{"id":"https://openalex.org/W2058927151","doi":"https://doi.org/10.1137/100799265","title":"Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides","display_name":"Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2058927151","doi":"https://doi.org/10.1137/100799265","mag":"2058927151"},"language":"en","primary_location":{"id":"doi:10.1137/100799265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100799265","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5085879019","display_name":"Ronald B. Morgan","orcid":"https://orcid.org/0000-0002-0623-3740"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronald B. Morgan","raw_affiliation_strings":["Ronald_Morgan@baylor.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ronald_Morgan@baylor.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068204016","display_name":"Dywayne A. Nicely","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dywayne A. Nicely","raw_affiliation_strings":["nicely@ohio.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"nicely@ohio.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9568,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.85823081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"5","first_page":"3037","last_page":"3056"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8654993176460266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7830529808998108},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.6342387199401855},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5636200308799744},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5141156315803528},{"id":"https://openalex.org/keywords/defective-matrix","display_name":"Defective matrix","score":0.48858222365379333},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.47991642355918884},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47740069031715393},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4448707103729248},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4164327383041382},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3282528817653656},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32570528984069824},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.15573275089263916},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.06463408470153809}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8654993176460266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7830529808998108},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.6342387199401855},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5636200308799744},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5141156315803528},{"id":"https://openalex.org/C36967811","wikidata":"https://www.wikidata.org/wiki/Q5251123","display_name":"Defective matrix","level":5,"score":0.48858222365379333},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.47991642355918884},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47740069031715393},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4448707103729248},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4164327383041382},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3282528817653656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32570528984069824},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.15573275089263916},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.06463408470153809},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100799265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100799265","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":55,"referenced_works":["https://openalex.org/W77858319","https://openalex.org/W101236918","https://openalex.org/W120643643","https://openalex.org/W612485192","https://openalex.org/W1506342804","https://openalex.org/W1563653928","https://openalex.org/W1588783887","https://openalex.org/W1638027600","https://openalex.org/W1964217357","https://openalex.org/W1970821534","https://openalex.org/W1975714268","https://openalex.org/W1979655951","https://openalex.org/W1980431326","https://openalex.org/W1982698949","https://openalex.org/W1984263725","https://openalex.org/W1986142001","https://openalex.org/W1990351032","https://openalex.org/W1995078542","https://openalex.org/W1995727286","https://openalex.org/W2009737642","https://openalex.org/W2012243521","https://openalex.org/W2014168697","https://openalex.org/W2025975230","https://openalex.org/W2027257397","https://openalex.org/W2031196824","https://openalex.org/W2035864055","https://openalex.org/W2040298674","https://openalex.org/W2040388588","https://openalex.org/W2042163658","https://openalex.org/W2047811252","https://openalex.org/W2048659456","https://openalex.org/W2052579356","https://openalex.org/W2059586807","https://openalex.org/W2067152104","https://openalex.org/W2069262775","https://openalex.org/W2070376917","https://openalex.org/W2071983880","https://openalex.org/W2073955633","https://openalex.org/W2074095860","https://openalex.org/W2074429407","https://openalex.org/W2074780612","https://openalex.org/W2077964086","https://openalex.org/W2094624803","https://openalex.org/W2095041371","https://openalex.org/W2117366131","https://openalex.org/W2117686912","https://openalex.org/W2123820077","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2167262293","https://openalex.org/W2462823246","https://openalex.org/W2610857016","https://openalex.org/W3103067505","https://openalex.org/W3122661961","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1970812947","https://openalex.org/W2156009096","https://openalex.org/W3176451595","https://openalex.org/W2027838537","https://openalex.org/W2058241770","https://openalex.org/W1980579360","https://openalex.org/W4248073715","https://openalex.org/W2095282848","https://openalex.org/W4243541541","https://openalex.org/W2044890344"],"abstract_inverted_index":{"A":[0,51],"restarted":[1],"nonsymmetric":[2],"Lanczos":[3],"algorithm":[4],"is":[5,25],"given":[6],"for":[7,44],"computing":[8],"eigenvalues":[9],"and":[10,13,47,87],"both":[11],"right":[12,86],"left":[14,88],"eigenvectors.":[15],"The":[16,85],"restarting":[17],"limits":[18],"the":[19,61,66,69,72,83,93],"storage":[20],"so":[21],"that":[22],"finding":[23],"eigenvectors":[24,70,89],"practical.":[26],"Restarting":[27],"also":[28],"makes":[29],"it":[30],"possible":[31],"to":[32,75,99],"deal":[33],"with":[34,60,103],"roundoff":[35],"error":[36],"in":[37,80],"new":[38],"ways.":[39],"We":[40],"give":[41],"a":[42],"scheme":[43],"avoiding":[45],"near-breakdown":[46],"discuss":[48],"maintaining":[49],"biorthogonality.":[50],"system":[52],"of":[53,68,82],"linear":[54,73,94],"equations":[55,74,95],"can":[56,96],"be":[57,97],"solved":[58],"simultaneously":[59],"eigenvalue":[62],"computations.":[63],"Deflation":[64],"from":[65],"presence":[67],"allows":[71],"generally":[76],"have":[77],"good":[78],"convergence":[79],"spite":[81],"restarting.":[84],"generated":[90],"while":[91],"solving":[92],"used":[98],"help":[100],"solve":[101],"systems":[102],"multiple":[104],"right-hand":[105],"sides.":[106]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
