{"id":"https://openalex.org/W7128724375","doi":"https://doi.org/10.48550/arxiv.2602.10424","title":"A Numerical Analysis of Sketched Linear Squares Problems and Stopping Criteria for Iterative Solvers","display_name":"A Numerical Analysis of Sketched Linear Squares Problems and Stopping Criteria for Iterative Solvers","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128724375","doi":"https://doi.org/10.48550/arxiv.2602.10424"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.10424","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"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/A5075750993","display_name":"Zhongxiao Jia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia, Zhongxiao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125717283","display_name":"Xinyuan Wan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wan, Xinyuan","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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.2079000025987625,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.2079000025987625,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.16329999268054962,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.05130000039935112,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.623199999332428},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5703999996185303},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5608000159263611},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5260999798774719},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5073999762535095},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5062999725341797},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47870001196861267},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46160000562667847},{"id":"https://openalex.org/keywords/iterative-refinement","display_name":"Iterative refinement","score":0.45730000734329224}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.623199999332428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985000133514404},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5703999996185303},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5608000159263611},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5260999798774719},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5156999826431274},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5073999762535095},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5062999725341797},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47870001196861267},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4528000056743622},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.446399986743927},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.41659998893737793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3962000012397766},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.30469998717308044},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.28999999165534973},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.10424","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.10424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.10424","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":"pmh:doi:10.48550/arxiv.2602.10424","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":{"Randomized":[0],"subspace":[1],"embedding":[2],"methods":[3],"have":[4],"had":[5],"a":[6,13,26,52,82,135,228],"great":[7],"impact":[8],"on":[9,55,69,85],"the":[10,35,38,46,56,70,86,89,93,96,103,109,112,117,125,128,132,147,151,156,164,187,199,207,213,219],"solution":[11,36,44,126,153],"of":[12,37,45,76,88,95,111,119,127,134,160,163,195],"linear":[14],"least":[15],"squares":[16],"(LS)":[17],"problem":[18,40,130,139,201],"by":[19],"reducing":[20],"its":[21,60],"row":[22],"dimension,":[23],"leading":[24],"to":[25,174],"randomized":[27],"or":[28],"sketched":[29],"LS":[30,47,97,138,165,200],"(sLS)":[31],"problem,":[32,58,189],"and":[33,64,73,98,144,155,166,178,203,216,225],"use":[34,75],"sLS":[39,57,99,113,129,167,188],"as":[41],"an":[42],"approximate":[43],"problem.":[48,114],"This":[49],"work":[50,223],"makes":[51],"numerical":[53],"analysis":[54],"establishes":[59],"numerous":[61],"theoretical":[62,170,214],"properties,":[63],"show":[65],"their":[66],"crucial":[67],"roles":[68],"most":[71],"effective":[72],"efficient":[74],"iterative":[77,184,196],"solvers.":[78],"We":[79],"first":[80,104],"establish":[81],"compact":[83],"bound":[84],"norm":[87],"residual":[90,158],"difference":[91],"between":[92],"solutions":[94],"problems,":[100],"which":[101,190],"is":[102,131],"key":[105],"result":[106,226],"towards":[107],"understanding":[108],"rationale":[110],"Then":[115],"from":[116],"perspective":[118],"backward":[120,142],"errors,":[121,154],"we":[122],"prove":[123],"that":[124,218],"one":[133],"certain":[136],"perturbed":[137],"with":[140],"minimal":[141],"error,":[143],"quantify":[145],"how":[146],"embedded":[148],"quality":[149],"affects":[150],"residuals,":[152],"relative":[157],"norms":[159],"normal":[161],"equations":[162],"problems.":[168],"These":[169],"results":[171],"enable":[172],"us":[173],"propose":[175],"new":[176,220],"novel":[177],"reliable":[179],"general-purpose":[180],"stopping":[181,221],"criteria":[182,222],"for":[183,186,198],"solvers":[185,197],"dynamically":[191],"monitor":[192],"stabilization":[193],"patterns":[194],"itself":[202],"terminate":[204],"them":[205],"at":[206],"earliest":[208],"iteration.":[209],"Numerical":[210],"experiments":[211],"justify":[212],"bounds":[215],"demonstrate":[217],"reliably":[224],"in":[227,231],"tremendous":[229],"reduction":[230],"computational":[232],"cost":[233],"without":[234],"sacrificing":[235],"attainable":[236],"accuracy.":[237]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-13T00:00:00"}