{"id":"https://openalex.org/W2047608802","doi":"https://doi.org/10.1177/109434209000400105","title":"Serial and Parallel Equilibration of Large-Scale Constrained Matrix Problems With Application To the Social and Economic Sciences","display_name":"Serial and Parallel Equilibration of Large-Scale Constrained Matrix Problems With Application To the Social and Economic Sciences","publication_year":1990,"publication_date":"1990-03-01","ids":{"openalex":"https://openalex.org/W2047608802","doi":"https://doi.org/10.1177/109434209000400105","mag":"2047608802"},"language":"en","primary_location":{"id":"doi:10.1177/109434209000400105","is_oa":false,"landing_page_url":"https://doi.org/10.1177/109434209000400105","pdf_url":null,"source":{"id":"https://openalex.org/S4210187582","display_name":"The International Journal of Supercomputing Applications","issn_l":"0890-2720","issn":["0890-2720"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Supercomputing 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/A5072294897","display_name":"Anna Nagurney","orcid":"https://orcid.org/0000-0002-1645-5363"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anna Nagurney","raw_affiliation_strings":["SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","School of Management, University of Massachusetts, Amherst, Massachusetts 01003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"School of Management, University of Massachusetts, Amherst, Massachusetts 01003","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103221173","display_name":"Dae\u2010Shik Kim","orcid":"https://orcid.org/0000-0002-9131-8086"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dae-Shik Kim","raw_affiliation_strings":["SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","School of Management, University of Massachusetts, Amherst, Massachusetts 01003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"School of Management, University of Massachusetts, Amherst, Massachusetts 01003","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048122262","display_name":"Alan Robinson","orcid":null},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan G. Robinson","raw_affiliation_strings":["SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","School of Management, University of Massachusetts, Amherst, Massachusetts 01003"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SCHOOL OF MANAGEMENT UNIVERSITY OF MASSACHUSETTS AMHERST,\rMASSACHUSETTS 01003","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"School of Management, University of Massachusetts, Amherst, Massachusetts 01003","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072294897"],"corresponding_institution_ids":["https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":38.3634,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.9980604,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"1","first_page":"49","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9451000094413757,"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/parallel-computing","display_name":"Parallel computing","score":0.6408981680870056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5711631178855896},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5239805579185486},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5145594477653503},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.49834465980529785},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4534658193588257},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.4526802897453308},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4494485557079315},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.444639652967453},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43615010380744934},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4354567229747772},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.43390321731567383},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3440440893173218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28000712394714355},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2309078872203827}],"concepts":[{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6408981680870056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5711631178855896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5239805579185486},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5145594477653503},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.49834465980529785},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4534658193588257},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.4526802897453308},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4494485557079315},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.444639652967453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43615010380744934},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4354567229747772},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.43390321731567383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3440440893173218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28000712394714355},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2309078872203827},{"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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1177/109434209000400105","is_oa":false,"landing_page_url":"https://doi.org/10.1177/109434209000400105","pdf_url":null,"source":{"id":"https://openalex.org/S4210187582","display_name":"The International Journal of Supercomputing Applications","issn_l":"0890-2720","issn":["0890-2720"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Supercomputing Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.umass.edu:math_faculty_pubs-1626","is_oa":false,"landing_page_url":"https://scholarworks.umass.edu/math_faculty_pubs/627","pdf_url":null,"source":{"id":"https://openalex.org/S4306402057","display_name":"Scholarworks (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Department Faculty Publication Series","raw_type":"text"},{"id":"pmh:oai:works.bepress.com:anna_nagurney-1067","is_oa":false,"landing_page_url":"https://works.bepress.com/anna_nagurney/68","pdf_url":null,"source":{"id":"https://openalex.org/S4306402240","display_name":"ScholarWorks@UMassAmherst (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Anna Nagurney","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W25587163","https://openalex.org/W228547482","https://openalex.org/W294645195","https://openalex.org/W1493472778","https://openalex.org/W1515086266","https://openalex.org/W1515342288","https://openalex.org/W1978456425","https://openalex.org/W1985248134","https://openalex.org/W1988859471","https://openalex.org/W1999001984","https://openalex.org/W2003260134","https://openalex.org/W2006122291","https://openalex.org/W2006222780","https://openalex.org/W2011013337","https://openalex.org/W2013615502","https://openalex.org/W2018672944","https://openalex.org/W2021285203","https://openalex.org/W2022393739","https://openalex.org/W2024983129","https://openalex.org/W2029420412","https://openalex.org/W2033619170","https://openalex.org/W2074610527","https://openalex.org/W2078675418","https://openalex.org/W2113015425","https://openalex.org/W2117379131","https://openalex.org/W2123825441","https://openalex.org/W2125913552","https://openalex.org/W2126257586","https://openalex.org/W2147380579","https://openalex.org/W2167137923","https://openalex.org/W2796628690","https://openalex.org/W2797434953","https://openalex.org/W2800289289","https://openalex.org/W3125212503"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2066731161","https://openalex.org/W1986195078","https://openalex.org/W2052835778","https://openalex.org/W1974990957","https://openalex.org/W4250743593","https://openalex.org/W2339733346","https://openalex.org/W2371352078","https://openalex.org/W2049003611","https://openalex.org/W2056770221"],"abstract_inverted_index":{"We":[0,77,98,126],"have":[1],"considered":[2],"the":[3,18,25,36,40,56,61,79,82,128,137,171,178,184,191],"computation":[4],"of":[5,60,81,87,162,195],"large-scale":[6],"con":[7],"strained":[8],"matrix":[9,146,197],"problems,":[10],"which":[11,54],"arise":[12],"in":[13,17,75,160,165],"numerous":[14],"ap":[15],"plications":[16],"social":[19],"and":[20,38,74,92,110,119,181],"economic":[21,116],"sciences\u2014in":[22],"par":[23],"ticular,":[24],"general":[26,185],"quadratic":[27,123],"problem":[28,62,147],"that":[29,69,86,94,143],"permits":[30],"alter":[31],"native":[32],"weighting":[33],"mechanisms":[34],"on":[35,115,120,136],"data":[37,117],"includes":[39],"much-studied":[41],"diagonal":[42,124,179],"problem.":[43],"The":[44,140],"procedure":[45],"uti":[46],"lized":[47],"is":[48],"row":[49],"equilibration,":[50],"column":[51],"equilibration":[52],"(RC),":[53],"exploits":[55],"bipartite":[57],"network":[58],"structure":[59],"by":[63],"decomposing":[64],"it":[65],"into":[66],"simpler":[67],"subproblems":[68],"can":[70,155],"be":[71,156],"solved":[72,157],"exactly":[73],"parallel.":[76],"compared":[78],"efficiency":[80,114],"RC":[83,95,101,129,159,173],"algorithm":[84,91,130,174],"to":[85],"a":[88,103,144,152,166],"well-":[89],"known":[90],"established":[93],"was":[96],"faster.":[97],"used":[99],"serial":[100,167],"as":[102,149,151],"benchmark":[104],"for":[105,177,183],"our":[106],"parallel":[107],"experi":[108],"mentation":[109],"investigated":[111],"its":[112],"absolute":[113],"sets":[118],"very":[121],"large":[122],"problems.":[125,186],"implemented":[127],"using":[131,158],"Par":[132],"allel":[133],"Fortran":[134],"Prototype":[135],"IBM":[138],"3090-600E.":[139],"results":[141,189],"demonstrate":[142],"constrained":[145,196],"with":[148,170],"many":[150],"million":[153],"variables":[154],"minutes":[161],"CPU":[163],"time":[164],"environment.":[168],"Speedups":[169],"parallelized":[172],"were":[175],"substantial":[176],"problems":[180],"moderate":[182],"These":[187],"computational":[188],"broaden":[190],"po":[192],"tential":[193],"domain":[194],"applications.":[198]},"counts_by_year":[],"updated_date":"2026-05-02T06:04:40.494371","created_date":"2025-10-10T00:00:00"}