{"id":"https://openalex.org/W2139002888","doi":"https://doi.org/10.1137/0613079","title":"Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares","display_name":"Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares","publication_year":1992,"publication_date":"1992-10-01","ids":{"openalex":"https://openalex.org/W2139002888","doi":"https://doi.org/10.1137/0613079","mag":"2139002888"},"language":"en","primary_location":{"id":"doi:10.1137/0613079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613079","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/A5025647215","display_name":"M\u00e5rten Gulliksson","orcid":"https://orcid.org/0000-0003-0332-2315"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M\u00e5rten Gulliksson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053176705","display_name":"Per-\u00c5ke Wedin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Per-\u00e5ke Wedin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025647215"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.766,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.94622544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"4","first_page":"1298","last_page":"1313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.992900013923645,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9868999719619751,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.8527526259422302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8225356936454773},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5058274269104004},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.46913430094718933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4685170650482178},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4487525224685669},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.4447520077228546},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4000174105167389},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3730071187019348},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35400116443634033},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.3377818465232849},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.26819002628326416},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.21901503205299377},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20946207642555237},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.13125193119049072},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.07701903581619263}],"concepts":[{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.8527526259422302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225356936454773},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5058274269104004},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.46913430094718933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4685170650482178},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4487525224685669},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.4447520077228546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4000174105167389},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3730071187019348},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35400116443634033},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.3377818465232849},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26819002628326416},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.21901503205299377},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20946207642555237},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.13125193119049072},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.07701903581619263},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0613079","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613079","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":12,"referenced_works":["https://openalex.org/W141418607","https://openalex.org/W1967281400","https://openalex.org/W1998741578","https://openalex.org/W2016182223","https://openalex.org/W2027634563","https://openalex.org/W2031766448","https://openalex.org/W2041752389","https://openalex.org/W2046696187","https://openalex.org/W2083715802","https://openalex.org/W2150200785","https://openalex.org/W4244347919","https://openalex.org/W4251656402"],"related_works":["https://openalex.org/W2035885121","https://openalex.org/W2549446753","https://openalex.org/W2026673180","https://openalex.org/W4380487384","https://openalex.org/W1959514624","https://openalex.org/W327962130","https://openalex.org/W4378552425","https://openalex.org/W200101083","https://openalex.org/W2034819163","https://openalex.org/W4319880936"],"abstract_inverted_index":{"A":[0],"new":[1],"way":[2],"of":[3,8,52],"looking":[4],"at":[5],"a":[6,42],"class":[7],"methods":[9],"for":[10,86],"the":[11,53,68,88,102,113,120,124],"weighted":[12,91],"linear":[13,61,92],"least":[14,93],"squares":[15,94],"problem":[16,95],"$\\min":[17],"_x":[18],"\\|":[19],"M^{":[20],"-":[21,27],"(":[22,25],"1/2":[23],")}":[24],"b":[26],"Ax":[28],")":[29],"\\|_2":[30],"$":[31],"where":[32],"$M":[33],"=":[34,49],"{\\operatorname{diag}}(\\mu":[35],"_i":[36],")$":[37],"is":[38,59,96,126],"presented":[39],"by":[40,66],"introducing":[41],"modified":[43],"QR-decomposition":[44],"with":[45,56],"QM-invariant,":[46],"i.e.,":[47],"$QMQ^T":[48],"M$.":[50],"One":[51],"main":[54],"advantages":[55],"this":[57],"approach":[58],"that":[60],"constraints":[62],"are":[63,78,106],"easily":[64],"incorporated":[65],"letting":[67],"corresponding":[69],"diagonal":[70],"elements":[71],"in":[72,123],"M":[73],"become":[74],"zero.":[75],"Householder":[76],"reflections":[77],"generalized":[79],"to":[80,108],"M-invariant":[81],"reflections,":[82],"and":[83,90,112,119],"an":[84],"algorithm":[85],"solving":[87],"constrained":[89],"described.":[97],"The":[98],"system":[99,104],"equations":[100],"(or":[101],"augmented":[103],"equations)":[105],"used":[107],"derive":[109],"condition":[110,117],"numbers,":[111],"connection":[114],"between":[115],"these":[116],"numbers":[118],"rounding":[121],"error":[122],"solution":[125],"investigated.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
