{"id":"https://openalex.org/W2046040002","doi":"https://doi.org/10.1137/s0895479891222088","title":"Scaling Matrices to Prescribed Row and Column Maxima","display_name":"Scaling Matrices to Prescribed Row and Column Maxima","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2046040002","doi":"https://doi.org/10.1137/s0895479891222088","mag":"2046040002"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479891222088","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891222088","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/A5044612344","display_name":"Uriel G. Rothblum","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uriel G. Rothblum","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Hans Schneider","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hans Schneider","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011957337","display_name":"Michael Schneider","orcid":"https://orcid.org/0000-0001-9846-7132"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael H. Schneider","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.858,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.86001858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"1","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9646000266075134,"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":0.9646000266075134,"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/T11106","display_name":"Data Management and Algorithms","score":0.9562000036239624,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.9366000294685364,"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":0.8922144174575806},{"id":"https://openalex.org/keywords/maxima","display_name":"Maxima","score":0.8544789552688599},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.7771652936935425},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6720814108848572},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6719767451286316},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.6341469287872314},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6322495341300964},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.587371826171875},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5366937518119812},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.46632152795791626},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.4452197551727295},{"id":"https://openalex.org/keywords/main-diagonal","display_name":"Main diagonal","score":0.4204220473766327},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4113272428512573},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.39227113127708435},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14996305108070374},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09120842814445496}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8922144174575806},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.8544789552688599},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.7771652936935425},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6720814108848572},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6719767451286316},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.6341469287872314},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6322495341300964},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.587371826171875},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5366937518119812},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.46632152795791626},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.4452197551727295},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.4204220473766327},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4113272428512573},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.39227113127708435},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14996305108070374},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09120842814445496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C554144382","wikidata":"https://www.wikidata.org/wiki/Q213156","display_name":"Performance art","level":2,"score":0.0},{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479891222088","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891222088","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:10.1.1.178.6968","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.6968","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.wisc.edu/%7Ehans/paper_archive/other_papers/hs105.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1975457501","https://openalex.org/W1979013777","https://openalex.org/W1990283121","https://openalex.org/W1993954981","https://openalex.org/W2003447360","https://openalex.org/W2011848437","https://openalex.org/W2047354852","https://openalex.org/W2059949081","https://openalex.org/W2060220641","https://openalex.org/W2092040882","https://openalex.org/W2317672581","https://openalex.org/W2330701221","https://openalex.org/W4230627818","https://openalex.org/W4255280903"],"related_works":["https://openalex.org/W4230141039","https://openalex.org/W2161036871","https://openalex.org/W351236607","https://openalex.org/W2137006336","https://openalex.org/W2363023558","https://openalex.org/W2096672779","https://openalex.org/W2046608052","https://openalex.org/W2748456403","https://openalex.org/W3024316797","https://openalex.org/W2073200411"],"abstract_inverted_index":{"A":[0,46,173],"nonnegative":[1,43,170,209],"symmetric":[2,44],"matrix":[3,45,56,79,86,172,210,227],"B":[4,27],"has":[5,63,183],"row":[6,25,64,155,185,214],"maxima":[7,65],"prescribed":[8,66,184,213,231],"by":[9,67],"a":[10,41,53,78,168,208,226],"given":[11,42,169],"vector":[12,49],"r,":[13],"if":[14],"for":[15,40,148,167,206],"each":[16],"index":[17],"i,":[18],"the":[19,23,114,117,121,130,149,163,197,222],"maximum":[20],"entry":[21],"in":[22],"ith":[24],"of":[26,116,123,132,165,196,224],"equals":[28],"$r_i":[29],"$.":[30],"This":[31],"paper":[32,190],"presents":[33,191],"necessary":[34],"and":[35,47,102,104,127,142,178,186,215,218],"sufficient":[36],"conditions":[37,139,147],"so":[38],"that":[39,59,74,83,181],"positive":[48,54],"r":[50],"there":[51],"exists":[52],"diagonal":[55,135,175],"D":[57,80,177],"such":[58,77,85,180],"$B":[60],"=":[61],"DAD$":[62],"r.":[68],"Further,":[69],"an":[70,192],"algorithm":[71,89],"is":[72,113,120,129],"described":[73],"either":[75],"finds":[76],"or":[81],"shows":[82],"no":[84],"exists.":[87],"The":[88,137,157,189,199],"requires":[90],"$O(":[91,98,105],"n\\lg":[92],"n":[93,112],"+":[94],"p":[95,99,119],")$":[96,100,107],"comparisons,":[97],"multiplications":[101],"divisions,":[103],"q":[106,128],"square":[108],"root":[109],"calculations":[110],"where":[111],"order":[115],"matrix,":[118],"number":[122,131],"its":[124,133],"nonzero":[125,134],"elements,":[126],"elements.":[136],"solvability":[138,146],"are":[140,159,201,219],"compared":[141,202],"contrasted":[143],"with":[144,152],"known":[145],"analogous":[150,204],"problem":[151,164,223],"respect":[153],"to":[154,161,203,211,221],"sums.":[156],"results":[158,200,205],"applied":[160],"solve":[162],"determining":[166,225],"rectangular":[171],"positive,":[174],"matrices":[176],"E":[179],"$DAE$":[182],"column":[187,216],"maxima.":[188],"equivalent":[193],"graph":[194],"formulation":[195],"problem.":[198],"scaling":[207],"have":[212,230],"sums":[217],"extended":[220],"whose":[228],"rows":[229],"$l_p":[232],"$":[233],"norms.":[234]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}