{"id":"https://openalex.org/W1976478925","doi":"https://doi.org/10.1137/s0036142903427664","title":"A Piecewise Constant Algorithm for Weighted<i>L</i><sub>1</sub>Approximation over Bounded or Unbounded Regions in $\\R^s$","display_name":"A Piecewise Constant Algorithm for Weighted<i>L</i><sub>1</sub>Approximation over Bounded or Unbounded Regions in $\\R^s$","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1976478925","doi":"https://doi.org/10.1137/s0036142903427664","mag":"1976478925"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903427664","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903427664","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":"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/A5049806335","display_name":"Fred J. Hickernell","orcid":"https://orcid.org/0000-0001-6677-1324"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fred J. Hickernell","raw_affiliation_strings":["Illinois Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Illinois Institute of Technology","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075686837","display_name":"Ian H. Sloan","orcid":"https://orcid.org/0000-0003-3769-0538"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ian H. Sloan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108372354","display_name":"Grzegorz W. Wasilkowski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grzegorz W. Wasilkowski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2927,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78870179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"43","issue":"3","first_page":"1003","last_page":"1020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9957000017166138,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.8106143474578857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.804638683795929},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7010924816131592},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5670176148414612},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.487102746963501},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42857927083969116},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42794692516326904},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4259503185749054},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2524506449699402},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06704986095428467}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8106143474578857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.804638683795929},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7010924816131592},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5670176148414612},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.487102746963501},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42857927083969116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42794692516326904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4259503185749054},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2524506449699402},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06704986095428467},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142903427664","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903427664","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W152683667","https://openalex.org/W155604529","https://openalex.org/W645185567","https://openalex.org/W1554388601","https://openalex.org/W1560266390","https://openalex.org/W1620981000","https://openalex.org/W1970476229","https://openalex.org/W1976544585","https://openalex.org/W1981117732","https://openalex.org/W1981743146","https://openalex.org/W1991092247","https://openalex.org/W1998213879","https://openalex.org/W2004485838","https://openalex.org/W2010722609","https://openalex.org/W2013576021","https://openalex.org/W2021382991","https://openalex.org/W2035087858","https://openalex.org/W2041530119","https://openalex.org/W2042587009","https://openalex.org/W2043419861","https://openalex.org/W2043997216","https://openalex.org/W2067393519","https://openalex.org/W2091465347","https://openalex.org/W2099702616","https://openalex.org/W2798679239","https://openalex.org/W3021898623","https://openalex.org/W4212933304","https://openalex.org/W4213027339","https://openalex.org/W4299521717","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W1454600515","https://openalex.org/W2385263368","https://openalex.org/W2347422947","https://openalex.org/W1645056428","https://openalex.org/W2368296458","https://openalex.org/W2040445660","https://openalex.org/W2004238570","https://openalex.org/W2050773296","https://openalex.org/W1979725436","https://openalex.org/W2268549697"],"abstract_inverted_index":{"Using":[0],"Smolyak's":[1,126],"construction":[2],"[S.":[3],"A.":[4],"Smolyak,":[5],"Dokl.":[6],"Akad.":[7],"Nauk":[8],"SSSR,":[9],"4":[10],"(1963),":[11],"pp.":[12],"240--243],":[13],"we":[14,68],"derive":[15],"a":[16,35,50,118],"new":[17],"algorithm":[18],"for":[19,43,49],"approximating":[20],"multivariate":[21],"functions":[22,53],"over":[23],"bounded":[24,61,152],"or":[25],"unbounded":[26],"regions":[27],"in":[28,34,62,77,125,153],"$\\R^s$":[29],"with":[30,149],"the":[31,44,63,71,74,80,86,96,103,110,122,130,137,144,147,150],"error":[32,48,72,89],"measured":[33],"weighted":[36],"L1":[37,64],"-norm.":[38,65],"We":[39,139],"provide":[40],"upper":[41],"bounds":[42],"algorithm's":[45],"cost":[46,75,97],"and":[47,73,128],"class":[51],"of":[52,79,82,106,132,143],"whose":[54],"mixed":[55],"first":[56],"order":[57],"partial":[58],"derivatives":[59,151],"are":[60],"In":[66],"particular,":[67],"prove":[69],"that":[70],"(measured":[76],"terms":[78],"number":[81,104,131],"function":[83,133],"evaluations)":[84],"satisfy":[85],"relation":[87],"$$":[88,94],"\\le":[90],"\\frac{s\\,\\exp\\big(\\frac1{12(s-1)}\\big)}{(s-1)\\pi}\\,":[91],"\\left(\\frac{e\\,\\ln(\\mbox{cost})}{(s-1)\\sqrt{2}\\ln(2)}\\right)^{2(s-1)}\\,":[92],"\\frac1{{cost}}":[93],"whenever":[95],"is":[98,117],"sufficiently":[99],"large":[100],"relative":[101],"to":[102,146],"s":[105],"variables.":[107],"More":[108],"specifically,":[109],"inequality":[111],"holds":[112],"when":[113],"$q\\ge2(s-1)$,":[114],"where":[115],"q":[116],"special":[119],"parameter":[120],"defining":[121],"refinement":[123],"level":[124],"algorithm,":[127],"hence":[129],"evaluations":[134],"used":[135],"by":[136],"algorithm.":[138],"also":[140],"discuss":[141],"extensions":[142],"results":[145],"spaces":[148],"Lp":[154],"-norms.":[155]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}