{"id":"https://openalex.org/W1990351032","doi":"https://doi.org/10.1137/s0895479893253975","title":"A Restarted GMRES Method Augmented with Eigenvectors","display_name":"A Restarted GMRES Method Augmented with Eigenvectors","publication_year":1995,"publication_date":"1995-10-01","ids":{"openalex":"https://openalex.org/W1990351032","doi":"https://doi.org/10.1137/s0895479893253975","mag":"1990351032"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893253975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893253975","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/A5085879019","display_name":"Ronald B. Morgan","orcid":"https://orcid.org/0000-0002-0623-3740"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ronald B. Morgan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085879019"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4092,"has_fulltext":false,"cited_by_count":306,"citation_normalized_percentile":{"value":0.96919977,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"16","issue":"4","first_page":"1154","last_page":"1171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994000196456909,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.992900013923645,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9828336834907532},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.9151724576950073},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8232526779174805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.787142276763916},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7318648099899292},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6458710432052612},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5839143991470337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5493587255477905},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.507532000541687},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.49366816878318787},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4390425980091095},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.35652434825897217},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33775410056114197},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28231021761894226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1929481327533722},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07270991802215576}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9828336834907532},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.9151724576950073},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8232526779174805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.787142276763916},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7318648099899292},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6458710432052612},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5839143991470337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5493587255477905},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.507532000541687},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.49366816878318787},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4390425980091095},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.35652434825897217},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33775410056114197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28231021761894226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1929481327533722},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07270991802215576},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479893253975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893253975","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.385.9595","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.9595","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://bearspace.baylor.edu/Ronald_Morgan/www/papers/GMRES-E.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W101236918","https://openalex.org/W141418607","https://openalex.org/W1854226152","https://openalex.org/W1984283576","https://openalex.org/W1986914969","https://openalex.org/W1998366068","https://openalex.org/W2018850201","https://openalex.org/W2021810545","https://openalex.org/W2023488486","https://openalex.org/W2027764906","https://openalex.org/W2030963577","https://openalex.org/W2031635595","https://openalex.org/W2040298674","https://openalex.org/W2048659456","https://openalex.org/W2061813658","https://openalex.org/W2064616889","https://openalex.org/W2067712793","https://openalex.org/W2070462538","https://openalex.org/W2081696668","https://openalex.org/W2085259167","https://openalex.org/W2117366131","https://openalex.org/W2117686912","https://openalex.org/W2137029533","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2313084557","https://openalex.org/W2316564661","https://openalex.org/W4251074344","https://openalex.org/W4300938688"],"related_works":["https://openalex.org/W2000690703","https://openalex.org/W2042846224","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2484832770","https://openalex.org/W2040391781","https://openalex.org/W2002097440","https://openalex.org/W3152060313","https://openalex.org/W62853295"],"abstract_inverted_index":{"The":[0,62],"GMRES":[1],"method":[2],"for":[3,60],"solving":[4],"nonsymmetric":[5],"linear":[6],"equations":[7],"is":[8,26,40,73],"generally":[9],"used":[10],"with":[11],"restarting":[12],"to":[13,28,46,57],"reduce":[14],"storage":[15],"and":[16,55,68],"orthogonalization":[17],"costs.":[18],"Restarting":[19],"slows":[20],"down":[21],"the":[22,34,37,50,58,69],"convergence.":[23],"However,":[24],"it":[25],"possible":[27],"save":[29],"some":[30],"important":[31],"information":[32],"at":[33],"time":[35],"of":[36,49],"restart.":[38],"It":[39],"proposed":[41],"that":[42],"approximate":[43],"eigenvectors":[44],"corresponding":[45],"a":[47],"few":[48],"smallest":[51],"eigenvalues":[52],"be":[53,65],"formed":[54],"added":[56],"subspace":[59],"GMRES.":[61],"convergence":[63],"can":[64],"much":[66],"faster,":[67],"minimum":[70],"residual":[71],"property":[72],"retained.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":14}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
