{"id":"https://openalex.org/W7214049592","doi":"https://doi.org/10.48550/arxiv.2609.24751","title":"Constraints on admissible behavior of GMRES applied to tridiagonal Toeplitz systems","display_name":"Constraints on admissible behavior of GMRES applied to tridiagonal Toeplitz systems","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214049592","doi":"https://doi.org/10.48550/arxiv.2609.24751"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24751","pdf_url":"https://arxiv.org/pdf/2609.24751","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.24751","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152472076","display_name":"Fei Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Fei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071268820","display_name":"Kirk M. Soodhalter","orcid":"https://orcid.org/0000-0003-0612-1199","observed_orcids":["https://orcid.org/0000-0003-0612-1199"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Soodhalter, Kirk M.","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":true,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":9.999999747378752e-05,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/gmres","display_name":"GMRES","score":0.9319999814033508},{"id":"https://openalex.org/keywords/tridiagonal-toeplitz-matrices","display_name":"tridiagonal Toeplitz matrices","score":0.9670000076293945},{"id":"https://openalex.org/keywords/non-hermitian-matrices","display_name":"non-Hermitian matrices","score":0.8679999709129333},{"id":"https://openalex.org/keywords/convergence-curves","display_name":"convergence curves","score":0.6600000262260437},{"id":"https://openalex.org/keywords/eigenvalues","display_name":"eigenvalues","score":0.5820000171661377},{"id":"https://openalex.org/keywords/structured-matrices","display_name":"structured matrices","score":0.46799999475479126}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.8720999956130981},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8102999925613403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7883999943733215},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6534000039100647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5428000092506409},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4383000135421753},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.43720000982284546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.375},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25839999318122864}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24751","pdf_url":"https://arxiv.org/pdf/2609.24751","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.24751","doi":"https://doi.org/10.48550/arxiv.2609.24751","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24751","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24751","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24751","pdf_url":"https://arxiv.org/pdf/2609.24751","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214049592.pdf","grobid_xml":"https://content.openalex.org/works/W7214049592.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2085912196","https://openalex.org/W7099895428","https://openalex.org/W2100726879","https://openalex.org/W7097121867","https://openalex.org/W6942309968","https://openalex.org/W1502304199","https://openalex.org/W2908133818","https://openalex.org/W7100621406","https://openalex.org/W2331268583","https://openalex.org/W7096118921"],"abstract_inverted_index":{"The":[0],"result":[1],"of":[2,12,25,31,42,53,106],"Greenbaum,":[3],"Pt\u00e1k,":[4,33],"and":[5,21,34,70],"Strako\u0161":[6,35],"that":[7,39,88,103],"for":[8,74],"a":[9,104],"given":[10],"set":[11],"eigenvalues,":[13],"any":[14],"convergence":[15],"curve":[16],"is":[17,109],"possible":[18],"[SIMAX":[19],"1996]":[20],"the":[22,40,43,51,68,93,95],"subsequent":[23],"parameterization":[24],"such":[26],"matrix-right-hand":[27],"side":[28],"pairs":[29],"$(A,\\mathbf{b})$":[30],"Arioli,":[32],"[BIT":[36],"1998]":[37],"demonstrated":[38],"behavior":[41,73],"GMRES":[44],"could":[45],"not":[46],"be":[47],"completely":[48],"characterized":[49],"by":[50],"eigenvalues":[52],"$A$":[54],"alone.":[55],"In":[56],"this":[57,64],"paper,":[58],"we":[59],"consider":[60],"how":[61,94],"to":[62,66],"use":[63],"theory":[65,96],"understand":[67],"admissible":[69,107],"attainable":[71],"\\gmres":[72],"matrices":[75],"with":[76],"constrained":[77],"structure,":[78],"focussing":[79],"on":[80],"non-Hermitian":[81],"(non-symmetric)":[82],"tridiagonal":[83],"Toeplitz":[84],"matrices.":[85],"We":[86],"show":[87],"Toeptliz":[89],"structure":[90],"necessarily":[91],"constrains":[92],"from":[97],"these":[98],"papers":[99],"can":[100],"manifest":[101],"but":[102],"continuum":[105],"behaviors":[108],"still":[110],"attainable.":[111]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-09-23T00:00:00"}
