{"id":"https://openalex.org/W1995376194","doi":"https://doi.org/10.1137/0613047","title":"The Analysis for the Total Least Squares Problem with More Than One Solution","display_name":"The Analysis for the Total Least Squares Problem with More Than One Solution","publication_year":1992,"publication_date":"1992-07-01","ids":{"openalex":"https://openalex.org/W1995376194","doi":"https://doi.org/10.1137/0613047","mag":"1995376194"},"language":"en","primary_location":{"id":"doi:10.1137/0613047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613047","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/A5106381930","display_name":"Musheng Wei","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Musheng Wei","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5106381930"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1872,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.90705197,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"3","first_page":"746","last_page":"763"},"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/T11405","display_name":"Geophysics and Gravity Measurements","score":0.9703999757766724,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9320999979972839,"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/mathematics","display_name":"Mathematics","score":0.8521131873130798},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6791163682937622},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5861968994140625},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5364905595779419},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5171079635620117},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5072073936462402},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.504428505897522},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.49732473492622375},{"id":"https://openalex.org/keywords/total-least-squares","display_name":"Total least squares","score":0.48331737518310547},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4612163305282593},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.43987542390823364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24800148606300354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21086212992668152},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12127435207366943},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.06819018721580505},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06694066524505615},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.05283883213996887}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8521131873130798},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6791163682937622},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5861968994140625},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5364905595779419},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5171079635620117},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5072073936462402},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.504428505897522},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.49732473492622375},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.48331737518310547},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4612163305282593},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.43987542390823364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24800148606300354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21086212992668152},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12127435207366943},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.06819018721580505},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06694066524505615},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05283883213996887},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials 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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0613047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613047","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1504797307","https://openalex.org/W1979541162","https://openalex.org/W1983992752","https://openalex.org/W1985852691","https://openalex.org/W2006860831","https://openalex.org/W2008229822","https://openalex.org/W2030755808","https://openalex.org/W2070162767","https://openalex.org/W2078841894","https://openalex.org/W2088028136","https://openalex.org/W2094358944","https://openalex.org/W2107187130","https://openalex.org/W2150200785","https://openalex.org/W2989457786"],"related_works":["https://openalex.org/W1986698577","https://openalex.org/W2034819163","https://openalex.org/W2352570898","https://openalex.org/W2043225268","https://openalex.org/W2125225254","https://openalex.org/W2374560502","https://openalex.org/W4380487384","https://openalex.org/W2368940260","https://openalex.org/W1997267293","https://openalex.org/W2393100698"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3],"analysis":[4,67],"of":[5,8,79],"the":[6,9,21,33,40,43,46,51,55,101],"solutions":[7,37,48,58],"total":[10],"least":[11],"squares":[12],"problem":[13],"(TLS)":[14],"$AX":[15],"\\approx":[16],"B$":[17],"in":[18],"cases":[19],"where":[20],"matrix":[22],"$(A,B)$":[23],"may":[24],"have":[25],"multiple":[26],"smallest":[27],"singular":[28],"values.":[29],"General":[30],"formulas":[31],"for":[32,54,71,92],"minimum":[34],"norm":[35],"TLS":[36,44,57],"are":[38,64,96],"given;":[39],"difference":[41],"between":[42],"and":[45,75,81,86,88],"LS":[47],"is":[49,68],"obtained;":[50],"error":[52,102],"bounds":[53],"perturbed":[56],"with":[59],"or":[60],"without":[61],"minimal":[62],"length":[63],"deduced.":[65],"The":[66],"useful":[69],"especially":[70],"rank":[72],"deficient":[73],"problems":[74],"generalizes":[76],"previous":[77],"results":[78,91],"Golub":[80],"Van":[82,84],"Loan,":[83],"Huffel":[85],"Vandewalle,":[87],"Zoltowski.":[89],"Numerical":[90],"a":[93],"practical":[94],"application":[95],"also":[97],"given":[98],"to":[99],"verify":[100],"bounds.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}