{"id":"https://openalex.org/W2279865562","doi":"https://doi.org/10.1137/151005142","title":"Stability Analysis of the Two-level Orthogonal Arnoldi Procedure","display_name":"Stability Analysis of the Two-level Orthogonal Arnoldi Procedure","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2279865562","doi":"https://doi.org/10.1137/151005142","mag":"2279865562"},"language":"en","primary_location":{"id":"doi:10.1137/151005142","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151005142","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","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/A5102002819","display_name":"Ding Lu","orcid":"https://orcid.org/0009-0009-5493-0696"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ding Lu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101680116","display_name":"Yangfeng Su","orcid":"https://orcid.org/0000-0002-8744-1591"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yangfeng Su","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053733794","display_name":"Zhaojun Bai","orcid":"https://orcid.org/0000-0002-1143-2429"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaojun Bai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102002819"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9655,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.95506156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"1","first_page":"195","last_page":"214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11222","display_name":"Magnetic Properties and Applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8839372396469116},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.8748279809951782},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.8235101699829102},{"id":"https://openalex.org/keywords/soar","display_name":"Soar","score":0.7270486950874329},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.7160247564315796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6935487985610962},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6295433044433594},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6196886301040649},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.5343064069747925},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5138252377510071},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5014228820800781},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4865771532058716},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.38663363456726074},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3353051543235779},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24058517813682556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14167049527168274}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8839372396469116},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8748279809951782},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.8235101699829102},{"id":"https://openalex.org/C17305859","wikidata":"https://www.wikidata.org/wiki/Q382944","display_name":"Soar","level":2,"score":0.7270486950874329},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.7160247564315796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6935487985610962},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6295433044433594},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6196886301040649},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.5343064069747925},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5138252377510071},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5014228820800781},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4865771532058716},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.38663363456726074},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3353051543235779},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24058517813682556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14167049527168274},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/151005142","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151005142","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W35420751","https://openalex.org/W149759302","https://openalex.org/W210346111","https://openalex.org/W1506690472","https://openalex.org/W1537034094","https://openalex.org/W1563813142","https://openalex.org/W1605099509","https://openalex.org/W1679305771","https://openalex.org/W1966343138","https://openalex.org/W1971662204","https://openalex.org/W1981265672","https://openalex.org/W1985185971","https://openalex.org/W1990981972","https://openalex.org/W1995554391","https://openalex.org/W2007101284","https://openalex.org/W2014759801","https://openalex.org/W2020804487","https://openalex.org/W2037502605","https://openalex.org/W2040293765","https://openalex.org/W2040695471","https://openalex.org/W2041619874","https://openalex.org/W2041957061","https://openalex.org/W2042696716","https://openalex.org/W2051096875","https://openalex.org/W2052005273","https://openalex.org/W2059586807","https://openalex.org/W2095222360","https://openalex.org/W2114185620","https://openalex.org/W2129917554","https://openalex.org/W2144769419","https://openalex.org/W2150715511","https://openalex.org/W2151153690","https://openalex.org/W2243605038","https://openalex.org/W2342316458","https://openalex.org/W2798909945","https://openalex.org/W2946266054","https://openalex.org/W4240000608"],"related_works":["https://openalex.org/W2107329629","https://openalex.org/W2015942935","https://openalex.org/W2018896957","https://openalex.org/W1986035204","https://openalex.org/W2037894849","https://openalex.org/W2090501010","https://openalex.org/W2136866714","https://openalex.org/W3134028852","https://openalex.org/W2016713983","https://openalex.org/W2804908571"],"abstract_inverted_index":{"The":[0,45,100],"second-order":[1,15,32,120],"Arnoldi":[2,48],"(SOAR)":[3],"procedure":[4,40,50,85],"is":[5,86,108],"an":[6,10,55,91],"algorithm":[7],"for":[8],"computing":[9,90],"orthonormal":[11,92],"basis":[12,93],"of":[13,31,73,94,102,106,119],"the":[14,38,61,74,83,95,103],"Krylov":[16,98],"subspace.":[17,99],"It":[18],"has":[19,51],"found":[20],"applications":[21],"in":[22,89,114],"solving":[23],"quadratic":[24],"eigenvalue":[25],"problems":[26],"and":[27],"model":[28,116],"order":[29,117],"reduction":[30,118],"dynamical":[33,121],"systems":[34],"among":[35],"others.":[36],"Unfortunately,":[37],"SOAR":[39,58],"can":[41],"be":[42],"numerically":[43],"unstable.":[44],"two-level":[46],"orthogonal":[47],"(TOAR)":[49],"been":[52],"proposed":[53],"as":[54],"alternative":[56],"to":[57,59],"cure":[60],"numerical":[62],"instability.":[63],"In":[64],"this":[65],"paper,":[66],"we":[67],"provide":[68],"a":[69],"rigorous":[70],"stability":[71,105],"analysis":[72],"TOAR":[75,84,107],"procedure.":[76],"We":[77],"prove":[78],"that":[79],"under":[80],"mild":[81],"assumptions,":[82],"backward":[87,104],"stable":[88],"associated":[96],"linear":[97],"benefit":[101],"demonstrated":[109],"by":[110],"its":[111],"high":[112],"accuracy":[113],"structure-preserving":[115],"systems.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
