{"id":"https://openalex.org/W7225626446","doi":"https://doi.org/10.4208/eajam.2025-198.310826","title":"A Block Rational Arnoldi Method for Solving Large-Scale Sylvester Equations","display_name":"A Block Rational Arnoldi Method for Solving Large-Scale Sylvester Equations","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225626446","doi":"https://doi.org/10.4208/eajam.2025-198.310826"},"language":"en","primary_location":{"id":"doi:10.4208/eajam.2025-198.310826","doi":"https://doi.org/10.4208/eajam.2025-198.310826","is_oa":false,"landing_page_url":"https://doi.org/10.4208/eajam.2025-198.310826","pdf_url":null,"source":{"id":"https://openalex.org/S2504294749","display_name":"East Asian Journal on Applied Mathematics","issn_l":"2079-7362","issn":["2079-7362","2079-7370"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"East Asian Journal on Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161338511","display_name":"Song Nie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song Nie","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102023258","display_name":"Hua Dai","orcid":"https://orcid.org/0000-0003-2983-8627","observed_orcids":["https://orcid.org/0000-0003-2983-8627"]},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Dai","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"3","first_page":"649","last_page":"672"},"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/T13487","display_name":"Statistical and numerical algorithms","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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sylvester-equation","display_name":"Sylvester equation","score":0.9190000295639038},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"low-rank approximation","score":0.8479999899864197},{"id":"https://openalex.org/keywords/large-scale-linear-systems","display_name":"large-scale linear systems","score":0.7889999747276306},{"id":"https://openalex.org/keywords/matrix-factorization","display_name":"matrix factorization","score":0.8080000281333923}],"concepts":[{"id":"https://openalex.org/C20160815","wikidata":"https://www.wikidata.org/wiki/Q1482452","display_name":"Sylvester matrix","level":5,"score":0.6640999913215637},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6564000248908997},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6180999875068665},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5989000201225281},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5710999965667725},{"id":"https://openalex.org/C100468782","wikidata":"https://www.wikidata.org/wiki/Q3730848","display_name":"Sylvester equation","level":3,"score":0.5658000111579895},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5622000098228455},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5540000200271606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5353000164031982},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5113999843597412},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.4242999851703644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3580999970436096},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.322299987077713},{"id":"https://openalex.org/C56828936","wikidata":"https://www.wikidata.org/wiki/Q1752621","display_name":"Sylvester's law of inertia","level":4,"score":0.29429998993873596}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4208/eajam.2025-198.310826","doi":"https://doi.org/10.4208/eajam.2025-198.310826","is_oa":false,"landing_page_url":"https://doi.org/10.4208/eajam.2025-198.310826","pdf_url":null,"source":{"id":"https://openalex.org/S2504294749","display_name":"East Asian Journal on Applied Mathematics","issn_l":"2079-7362","issn":["2079-7362","2079-7370"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"East Asian Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W316055377","https://openalex.org/W574171861","https://openalex.org/W1488435683","https://openalex.org/W1506342804","https://openalex.org/W1551480811","https://openalex.org/W1561849568","https://openalex.org/W1580973103","https://openalex.org/W1591076264","https://openalex.org/W1654663724","https://openalex.org/W1659539761","https://openalex.org/W1978115611","https://openalex.org/W1986448409","https://openalex.org/W1996271504","https://openalex.org/W2000118250","https://openalex.org/W2016891181","https://openalex.org/W2022615414","https://openalex.org/W2024384195","https://openalex.org/W2033029203","https://openalex.org/W2033307991","https://openalex.org/W2041118838","https://openalex.org/W2052604766","https://openalex.org/W2054689585","https://openalex.org/W2056589646","https://openalex.org/W2065635671","https://openalex.org/W2075097820","https://openalex.org/W2081128548","https://openalex.org/W2085881863","https://openalex.org/W2086590360","https://openalex.org/W2088748973","https://openalex.org/W2097660079","https://openalex.org/W2117799929","https://openalex.org/W2120972041","https://openalex.org/W2136556155","https://openalex.org/W2140153041","https://openalex.org/W2152896489","https://openalex.org/W2154062528","https://openalex.org/W2167262293","https://openalex.org/W2168947999","https://openalex.org/W2345047788","https://openalex.org/W2480611454","https://openalex.org/W2584548894","https://openalex.org/W2609701076","https://openalex.org/W2735961795","https://openalex.org/W2769190193","https://openalex.org/W2889970546","https://openalex.org/W2924691308","https://openalex.org/W2962856060","https://openalex.org/W2970193614","https://openalex.org/W3044382531","https://openalex.org/W4392517295"],"related_works":["https://openalex.org/W2001876169","https://openalex.org/W2945169821","https://openalex.org/W1580973103","https://openalex.org/W1973485705","https://openalex.org/W4403018702","https://openalex.org/W2041118838","https://openalex.org/W2391931735","https://openalex.org/W2181446379","https://openalex.org/W2115779696","https://openalex.org/W1988736270"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,21,72],"concerned":[3],"with":[4,60],"the":[5,10,24,32,54,61,84,87],"low-rank":[6],"approximate":[7,62],"solution":[8,63],"of":[9,86],"large-scale":[11,25],"Sylvester":[12,26],"matrix":[13,27,49],"equations.":[14],"A":[15],"simple":[16],"block":[17,33],"rational":[18,34],"Arnoldi":[19],"decomposition":[20],"derived,":[22],"and":[23,56,66,69],"equations":[28],"are":[29,40,64,80],"projected":[30,38],"into":[31],"Krylov":[35],"subspace.":[36],"The":[37],"problems":[39],"solved":[41],"by":[42],"using":[43],"some":[44],"direct":[45],"methods":[46],"based":[47],"on":[48],"factorizations.":[50],"Some":[51],"estimates":[52],"for":[53,74],"residual":[55],"error":[57],"norms":[58],"associated":[59],"provided,":[65],"a":[67],"reasonable":[68],"effective":[70],"rule":[71],"proposed":[73,88],"selecting":[75],"shift":[76],"parameters.":[77],"Experimental":[78],"results":[79],"included":[81],"to":[82],"demonstrate":[83],"efficiency":[85],"method.":[89]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
