{"id":"https://openalex.org/W7109137488","doi":"https://doi.org/10.1145/3779224","title":"Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm","display_name":"Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm","publication_year":2025,"publication_date":"2025-12-06","ids":{"openalex":"https://openalex.org/W7109137488","doi":"https://doi.org/10.1145/3779224"},"language":"en","primary_location":{"id":"doi:10.1145/3779224","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3779224","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3779224","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xufeng Cai","orcid":"https://orcid.org/0009-0007-4379-6204"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xufeng Cai","raw_affiliation_strings":["Department of Computer Sciences, University of Wisconsin-Madison"],"raw_orcid":"https://orcid.org/0009-0007-4379-6204","affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jason Altschuler","orcid":"https://orcid.org/0000-0001-7367-0097"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jason Altschuler","raw_affiliation_strings":["Department of Statistics and Data Science, University of Pennsylvania"],"raw_orcid":"https://orcid.org/0000-0001-7367-0097","affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, University of Pennsylvania","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jelena Diakonikolas","orcid":"https://orcid.org/0000-0003-3439-0310"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jelena Diakonikolas","raw_affiliation_strings":["Department of Computer Sciences, University of Wisconsin-Madison"],"raw_orcid":"https://orcid.org/0000-0003-3439-0310","affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58922419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"1","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.6823999881744385,"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":0.6823999881744385,"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/T12303","display_name":"Tensor decomposition and applications","score":0.09669999778270721,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.055399999022483826,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.6891000270843506},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6248999834060669},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.623199999332428},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5929999947547913},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5703999996185303},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5558000206947327},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5527999997138977},{"id":"https://openalex.org/keywords/iterative-refinement","display_name":"Iterative refinement","score":0.45489999651908875},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.41780000925064087}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7239000201225281},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.6891000270843506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.673799991607666},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6248999834060669},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.623199999332428},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5929999947547913},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5703999996185303},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5558000206947327},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5527999997138977},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.41780000925064087},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3871999979019165},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C2778400913","wikidata":"https://www.wikidata.org/wiki/Q1639024","display_name":"Mathematical software","level":3,"score":0.34470000863075256},{"id":"https://openalex.org/C109565186","wikidata":"https://www.wikidata.org/wiki/Q6766437","display_name":"Eigenvalue algorithm","level":5,"score":0.33799999952316284},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2953000068664551},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.28790000081062317},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28600001335144043},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.2727999985218048},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2547000050544739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3779224","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3779224","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3779224","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3779224","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1993677524","https://openalex.org/W2000769684","https://openalex.org/W2023901033","https://openalex.org/W2054027956","https://openalex.org/W2069188165","https://openalex.org/W2070461982","https://openalex.org/W2083408955","https://openalex.org/W2118382442","https://openalex.org/W2120516507","https://openalex.org/W2312355711","https://openalex.org/W2614899618","https://openalex.org/W2979298859","https://openalex.org/W3006529314","https://openalex.org/W3008055938","https://openalex.org/W3015540189","https://openalex.org/W3105140593","https://openalex.org/W3181224955","https://openalex.org/W4206471589","https://openalex.org/W4252461740","https://openalex.org/W4252973173","https://openalex.org/W4388263504"],"related_works":[],"abstract_inverted_index":{"In":[0,95],"1960,":[1],"Osborne":[2],"proposed":[3],"a":[4,122,139],"simple":[5],"iterative":[6],"algorithm":[7,52,82,149],"for":[8,30,58,147,169],"matrix":[9,115],"balancing":[10,116],"with":[11,83],"outstanding":[12],"numerical":[13],"performance.":[14],"Today,":[15],"it":[16],"is":[17,129,143],"the":[18,61,69,132,144,154,166],"default":[19],"preconditioning":[20],"procedure":[21],"before":[22],"eigenvalue":[23,160],"computation":[24],"and":[25,45,72,105,162],"other":[26,171],"linear":[27],"algebra":[28],"subroutines":[29],"square":[31],"non-symmetric":[32],"matrices":[33],"in":[34,68,118,131],"mainstream":[35],"software":[36],"packages":[37],"such":[38],"as":[39],"Python,":[40],"Julia,":[41],"MATLAB,":[42],"EISPACK,":[43],"LAPACK,":[44],"more.":[46],"Despite":[47],"its":[48,59],"widespread":[49],"usage,":[50],"Osborne\u2019s":[51,81,110,148,174],"has":[53,121],"long":[54],"resisted":[55],"theoretical":[56,167],"guarantees":[57,64],"runtime:":[60],"first":[62,145],"polynomial-time":[63],"were":[65],"obtained":[66],"only":[67],"past":[70],"decade,":[71],"recent":[73],"near-linear":[74,123],"runtimes":[75,168],"remain":[76],"confined":[77],"to":[78,90,136],"variants":[79,172],"of":[80,156,173],"important":[84],"differences":[85],"that":[86,109,150],"make":[87],"them":[88],"simpler":[89],"analyze":[91],"but":[92],"empirically":[93],"slower.":[94],"this":[96,100],"paper,":[97],"we":[98],"address":[99],"longstanding":[101],"gap":[102],"between":[103],"theory":[104],"practice":[106],"by":[107],"proving":[108],"original":[111],"algorithm\u2014the":[112],"de":[113],"facto":[114],"preconditioner":[117],"practice\u2014in":[119],"fact":[120],"runtime.":[124],"This":[125],"runtime":[126,146,155],"guarantee":[127],"(1)":[128],"optimal":[130],"input":[133],"size":[134],"up":[135],"at":[137],"most":[138],"single":[140],"logarithm,":[141],"(2)":[142],"does":[151],"not":[152],"dominate":[153],"downstream":[157],"tasks":[158],"like":[159],"computation,":[161],"(3)":[163],"improves":[164],"upon":[165],"all":[170],"algorithm.":[175]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-12-06T00:00:00"}
