{"id":"https://openalex.org/W2049757530","doi":"https://doi.org/10.1137/s0895479893258802","title":"Total Least Norm Formulation and Solution for Structured Problems","display_name":"Total Least Norm Formulation and Solution for Structured Problems","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2049757530","doi":"https://doi.org/10.1137/s0895479893258802","mag":"2049757530"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893258802","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893258802","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/A5055740369","display_name":"J. B. Rosen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Ben Rosen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101728710","display_name":"Haesun Park","orcid":"https://orcid.org/0000-0001-6259-7170"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haesun Park","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061172163","display_name":"John Glick","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Glick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8392,"has_fulltext":false,"cited_by_count":189,"citation_normalized_percentile":{"value":0.96876116,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"110","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":1.0,"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/T11236","display_name":"Control Systems and Identification","score":0.964900016784668,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9603999853134155,"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/overdetermined-system","display_name":"Overdetermined system","score":0.8861321210861206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7646267414093018},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6201980113983154},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.613743782043457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5297126770019531},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4796743392944336},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4447416365146637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4268980324268341},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.4188550114631653},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3922218084335327},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36530256271362305},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.25579598546028137},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20597541332244873},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.193454772233963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16843336820602417}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.8861321210861206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646267414093018},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6201980113983154},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.613743782043457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5297126770019531},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4796743392944336},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4447416365146637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4268980324268341},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.4188550114631653},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3922218084335327},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36530256271362305},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.25579598546028137},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20597541332244873},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.193454772233963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16843336820602417},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/s0895479893258802","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893258802","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":12,"referenced_works":["https://openalex.org/W1970859043","https://openalex.org/W1971013425","https://openalex.org/W1999542175","https://openalex.org/W2006860831","https://openalex.org/W2008229822","https://openalex.org/W2025680668","https://openalex.org/W2084924291","https://openalex.org/W2092086025","https://openalex.org/W2101120656","https://openalex.org/W2105292630","https://openalex.org/W2114449024","https://openalex.org/W4206428854"],"related_works":["https://openalex.org/W2051277630","https://openalex.org/W1997267293","https://openalex.org/W2493516920","https://openalex.org/W2145045474","https://openalex.org/W1014435275","https://openalex.org/W2226451926","https://openalex.org/W2753658416","https://openalex.org/W2046580780","https://openalex.org/W137154706","https://openalex.org/W129558112"],"abstract_inverted_index":{"A":[0,24,34,152,171],"new":[1],"formulation":[2],"and":[3,25,46,74,95,97,105,128,172],"algorithm":[4,89,103,143],"is":[5,86,93,144],"described":[6],"for":[7,90,148],"computing":[8],"the":[9,53,88,102,119,141,168],"solution":[10,92],"to":[11],"an":[12,145],"overdetermined":[13],"linear":[14],"system,":[15],"$Ax":[16],"\\approx":[17],"b$,":[18],"with":[19,130],"possible":[20],"errors":[21,161],"in":[22,52,164],"both":[23],"b.":[26,173],"This":[27],"approach":[28],"preserves":[29],"any":[30],"affine":[31],"structure":[32,158],"of":[33,50,70,110,167,170],"or":[35,43,153,159],"$[":[36],"A\\mid":[37],"b":[38,154],"]$,":[39],"such":[40],"as":[41,67],"Toeplitz":[42],"sparse":[44],"structure,":[45],"minimizes":[47],"a":[48,68,108,156],"measure":[49],"error":[51],"discrete":[54],"$L_p":[55],"$":[56,134],"norm,":[57],"where":[58,151,160],"$p":[59,131],"=":[60,132],"1,2,\\,{\\text{or}}\\,\\infty":[61],"$.":[62],"It":[63],"can":[64,162],"be":[65],"considered":[66],"generalization":[69],"total":[71,79,125],"least":[72,80,123,126],"squares":[73],"we":[75],"call":[76],"it":[77],"structured":[78,111],"norm":[81],"(STLN).":[82],"The":[83],"STLN":[84,129,142],"problem":[85],"formulated,":[87],"its":[91],"presented":[94],"analyzed,":[96],"computational":[98],"results":[99,138],"that":[100,140],"illustrate":[101],"convergence":[104],"performance":[106],"on":[107],"variety":[109],"problems":[112,150],"are":[113],"summarized.":[114],"For":[115],"each":[116],"test":[117],"problem,":[118],"solutions":[120],"obtained":[121],"by":[122],"squares,":[124,127],"1,2,\\,{\\text{and}}\\,\\infty":[133],"were":[135],"compared.":[136],"These":[137],"confirm":[139],"effective":[146],"method":[147],"solving":[149],"has":[155],"special":[157],"occur":[163],"only":[165],"some":[166],"elements":[169]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
