":[100],"compared":[101],"existing":[103],"methods.":[104],"Several":[105],"approaches":[106],"used":[108],"approximate":[110],"including":[119],"grid":[122],"radial":[124],"basis":[125],"interpolation,":[127],"discrete":[128],"least":[129],"squares":[130],"projection,":[131],"compressed":[133],"sensing":[134],"approximation.":[135],"Moreover,":[136],"hierarchical":[137],"acceleration":[138],"techniques":[139],"also":[141],"incorporated":[142],"further":[144],"reduce":[145],"overall":[147],"complexity.":[148],"Rigorous":[149],"complexity":[150],"analyses":[151],"methods":[155],"provided,":[157],"several":[160],"numerical":[161],"examples":[162],"that":[163],"illustrate":[164],"effectiveness":[166],"our":[168],"approach.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}