{"id":"https://openalex.org/W1979952360","doi":"https://doi.org/10.1137/s0895479898336306","title":"Upper Perturbation Bounds of Weighted Projections, Weighted and Constrained Least Squares Problems","display_name":"Upper Perturbation Bounds of Weighted Projections, Weighted and Constrained Least Squares Problems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1979952360","doi":"https://doi.org/10.1137/s0895479898336306","mag":"1979952360"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479898336306","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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":false,"raw_author_name":"Musheng Wei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103402401","display_name":"Alvaro R. De Pierro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alvaro R. De Pierro","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.526,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":30,"citation_normalized_percentile":{"value":0.808476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":89},"biblio":{"volume":"21","issue":"3","first_page":"931","last_page":"951"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9999,"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":0.9999,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9979,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9975,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4684534},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite Programming","score":0.4447381},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4327644}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8609315},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.654259},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6042297},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.57318246},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5009351},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4684534},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45902663},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4447381},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.44324243},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4327644},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38919917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2747058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21788827},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12966907},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10163537},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.08293733},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07147583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479898336306","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":21,"referenced_works":["https://openalex.org/W1964867652","https://openalex.org/W1975050092","https://openalex.org/W1988840691","https://openalex.org/W2017666390","https://openalex.org/W2023782398","https://openalex.org/W2024558657","https://openalex.org/W2036622774","https://openalex.org/W2040517289","https://openalex.org/W2044820276","https://openalex.org/W2046222402","https://openalex.org/W2046696187","https://openalex.org/W2055576996","https://openalex.org/W2064583534","https://openalex.org/W2065138478","https://openalex.org/W2077875563","https://openalex.org/W2083715802","https://openalex.org/W2084743588","https://openalex.org/W2103934737","https://openalex.org/W2139002888","https://openalex.org/W2150200785","https://openalex.org/W83404773"],"related_works":["https://openalex.org/W2386411162","https://openalex.org/W2269291726","https://openalex.org/W2239063252","https://openalex.org/W2185334956","https://openalex.org/W2128202699","https://openalex.org/W2121045497","https://openalex.org/W2036562274","https://openalex.org/W2014318473","https://openalex.org/W1997197201","https://openalex.org/W1985090152"],"abstract_inverted_index":{"At":[0],"each":[1],"iteration":[2],"step":[3],"for":[4],"solving":[5],"mathematical":[6],"programming":[7],"and":[8,36,65,86,115],"constrained":[9,37],"optimization":[10],"problems":[11,88,117],"by":[12],"using":[13],"interior-point":[14],"methods,":[15],"one":[16],"often":[17],"needs":[18],"to":[19,48,106,129],"solve":[20],"the":[21,34,84,93,127,130],"weighted":[22,35,80],"least":[23,38],"squares":[24,39],"(WLS)":[25],"problem":[26,41],"$\\min_{x":[27],"\\in":[28,44],"R^n}\\|":[29],"W^{1":[30],"\\over":[31],"2}(Ax-b)\\|$,":[32],"or":[33],"(WLSE)":[40],"$\\min_{":[42],"x":[43],"R^n}\\|W^{1\\over":[45],"2}(Kx-g)\\|$":[46],"subject":[47],"Lx=h,":[49],"where":[50],"W=":[51],"diag(w1":[52],",":[53,57],".":[54,55,56],"wl)>0":[58],"in":[59],"which":[60],"some":[61,66],"$w_i\\rightarrow":[62,67],"+\\infty":[63],"$":[64],"0$.":[68],"\\par":[69],"In":[70],"this":[71],"paper":[72],"we":[73],"will":[74],"derive":[75],"upper":[76,108],"perturbation":[77,109],"bounds":[78,105,110],"of":[79,97,111,113,138],"projections":[81],"associated":[82],"with":[83],"WLS":[85,114],"WLSE":[87,116],"when":[89,118,132],"W":[90,119,133],"ranges":[91,120,134],"over":[92,121,135],"set":[94],"$\\cal":[95,122],"D$":[96],"positive":[98,141],"diagonal":[99],"matrices.":[100,143],"We":[101,124],"then":[102],"apply":[103],"these":[104],"deduce":[107],"solutions":[112],"D$.":[123],"also":[125],"extend":[126],"estimates":[128],"cases":[131],"a":[136],"subset":[137],"real":[139],"symmetric":[140],"semidefinite":[142]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1979952360","counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-02-19T20:24:51.385889","created_date":"2016-06-24"}