{"id":"https://openalex.org/W3133673702","doi":"https://doi.org/10.1137/19m1307044","title":"Greed Works: An Improved Analysis of Sampling Kaczmarz--Motzkin","display_name":"Greed Works: An Improved Analysis of Sampling Kaczmarz--Motzkin","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3133673702","doi":"https://doi.org/10.1137/19m1307044","mag":"3133673702"},"language":"en","primary_location":{"id":"doi:10.1137/19m1307044","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1307044","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/19m1307044","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048004087","display_name":"Jamie Haddock","orcid":"https://orcid.org/0000-0002-1449-2574"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jamie Haddock","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1449-2574","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103201778","display_name":"Anna Ma","orcid":"https://orcid.org/0000-0002-0099-053X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anna Ma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048004087"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3194,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.96256598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"342","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9998000264167786,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/greedy-algorithm","display_name":"Greedy algorithm","score":0.6540549397468567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6366931200027466},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.6114347577095032},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5733429789543152},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.545259952545166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5272164344787598},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4826374650001526},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4662906527519226},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4455907940864563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43242383003234863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32728564739227295},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3211537003517151},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.21334132552146912},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12821492552757263}],"concepts":[{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.6540549397468567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6366931200027466},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.6114347577095032},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5733429789543152},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.545259952545166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5272164344787598},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4826374650001526},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4662906527519226},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4455907940864563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43242383003234863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32728564739227295},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3211537003517151},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.21334132552146912},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12821492552757263},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1307044","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1307044","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/19m1307044","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1307044","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1477373385","display_name":null,"funder_award_id":"DMS-1522158","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G1871087456","display_name":null,"funder_award_id":"1740325","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3033480746","display_name":null,"funder_award_id":"FA9550-18-1-0031","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G444277139","display_name":null,"funder_award_id":"DMS-1348721","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4661397466","display_name":null,"funder_award_id":"DMS-1818969","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G5969482202","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W600180659","https://openalex.org/W1500306269","https://openalex.org/W1754711404","https://openalex.org/W1775859518","https://openalex.org/W1976661283","https://openalex.org/W1977769089","https://openalex.org/W1988844573","https://openalex.org/W1990919278","https://openalex.org/W1999437445","https://openalex.org/W2000748685","https://openalex.org/W2004042106","https://openalex.org/W2007691909","https://openalex.org/W2014513111","https://openalex.org/W2025424390","https://openalex.org/W2031822344","https://openalex.org/W2035080386","https://openalex.org/W2036835849","https://openalex.org/W2043324428","https://openalex.org/W2048305372","https://openalex.org/W2071903345","https://openalex.org/W2074796812","https://openalex.org/W2086580845","https://openalex.org/W2091826725","https://openalex.org/W2117905067","https://openalex.org/W2124637492","https://openalex.org/W2131023055","https://openalex.org/W2135294617","https://openalex.org/W2148778537","https://openalex.org/W2162287622","https://openalex.org/W2166417226","https://openalex.org/W2170166494","https://openalex.org/W2267771847","https://openalex.org/W2288570682","https://openalex.org/W2296319761","https://openalex.org/W2321466613","https://openalex.org/W2329579984","https://openalex.org/W2537224055","https://openalex.org/W2753690731","https://openalex.org/W2790998159","https://openalex.org/W2793070439","https://openalex.org/W2917867399","https://openalex.org/W2949745249","https://openalex.org/W2962890513","https://openalex.org/W2963227338","https://openalex.org/W2963584881","https://openalex.org/W2964345834","https://openalex.org/W2971685521","https://openalex.org/W2971790219","https://openalex.org/W2982556428","https://openalex.org/W2989951989","https://openalex.org/W3010837853","https://openalex.org/W3048811459","https://openalex.org/W3088745370","https://openalex.org/W3099862346","https://openalex.org/W3100892251","https://openalex.org/W3102157992","https://openalex.org/W3112635593","https://openalex.org/W3126008680"],"related_works":["https://openalex.org/W2313440505","https://openalex.org/W3123744736","https://openalex.org/W1505848319","https://openalex.org/W2137691148","https://openalex.org/W2905020035","https://openalex.org/W4281399881","https://openalex.org/W3166006430","https://openalex.org/W4281971614","https://openalex.org/W2184455175","https://openalex.org/W2186463938"],"abstract_inverted_index":{"Stochastic":[0],"iterative":[1],"algorithms":[2,65,100],"have":[3,101,105,175],"gained":[4],"recent":[5],"interest":[6],"in":[7,67],"machine":[8],"learning":[9],"and":[10,83,171],"signal":[11],"processing":[12],"for":[13,141],"solving":[14],"large-scale":[15],"systems":[16],"of":[17,35,48,78,81,90,121,124,146],"equations,":[18],"$A{x}={b}$.":[19],"One":[20],"such":[21],"example":[22],"is":[23,131],"the":[24,36,63,68,87,91,106,112,122,144,160],"randomized":[25],"Kaczmarz":[26],"(RK)":[27,126],"algorithm,":[28,72],"which":[29,73],"acts":[30],"only":[31],"on":[32,111],"single":[33],"rows":[34,80],"matrix":[37],"$A$":[38,49,82,173],"at":[39,168],"a":[40,46,57,75],"time.":[41],"While":[42],"RK":[43],"randomly":[44],"selects":[45,86],"row":[47,59,89],"to":[50,104,127],"work":[51,152],"with,":[52],"Motzkin's":[53],"Method":[54],"(MM)":[55,129],"employs":[56],"greedy":[58,128,148],"selection.":[60],"Connections":[61],"between":[62],"two":[64],"resulted":[66],"Sampling":[69],"Kaczmarz--Motzkin":[70],"(SKM)":[71],"samples":[74],"random":[76,125],"subset":[77],"$\\beta$":[79,164],"then":[84],"greedily":[85],"best":[88],"subset.":[92],"Despite":[93],"their":[94],"variable":[95],"computational":[96],"costs,":[97],"all":[98],"three":[99],"been":[102],"proven":[103],"same":[107],"theoretical":[108,161],"upper":[109],"bound":[110],"convergence":[113,139],"rate.":[114],"In":[115],"this":[116],"work,":[117],"an":[118],"improved":[119],"analysis":[120,134],"range":[123],"methods":[130],"presented.":[132],"This":[133,151],"improves":[135],"upon":[136],"previous":[137,156],"known":[138,157],"bounds":[140],"SKM,":[142],"capturing":[143],"benefit":[145],"partially":[147],"selection":[149],"schemes.":[150],"also":[153],"further":[154],"generalizes":[155],"results,":[158],"removing":[159],"assumptions":[162],"that":[163,172],"must":[165,174],"be":[166],"fixed":[167],"every":[169],"iteration":[170],"normalized":[176],"rows.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}