{"id":"https://openalex.org/W2166627125","doi":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","title":"A parallel multisplitting solution of the least squares problem","display_name":"A parallel multisplitting solution of the least squares problem","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2166627125","doi":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","mag":"2166627125"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5033871686","display_name":"Rosemary A. Renaut","orcid":"https://orcid.org/0000-0001-9296-0890"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. A. Renaut","raw_affiliation_strings":["Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033871686"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.4909,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.68460196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"11","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955999851226807,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9937000274658203,"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":0.793958306312561},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.6931290030479431},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.6107581853866577},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5726319551467896},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5643254518508911},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5191799402236938},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.5132184028625488},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.506672203540802},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.47965648770332336},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4703020453453064},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4686882793903351},{"id":"https://openalex.org/keywords/total-least-squares","display_name":"Total least squares","score":0.4678317606449127},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46432891488075256},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4017508625984192},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38160479068756104},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.19248521327972412},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1730124056339264},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.12480130791664124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0955202579498291}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.793958306312561},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.6931290030479431},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.6107581853866577},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5726319551467896},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5643254518508911},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5191799402236938},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.5132184028625488},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.506672203540802},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.47965648770332336},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4703020453453064},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4686882793903351},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.4678317606449127},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46432891488075256},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4017508625984192},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38160479068756104},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.19248521327972412},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1730124056339264},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.12480130791664124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0955202579498291},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199801/02)5:1<11::aid-nla123>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W349985708","https://openalex.org/W1493749856","https://openalex.org/W1500921805","https://openalex.org/W1575701986","https://openalex.org/W1590879322","https://openalex.org/W1967281400","https://openalex.org/W1970261865","https://openalex.org/W1980792329","https://openalex.org/W2005470604","https://openalex.org/W2015032904","https://openalex.org/W2016182223","https://openalex.org/W2030942503","https://openalex.org/W2039522364","https://openalex.org/W2068514004","https://openalex.org/W2087314423","https://openalex.org/W2090963365","https://openalex.org/W4295016751","https://openalex.org/W4299512035","https://openalex.org/W4300938688","https://openalex.org/W6635394987","https://openalex.org/W6673553526"],"related_works":["https://openalex.org/W4380487384","https://openalex.org/W2388513917","https://openalex.org/W2123913166","https://openalex.org/W2034819163","https://openalex.org/W200101083","https://openalex.org/W1522321652","https://openalex.org/W2387406429","https://openalex.org/W3127498980","https://openalex.org/W2083446492","https://openalex.org/W1565959718"],"abstract_inverted_index":{"The":[0,28,40,172],"linear":[1],"least":[2,42,53,123,137],"squares":[3,43,54,124,138],"problem,":[4],"minx\u2225Ax":[5],"\u2212":[6],"b\u22252,":[7],"is":[8,21,45,98,176],"solved":[9,59],"by":[10,23,48,62,108],"applying":[11],"a":[12,49,136],"multisplitting":[13],"(MS)":[14],"strategy":[15,175],"in":[16,60],"which":[17,56,91,147,156],"the":[18,37,66,69,80,93,104,110,116,119,122,127,149,152,158],"system":[19],"matrix":[20,38],"decomposed":[22],"columns":[24],"into":[25],"p":[26],"blocks.":[27],"b":[29],"and":[30,167],"x":[31],"vectors":[32],"are":[33,72,106,145,170],"partitioned":[34],"consistently":[35],"with":[36,113],"decomposition.":[39],"global":[41,94,128],"problem":[44,125,139],"then":[46],"replaced":[47],"sequence":[50],"of":[51,83,118,140,151],"local":[52,70],"problems":[55,71],"can":[57,131],"be":[58,133,179],"parallel":[61],"MS.":[63],"In":[64],"MS":[65,174],"solutions":[67],"to":[68,77,115,162,178],"recombined":[73],"using":[74],"weighting":[75],"matrices":[76],"pick":[78],"out":[79],"appropriate":[81],"components":[82],"each":[84,96],"subproblem":[85,163],"solution.":[86],"A":[87],"new":[88],"two-stage":[89,173],"algorithm":[90,103],"optimizes":[92],"update":[95,112,129],"iteration":[97,159],"also":[99,132],"given.":[100,171],"For":[101,121],"this":[102],"updates":[105],"obtained":[107],"finding":[109],"optimal":[111],"respect":[114],"weights":[117],"recombination.":[120],"presented,":[126],"optimization":[130],"formulated":[134],"as":[135],"dimension":[141],"p.":[142],"Theoretical":[143],"results":[144,155],"presented":[146],"prove":[148],"convergence":[150,165],"iterations.":[153],"Numerical":[154],"detail":[157],"behavior":[160],"relative":[161],"size,":[164],"criteria":[166],"recombination":[168],"techniques":[169],"shown":[177],"effective":[180],"for":[181],"near-separable":[182],"problems.":[183],"\u00a9":[184],"1998":[185],"John":[186],"Wiley":[187],"&":[188],"Sons,":[189],"Ltd.":[190]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}