{"id":"https://openalex.org/W2605849147","doi":"https://doi.org/10.1137/17m1113552","title":"LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property","display_name":"LSLQ: An Iterative Method for Linear Least-Squares with an Error Minimization Property","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2605849147","doi":"https://doi.org/10.1137/17m1113552","mag":"2605849147"},"language":"en","primary_location":{"id":"doi:10.1137/17m1113552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1113552","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","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.13140/rg.2.2.17818.64966","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079342264","display_name":"Ron Estrin","orcid":"https://orcid.org/0000-0001-7576-7394"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ron Estrin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027758717","display_name":"Dominique Orban","orcid":"https://orcid.org/0000-0002-8017-7687"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominique Orban","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039807799","display_name":"Michael A. Saunders","orcid":"https://orcid.org/0000-0003-3800-4982"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael A. Saunders","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3800-4982","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00204107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"40","issue":"1","first_page":"254","last_page":"275"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9926999807357788,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9926999807357788,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9884999990463257,"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/T10057","display_name":"Face and Expression Recognition","score":0.9692000150680542,"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/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.6706807613372803},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6230718493461609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6160523891448975},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6117210984230042},{"id":"https://openalex.org/keywords/iteratively-reweighted-least-squares","display_name":"Iteratively reweighted least squares","score":0.5520680546760559},{"id":"https://openalex.org/keywords/iterative-and-incremental-development","display_name":"Iterative and incremental development","score":0.5488697290420532},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5349100232124329},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46285688877105713},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45738619565963745},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4263465404510498},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.4101869761943817},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3592383563518524},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3334646224975586},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15836948156356812},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.11248719692230225}],"concepts":[{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.6706807613372803},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6230718493461609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6160523891448975},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6117210984230042},{"id":"https://openalex.org/C126090379","wikidata":"https://www.wikidata.org/wiki/Q6094424","display_name":"Iteratively reweighted least squares","level":4,"score":0.5520680546760559},{"id":"https://openalex.org/C143587482","wikidata":"https://www.wikidata.org/wiki/Q1543216","display_name":"Iterative and incremental development","level":2,"score":0.5488697290420532},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5349100232124329},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46285688877105713},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45738619565963745},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4263465404510498},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.4101869761943817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3592383563518524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3334646224975586},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15836948156356812},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.11248719692230225},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1113552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1113552","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"},{"id":"pmh:oai:publications.polymtl.ca:37530","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/37530/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Rapport"},{"id":"pmh:oai:publications.polymtl.ca:43374","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/43374/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"doi:10.13140/rg.2.2.17818.64966","is_oa":true,"landing_page_url":"https://doi.org/10.13140/rg.2.2.17818.64966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2605849147","is_oa":false,"landing_page_url":"https://www.gerad.ca/en/papers/G-2017-05","pdf_url":null,"source":{"id":"https://openalex.org/S4306518497","display_name":"Les Cahiers du GERAD","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Les Cahiers du GERAD","raw_type":null}],"best_oa_location":{"id":"doi:10.13140/rg.2.2.17818.64966","is_oa":true,"landing_page_url":"https://doi.org/10.13140/rg.2.2.17818.64966","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1387674867","display_name":null,"funder_award_id":"U01GM102098","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1971806979","https://openalex.org/W1981196578","https://openalex.org/W1983886273","https://openalex.org/W1992793565","https://openalex.org/W2005423095","https://openalex.org/W2006340475","https://openalex.org/W2018850201","https://openalex.org/W2023891589","https://openalex.org/W2075998338","https://openalex.org/W2097897435","https://openalex.org/W2104802194","https://openalex.org/W2117686912","https://openalex.org/W2313084557","https://openalex.org/W2316564661","https://openalex.org/W2611252285","https://openalex.org/W2802164368"],"related_works":["https://openalex.org/W2285724574","https://openalex.org/W3014840260","https://openalex.org/W3149596771","https://openalex.org/W2002878344","https://openalex.org/W2494245018","https://openalex.org/W2033188633","https://openalex.org/W2081056570","https://openalex.org/W2917608879","https://openalex.org/W2359835307","https://openalex.org/W2062814491","https://openalex.org/W2368062247","https://openalex.org/W3004048095","https://openalex.org/W2501322201","https://openalex.org/W2132030004","https://openalex.org/W2282450072","https://openalex.org/W1590725396","https://openalex.org/W2060951837","https://openalex.org/W2403457131","https://openalex.org/W1517552807","https://openalex.org/W2377830940"],"abstract_inverted_index":{"We":[0,77,127],"propose":[1],"an":[2,99,116,146,152],"iterative":[3],"method":[4,16],"named":[5],"LSLQ":[6,44,50,92],"for":[7],"solving":[8],"linear":[9,35],"least-squares":[10,48,148],"problems":[11,134],"of":[12,155],"any":[13],"shape.":[14],"The":[15,94],"is":[17,51,161],"based":[18],"on":[19,83,102,131,136],"the":[20,27,34,41,46,58,63,71,84,87,91,103,107,124],"Golub":[21],"and":[22,37,80,114,135],"Kahan":[23],"(1965)":[24],"process,":[25],"where":[26],"dominant":[28],"cost":[29],"consists":[30],"in":[31,86,144],"products":[32],"with":[33],"operator":[36],"its":[38],"transpose.":[39],"In":[40],"rank-deficient":[42],"case,":[43],"identifies":[45],"minimum-length":[47],"solution.":[49],"formally":[52],"equivalent":[53],"to":[54,57,98,123,151,162],"SYMMLQ":[55],"applied":[56],"normal":[59],"equations,":[60],"so":[61],"that":[62,160],"current":[64],"estimate's":[65],"Euclidean":[66,88],"norm":[67,74,89,105],"increases":[68],"monotonically,":[69],"while":[70],"associated":[72],"error":[73,85,104],"decreases":[75],"monotonically.":[76],"provide":[78],"lower":[79],"upper":[81,95,100],"bounds":[82],"along":[90,106],"iterations.":[93],"bound":[96,101],"translates":[97],"LSQR":[108,125],"iterations,":[109],"which":[110,145],"was":[111],"previously":[112],"unavailable,":[113],"provides":[115],"error-based":[117],"stopping":[118],"criterion":[119],"involving":[120],"a":[121,137,156],"transition":[122],"point.":[126],"report":[128],"numerical":[129],"experiments":[130],"standard":[132],"test":[133],"full-wave":[138],"inversion":[139],"problem":[140],"arising":[141],"from":[142],"geophysics":[143],"approximate":[147,153],"solution":[149],"corresponds":[150],"gradient":[154],"relevant":[157],"penalty":[158],"function":[159],"be":[163],"minimized.":[164]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
