{"id":"https://openalex.org/W2089485155","doi":"https://doi.org/10.1137/110825753","title":"A Symmetry Preserving Algorithm for Matrix Scaling","display_name":"A Symmetry Preserving Algorithm for Matrix Scaling","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2089485155","doi":"https://doi.org/10.1137/110825753","mag":"2089485155"},"language":"en","primary_location":{"id":"doi:10.1137/110825753","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825753","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":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002885020","display_name":"Philip A. Knight","orcid":"https://orcid.org/0000-0001-9511-5692"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philip A. Knight","raw_affiliation_strings":["Department of Mathematics and Statistics [Univ Strathclyde]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics [Univ Strathclyde]","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106497787","display_name":"Daniel Ruiz","orcid":"https://orcid.org/0000-0002-3867-0179"},"institutions":[{"id":"https://openalex.org/I4387153255","display_name":"\u00c9cole Nationale Sup\u00e9rieure d'\u00c9lectrotechnique, d'\u00c9lectronique, d'Informatique, d'Hydraulique et des T\u00e9l\u00e9communications","ror":"https://ror.org/05wfw4946","country_code":"FR","type":"education","lineage":["https://openalex.org/I205747304","https://openalex.org/I4387153255"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniel Ruiz","raw_affiliation_strings":["Ecole Nationale Sup\u00e9rieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de T\u00e9l\u00e9communications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Nationale Sup\u00e9rieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de T\u00e9l\u00e9communications","institution_ids":["https://openalex.org/I4387153255"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106455635","display_name":"Bora U\u00e7ar","orcid":"https://orcid.org/0000-0002-4960-3545"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bora U\u00e7ar","raw_affiliation_strings":["Optimisation des ressources : mod\u00e8les, algorithmes et ordonnancement"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Optimisation des ressources : mod\u00e8les, algorithmes et ordonnancement","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.2179,"has_fulltext":true,"cited_by_count":73,"citation_normalized_percentile":{"value":0.99126349,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"35","issue":"3","first_page":"931","last_page":"955"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976000189781189,"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":0.758902370929718},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6648663282394409},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6431366801261902},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.595753014087677},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5863097906112671},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5674324631690979},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5255240797996521},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48983141779899597},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.418050616979599},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4168098568916321},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3783853054046631},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.332499623298645},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.2969422936439514},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16217559576034546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1374862790107727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.758902370929718},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6648663282394409},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6431366801261902},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.595753014087677},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5863097906112671},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5674324631690979},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5255240797996521},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48983141779899597},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.418050616979599},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4168098568916321},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3783853054046631},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.332499623298645},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.2969422936439514},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16217559576034546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1374862790107727},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/110825753","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825753","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:oatao.univ-toulouse.fr:22013","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:strathprints.strath.ac.uk:49349","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/19922.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:HAL:inria-00569250v4","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00569250","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2014, 35 (3), pp.25. &#x27E8;10.1137/110825753&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:oatao.univ-toulouse.fr:22013","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401987","display_name":"Open Archive Toulouse Archive Ouverte (University of Toulouse)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17866349","host_organization_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","host_organization_lineage":["https://openalex.org/I17866349"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4522132160","display_name":"SOLveurs et SimulaTIons en Calculs Extr\u00eame","funder_award_id":"ANR-06-CIS6-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1486210902","https://openalex.org/W1500921805","https://openalex.org/W1568175246","https://openalex.org/W1964061814","https://openalex.org/W1966824417","https://openalex.org/W1969526019","https://openalex.org/W1973166496","https://openalex.org/W1975457501","https://openalex.org/W1979710858","https://openalex.org/W1990283121","https://openalex.org/W1992907670","https://openalex.org/W1995393679","https://openalex.org/W1996042893","https://openalex.org/W2003447360","https://openalex.org/W2004972744","https://openalex.org/W2011848437","https://openalex.org/W2013429606","https://openalex.org/W2017431061","https://openalex.org/W2033460603","https://openalex.org/W2045361520","https://openalex.org/W2046040002","https://openalex.org/W2048403706","https://openalex.org/W2049013200","https://openalex.org/W2052602889","https://openalex.org/W2069849438","https://openalex.org/W2070299075","https://openalex.org/W2073320593","https://openalex.org/W2078675418","https://openalex.org/W2079639858","https://openalex.org/W2082205234","https://openalex.org/W2099438994","https://openalex.org/W2102368172","https://openalex.org/W2111577575","https://openalex.org/W2149454052","https://openalex.org/W2312355711","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2268131559","https://openalex.org/W27112594","https://openalex.org/W2393310703","https://openalex.org/W2153987743","https://openalex.org/W2086942802","https://openalex.org/W1664553927","https://openalex.org/W2351895651","https://openalex.org/W1982723514","https://openalex.org/W2060899753","https://openalex.org/W2012738485"],"abstract_inverted_index":{"We":[0,41,78],"present":[1],"an":[2,36],"iterative":[3],"algorithm":[4,23,46,84,119],"which":[5],"asymptotically":[6],"scales":[7],"the":[8,27,45,48,57,68,72,75,82,86,89,99,108,114,117],"$\\infty$-norm":[9],"of":[10,16,26,39,44,74,88,116],"each":[11,14],"row":[12],"and":[13,30,50,91,110],"column":[15],"a":[17],"matrix":[18,29,90],"to":[19,47,53],"one.":[20],"This":[21],"scaling":[22,83],"preserves":[24],"symmetry":[25],"original":[28],"shows":[31],"fast":[32],"linear":[33],"convergence":[34,64],"with":[35,67],"asymptotic":[37],"rate":[38,69],"1/2.":[40],"discuss":[42],"extensions":[43],"1-norm,":[49],"by":[51,97],"inference":[52],"other":[54],"norms.":[55],"For":[56],"1-norm":[58],"case,":[59],"we":[60],"show":[61],"again":[62],"that":[63,81,92],"is":[65],"linear,":[66],"dependent":[70],"on":[71],"spectrum":[73],"scaled":[76],"matrix.":[77],"demonstrate":[79],"experimentally":[80],"improves":[85],"conditioning":[87],"it":[93],"helps":[94],"direct":[95],"solvers":[96],"reducing":[98],"need":[100],"for":[101,105],"pivoting.":[102],"In":[103],"particular,":[104],"symmetric":[106],"matrices":[107],"theoretical":[109],"experimental":[111],"results":[112],"highlight":[113],"potential":[115],"proposed":[118],"over":[120],"existing":[121],"alternatives.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}
