{"id":"https://openalex.org/W7151915255","doi":"https://doi.org/10.48550/arxiv.2604.05726","title":"On convergence of residual-based extended randomized Kaczmarz methods for matrix equations","display_name":"On convergence of residual-based extended randomized Kaczmarz methods for matrix equations","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7151915255","doi":"https://doi.org/10.48550/arxiv.2604.05726"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05726","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05726","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.05726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133189395","display_name":"Wendi Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bao, Wendi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133161738","display_name":"Jing Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Jing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133217278","display_name":"Lili Xing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xing, Lili","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126242708","display_name":"Weiguo Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Weiguo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133180388","display_name":"Jichao Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jichao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7735999822616577,"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":0.7735999822616577,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.14630000293254852,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.017000000923871994,"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/convergence","display_name":"Convergence (economics)","score":0.6852999925613403},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5285000205039978},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5236999988555908},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5134000182151794},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4392000138759613},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.3953000009059906},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.326200008392334}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.789900004863739},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6852999925613403},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5774000287055969},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5285000205039978},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5236999988555908},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4392000138759613},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.3953000009059906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3301999866962433},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.2809999883174896},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2529999911785126}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05726","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05726","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.05726","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05726","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"for":[3,42,53],"solving":[4],"inconsistent":[5],"matrix":[6],"equations":[7],"we":[8,32],"propose":[9],"a":[10,34],"dual-space":[11],"residual-based":[12],"randomized":[13],"extended":[14],"Kaczmarz":[15],"method":[16,76],"and":[17,38],"its":[18],"version":[19],"with":[20,77],"Nesterov":[21],"momentum.":[22,78],"Without":[23],"the":[24,43,47,54,63,71,75],"full":[25],"column":[26],"rank":[27],"assumptions":[28],"on":[29],"coefficient":[30],"matrices,":[31],"provide":[33],"thorough":[35],"convergence":[36,44],"analysis,":[37],"derive":[39],"upper":[40],"bounds":[41],"rates":[45],"of":[46],"new":[48],"methods.":[49],"A":[50],"feasible":[51],"range":[52],"momentum":[55],"parameters":[56],"is":[57],"determined.":[58],"Numerical":[59],"experiments":[60],"demonstrate":[61],"that":[62],"proposed":[64],"methods":[65],"are":[66],"much":[67],"more":[68],"effective":[69],"than":[70],"existing":[72],"ones,":[73],"especially":[74]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-09T00:00:00"}
