{"id":"https://openalex.org/W2066109609","doi":"https://doi.org/10.1137/s0895479897316576","title":"Accurate Solution of Weighted Least Squares by Iterative Methods","display_name":"Accurate Solution of Weighted Least Squares by Iterative Methods","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2066109609","doi":"https://doi.org/10.1137/s0895479897316576","mag":"2066109609"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479897316576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897316576","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/A5077998527","display_name":"Elena Y. Bobrovnikova","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Elena Y. Bobrovnikova","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018511273","display_name":"Stephen A. Vavasis","orcid":"https://orcid.org/0000-0003-1519-6264"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephen A. Vavasis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077998527"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.17792132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":"4","first_page":"1153","last_page":"1174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9973999857902527,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7411693930625916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5773354768753052},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5065609216690063},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.496916800737381},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.486800879240036},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4280223250389099},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35822874307632446}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7411693930625916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5773354768753052},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5065609216690063},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.496916800737381},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.486800879240036},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4280223250389099},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35822874307632446},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0895479897316576","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897316576","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:CiteSeerX.psu:10.1.1.49.6691","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.6691","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://info.mcs.anl.gov/pub/tech_reports/reports/P644.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.8527","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.8527","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.tc.cornell.edu/pub/tech.reports/tr268.ps","raw_type":"text"},{"id":"pmh:oai:ecommons.cornell.edu:1813/5598","is_oa":false,"landing_page_url":"https://hdl.handle.net/1813/5598","pdf_url":null,"source":{"id":"https://openalex.org/S4306400757","display_name":"eCommons (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"technical report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W18468166","https://openalex.org/W200888161","https://openalex.org/W1006400076","https://openalex.org/W1518039036","https://openalex.org/W1542258000","https://openalex.org/W1560263223","https://openalex.org/W1973061863","https://openalex.org/W1981745143","https://openalex.org/W1984302541","https://openalex.org/W1985536181","https://openalex.org/W1988840691","https://openalex.org/W2010315317","https://openalex.org/W2014168697","https://openalex.org/W2018850201","https://openalex.org/W2019814079","https://openalex.org/W2022852340","https://openalex.org/W2032368946","https://openalex.org/W2033180095","https://openalex.org/W2037785139","https://openalex.org/W2040728226","https://openalex.org/W2044820276","https://openalex.org/W2059969305","https://openalex.org/W2064538920","https://openalex.org/W2067941796","https://openalex.org/W2075665712","https://openalex.org/W2076201771","https://openalex.org/W2077875563","https://openalex.org/W2084743588","https://openalex.org/W2097897435","https://openalex.org/W2140153041","https://openalex.org/W2506034932","https://openalex.org/W2798909945","https://openalex.org/W4243297076","https://openalex.org/W4285719527","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W2075472361","https://openalex.org/W4239780814","https://openalex.org/W2100710931","https://openalex.org/W2057289358","https://openalex.org/W2412311587","https://openalex.org/W2040941802","https://openalex.org/W2084415399","https://openalex.org/W4238207569","https://openalex.org/W2339251345","https://openalex.org/W2013314297"],"abstract_inverted_index":{"We":[0,64,126],"consider":[1],"the":[2,47,51,54,79,110],"weighted":[3],"least-squares":[4],"(WLS)":[5],"problem":[6,40],"with":[7,41,122],"a":[8,38,83,100,106],"very":[9],"ill-conditioned":[10,42],"weight":[11],"matrix.":[12],"WLS":[13,39,73],"problems":[14],"arise":[15],"in":[16],"many":[17],"applications":[18],"including":[19],"linear":[20,103],"programming,":[21],"electrical":[22],"networks,":[23],"boundary":[24],"value":[25],"problems,":[26],"and":[27,56,89],"structures.":[28],"Because":[29],"of":[30,81,109,112],"roundoff":[31,113],"errors,":[32],"standard":[33],"iterative":[34,67],"methods":[35],"for":[36,71,130],"solving":[37,72],"weights":[43],"may":[44,61],"not":[45],"give":[46],"correct":[48],"answer.":[49],"Indeed,":[50],"difference":[52],"between":[53],"true":[55],"computed":[57],"solution":[58],"(forward":[59],"error)":[60],"be":[62],"large.":[63],"propose":[65],"an":[66],"algorithm,":[68],"called":[69],"MINRES-L,":[70],"problems.":[74],"The":[75],"MINRES-L":[76,118],"method":[77,85],"is":[78],"application":[80],"MINRES,":[82],"Krylov-space":[84],"due":[86],"to":[87,99],"Paige":[88],"Saunders":[90],"[SIAM":[91],"J.":[92],"Numer.":[93],"Anal.,":[94],"12":[95],"(1975),":[96],"pp.":[97],"617--629],":[98],"certain":[101],"layered":[102],"system.":[104],"Using":[105],"simplified":[107],"model":[108],"effects":[111],"error,":[114],"we":[115],"prove":[116],"that":[117],"ultimately":[119],"yields":[120],"answers":[121],"small":[123],"forward":[124],"error.":[125],"present":[127],"computational":[128],"experiments":[129],"some":[131],"applications.":[132]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}