{"id":"https://openalex.org/W7133339946","doi":"https://doi.org/10.48550/arxiv.2603.00419","title":"Inexact versions of several block-splitting preconditioners for indefinite least squares problems","display_name":"Inexact versions of several block-splitting preconditioners for indefinite least squares problems","publication_year":2026,"publication_date":"2026-02-28","ids":{"openalex":"https://openalex.org/W7133339946","doi":"https://doi.org/10.48550/arxiv.2603.00419"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00419","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00419","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"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":"https://doi.org/10.48550/arxiv.2603.00419","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128014847","display_name":"Mohaddese Kaveh Shaldehi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shaldehi, Mohaddese Kaveh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023732680","display_name":"Davod Khojasteh Salkuyeh","orcid":"https://orcid.org/0000-0003-0228-8565"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Salkuyeh, Davod Khojasteh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9914000034332275,"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":0.9914000034332275,"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":0.002099999925121665,"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":0.0010999999940395355,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7361999750137329},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5989000201225281},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5809999704360962},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.48100000619888306},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.46889999508857727},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4587000012397766},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.45559999346733093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8525999784469604},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7361999750137329},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6425999999046326},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5989000201225281},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5809999704360962},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.48100000619888306},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.46889999508857727},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4587000012397766},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.45559999346733093},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32330000400543213},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.29120001196861267},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C126090379","wikidata":"https://www.wikidata.org/wiki/Q6094424","display_name":"Iteratively reweighted least squares","level":4,"score":0.2583000063896179}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00419","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00419","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.00419","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00419","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"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":{"This":[0,62],"paper":[1],"introduces":[2],"inexact":[3],"versions":[4],"of":[5,21,47,74,83,98,112],"several":[6],"block-splitting":[7],"preconditioners":[8,67],"for":[9,32,101],"solving":[10,102],"the":[11,29,33,48,72,75,81,84,96,103,110,113],"three-by-three":[12],"block":[13],"linear":[14],"systems":[15],"arising":[16],"from":[17],"a":[18,54,91],"special":[19],"class":[20],"indefinite":[22],"least":[23],"squares":[24],"problems.":[25],"We":[26],"first":[27],"establish":[28],"convergence":[30,73],"conditions":[31],"corresponding":[34],"stationary":[35],"iterative":[36],"methods.":[37],"Then,":[38],"it":[39],"follows":[40],"that":[41,65],"under":[42],"these":[43,66],"conditions,":[44],"all":[45],"eigenvalues":[46],"preconditioned":[49,85,104],"matrices":[50,86],"are":[51,68],"contained":[52],"within":[53],"circle":[55],"centered":[56],"at":[57],"$(1,0)$":[58],"with":[59],"radius":[60],"$1$.":[61],"property":[63],"implies":[64],"effective":[69],"in":[70,87],"accelerating":[71],"GMRES":[76,99],"method.":[77],"Furthermore,":[78],"we":[79],"analyze":[80],"eigenpairs":[82],"detail":[88],"and":[89],"derive":[90],"theoretical":[92],"upper":[93],"bound":[94],"on":[95],"number":[97],"iterations":[100],"systems.":[105],"Ultimately,":[106],"numerical":[107],"experiments":[108],"reveal":[109],"efficacy":[111],"proposed":[114],"preconditioners.":[115]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-04T00:00:00"}
