{"id":"https://openalex.org/W2026679679","doi":"https://doi.org/10.1007/s10208-013-9142-3","title":"On the Stability and Accuracy of Least Squares Approximations","display_name":"On the Stability and Accuracy of Least Squares Approximations","publication_year":2013,"publication_date":"2013-03-12","ids":{"openalex":"https://openalex.org/W2026679679","doi":"https://doi.org/10.1007/s10208-013-9142-3","mag":"2026679679"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-013-9142-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9142-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","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/A5108445641","display_name":"Albert Cohen","orcid":"https://orcid.org/0000-0003-1337-4012"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Albert Cohen","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France","Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, Paris, France 75005#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France","institution_ids":["https://openalex.org/I4210158291"]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Universit\u00e9 Pierre et Marie Curie, Paris, France 75005#TAB#","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064232831","display_name":"Mark A. Davenport","orcid":"https://orcid.org/0000-0001-6079-6328"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark A. Davenport","raw_affiliation_strings":["School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA, 30332, USA","School of Electrical and Computer Engineering, Georgia Institute of Technology. Atlanta USA 30332"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, Georgia Institute of Technology. Atlanta USA 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057868361","display_name":"D. Leviatan","orcid":"https://orcid.org/0000-0003-0180-5065"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Dany Leviatan","raw_affiliation_strings":["Raymond and Beverly Sackler School of Mathematics, Tel Aviv University, 69978, Tel Aviv, Israel","Raymond and Beverly Sackler School of Mathematics, Tel Aviv University, Tel Aviv, Israel 69978#TAB#"],"affiliations":[{"raw_affiliation_string":"Raymond and Beverly Sackler School of Mathematics, Tel Aviv University, 69978, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Raymond and Beverly Sackler School of Mathematics, Tel Aviv University, Tel Aviv, Israel 69978#TAB#","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108445641"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":27.1418,"has_fulltext":false,"cited_by_count":236,"citation_normalized_percentile":{"value":0.99902629,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"13","issue":"5","first_page":"819","last_page":"834"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9959999918937683,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.8874734044075012},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.670721173286438},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5697773694992065},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.5574811100959778},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5092359781265259},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5019104480743408},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47739142179489136},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44332975149154663},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4363557994365692},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.418689489364624},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4085410535335541},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.333202064037323},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10696399211883545}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8874734044075012},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.670721173286438},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5697773694992065},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.5574811100959778},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5092359781265259},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5019104480743408},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47739142179489136},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44332975149154663},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4363557994365692},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.418689489364624},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4085410535335541},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.333202064037323},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10696399211883545},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer 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},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-013-9142-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9142-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01432960v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01432960","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Foundations of Computational Mathematics, 2013, 13 (5), pp.819-834. ⟨10.1007/s10208-013-9142-3⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1484867920","https://openalex.org/W1957823995","https://openalex.org/W2086874647","https://openalex.org/W2107411554","https://openalex.org/W2134348739","https://openalex.org/W2156218552","https://openalex.org/W3021293439","https://openalex.org/W3098045837"],"related_works":["https://openalex.org/W1893285581","https://openalex.org/W2095736209","https://openalex.org/W4313271098","https://openalex.org/W3119134791","https://openalex.org/W2801788073","https://openalex.org/W228596958","https://openalex.org/W2295208482","https://openalex.org/W69573121","https://openalex.org/W1486766149","https://openalex.org/W3082698730"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":26},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}