{"id":"https://openalex.org/W2050721242","doi":"https://doi.org/10.1137/050643696","title":"Mean-Squared Error Estimation for Linear Systems with Block Circulant Uncertainty","display_name":"Mean-Squared Error Estimation for Linear Systems with Block Circulant Uncertainty","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2050721242","doi":"https://doi.org/10.1137/050643696","mag":"2050721242"},"language":"en","primary_location":{"id":"doi:10.1137/050643696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643696","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5069363394","display_name":"Amir Beck","orcid":"https://orcid.org/0000-0003-1493-291X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Amir Beck","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005913897","display_name":"Yonina C. Eldar","orcid":"https://orcid.org/0000-0003-4358-5304"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yonina C. Eldar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045105549","display_name":"Aharon Ben\u2010Tal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aharon Ben-Tal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069363394"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5942,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94488955,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"3","first_page":"712","last_page":"730"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8375016450881958},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6641549468040466},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5496840476989746},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.5340109467506409},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5339170098304749},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5200871229171753},{"id":"https://openalex.org/keywords/minimax-estimator","display_name":"Minimax estimator","score":0.4863746464252472},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4625989496707916},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4569641947746277},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4440326392650604},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.436272531747818},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4173396825790405},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37167367339134216},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18935853242874146},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.12136685848236084},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07787972688674927}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375016450881958},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6641549468040466},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5496840476989746},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.5340109467506409},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5339170098304749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5200871229171753},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.4863746464252472},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4625989496707916},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4569641947746277},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4440326392650604},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.436272531747818},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4173396825790405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37167367339134216},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18935853242874146},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.12136685848236084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07787972688674927},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050643696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050643696","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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":28,"referenced_works":["https://openalex.org/W1534416612","https://openalex.org/W1568307856","https://openalex.org/W1632601927","https://openalex.org/W1967073510","https://openalex.org/W2000267193","https://openalex.org/W2008229822","https://openalex.org/W2030255580","https://openalex.org/W2033242948","https://openalex.org/W2047066533","https://openalex.org/W2048679451","https://openalex.org/W2056340321","https://openalex.org/W2079784985","https://openalex.org/W2100115174","https://openalex.org/W2107467870","https://openalex.org/W2115483035","https://openalex.org/W2123523921","https://openalex.org/W2132105090","https://openalex.org/W2139114004","https://openalex.org/W2146695063","https://openalex.org/W2152976633","https://openalex.org/W2157298716","https://openalex.org/W2171542363","https://openalex.org/W2174883827","https://openalex.org/W2500266379","https://openalex.org/W2798766386","https://openalex.org/W2912522929","https://openalex.org/W3103961368","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2618253902","https://openalex.org/W4247363655","https://openalex.org/W1993095755","https://openalex.org/W2951136737","https://openalex.org/W1985938891","https://openalex.org/W185105768","https://openalex.org/W1926349254","https://openalex.org/W2044247672","https://openalex.org/W3038031637","https://openalex.org/W2152976633"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,11,44,69,74,92,121,141,144],"problem":[3,106],"of":[4,87,143],"estimating":[5],"a":[6,24,39,59,78,100,103,114,126],"vector":[7],"${\\bf":[8,14,21,33,48,51,119],"x}$":[9,34],"in":[10,65,148],"linear":[12,70],"model":[13],"A}{\\bf":[15],"x}":[16],"\\approx":[17],"{\\bf":[18],"y}$,":[19],"where":[20,46],"A}$":[22,49],"is":[23,35,123],"block":[25],"circulant":[26],"(BC)":[27],"matrix":[28],"with":[29,130,150],"N":[30],"blocks":[31],"and":[32,50],"assumed":[36],"to":[37,55,102,125],"have":[38],"weighted":[40],"norm":[41,116],"bound.":[42],"In":[43],"case":[45],"both":[47],"y}$":[52],"are":[53],"subjected":[54],"noise,":[56],"we":[57,67,89,134],"propose":[58],"minimax":[60,93,145],"mean-squared":[61],"error":[62],"(MSE)":[63],"approach":[64,147],"which":[66,108],"seek":[68],"estimator":[71,95],"that":[72,91],"minimizes":[73],"worst-case":[75],"MSE":[76,94,146],"over":[77],"BC":[79],"structured":[80],"uncertainty":[81],"region.":[82],"For":[83,113],"an":[84,137],"arbitrary":[85],"choice":[86],"weighting,":[88],"show":[90],"can":[96,109],"be":[97,110],"formulated":[98],"as":[99],"solution":[101],"semidefinite":[104],"programming":[105],"(SDP),":[107],"solved":[111],"efficiently.":[112],"Euclidean":[115],"bound":[117],"on":[118],"x}$,":[120],"SDP":[122],"reduced":[124],"simple":[127],"convex":[128],"program":[129],"$N+1$":[131],"unknowns.":[132],"Finally,":[133],"demonstrate":[135],"through":[136],"image":[138],"deblurring":[139],"example":[140],"potential":[142],"comparison":[149],"other":[151],"conventional":[152],"methods.":[153]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
