{"id":"https://openalex.org/W2047263139","doi":"https://doi.org/10.1007/s11075-014-9891-3","title":"The role eigenvalues play in forming GMRES residual norms with non-normal matrices","display_name":"The role eigenvalues play in forming GMRES residual norms with non-normal matrices","publication_year":2014,"publication_date":"2014-07-15","ids":{"openalex":"https://openalex.org/W2047263139","doi":"https://doi.org/10.1007/s11075-014-9891-3","mag":"2047263139"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-014-9891-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9891-3","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5038039221","display_name":"G\u00e9rard Meurant","orcid":"https://orcid.org/0000-0002-6036-3482"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G\u00e9rard Meurant","raw_affiliation_strings":["30 rue du sergent Bauchat, 75012, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"30 rue du sergent Bauchat, 75012, Paris, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022706753","display_name":"Jurjen Duintjer Tebbens","orcid":"https://orcid.org/0000-0003-0553-854X"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"id":"https://openalex.org/I4210137570","display_name":"University Hospital Hradec Kr\u00e1lov\u00e9","ror":"https://ror.org/04wckhb82","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I4210137570"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I75092371","display_name":"University of Hradec Kr\u00e1lov\u00e9","ror":"https://ror.org/05k238v14","country_code":"CZ","type":"education","lineage":["https://openalex.org/I75092371"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Jurjen Duintjer Tebbens","raw_affiliation_strings":["Faculty of Pharmacy in Hradec Kr\u00e1lov\u00e9, Charles University in Prague, Heyrovsk\u00e9ho 1203, 500 05, Hradec Kr\u00e1lov\u00e9, Czech Republic","Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 2, 18 207 Praha 8, Libe\u0148, Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Pharmacy in Hradec Kr\u00e1lov\u00e9, Charles University in Prague, Heyrovsk\u00e9ho 1203, 500 05, Hradec Kr\u00e1lov\u00e9, Czech Republic","institution_ids":["https://openalex.org/I75092371","https://openalex.org/I21250087","https://openalex.org/I4210137570"]},{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 2, 18 207 Praha 8, Libe\u0148, Prague, Czech Republic","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022706753"],"corresponding_institution_ids":["https://openalex.org/I202391551","https://openalex.org/I21250087","https://openalex.org/I4210137570","https://openalex.org/I4210155092","https://openalex.org/I75092371"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.5591,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89452118,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"1","first_page":"143","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T13487","display_name":"Statistical and numerical algorithms","score":0.9811000227928162,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9508931636810303},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8882923126220703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7871631979942322},{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.7760587930679321},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7111931443214417},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6073875427246094},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.4609975814819336},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4385266602039337},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.434771329164505},{"id":"https://openalex.org/keywords/spectrum-of-a-matrix","display_name":"Spectrum of a matrix","score":0.42922961711883545},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3615074157714844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32736122608184814},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3239750862121582},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.19198811054229736},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12729579210281372},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1266855001449585}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9508931636810303},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8882923126220703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7871631979942322},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.7760587930679321},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7111931443214417},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6073875427246094},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.4609975814819336},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4385266602039337},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.434771329164505},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.42922961711883545},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3615074157714844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32736122608184814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3239750862121582},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.19198811054229736},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12729579210281372},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1266855001449585},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11075-014-9891-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-014-9891-3","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:asep.lib.cas.cz:CavUnEpca/0430466","is_oa":false,"landing_page_url":"http://hdl.handle.net/11104/0235396","pdf_url":null,"source":{"id":"https://openalex.org/S7407055266","display_name":"ASEP","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W111644255","https://openalex.org/W149522324","https://openalex.org/W175988912","https://openalex.org/W1486449984","https://openalex.org/W1499179128","https://openalex.org/W1506342804","https://openalex.org/W1586935952","https://openalex.org/W1669374329","https://openalex.org/W1974565581","https://openalex.org/W1975714268","https://openalex.org/W1977061454","https://openalex.org/W1981908221","https://openalex.org/W1990351032","https://openalex.org/W1998574793","https://openalex.org/W1999476674","https://openalex.org/W2001911203","https://openalex.org/W2002358614","https://openalex.org/W2003215511","https://openalex.org/W2006651457","https://openalex.org/W2011389520","https://openalex.org/W2011561517","https://openalex.org/W2012547784","https://openalex.org/W2015326532","https://openalex.org/W2018627399","https://openalex.org/W2022056161","https://openalex.org/W2022844944","https://openalex.org/W2036735300","https://openalex.org/W2038904701","https://openalex.org/W2039576693","https://openalex.org/W2041786636","https://openalex.org/W2043348215","https://openalex.org/W2044262951","https://openalex.org/W2046160677","https://openalex.org/W2046982553","https://openalex.org/W2051133095","https://openalex.org/W2052579356","https://openalex.org/W2053893326","https://openalex.org/W2053939418","https://openalex.org/W2057359548","https://openalex.org/W2084864145","https://openalex.org/W2094437101","https://openalex.org/W2097897435","https://openalex.org/W2128836543","https://openalex.org/W2132719389","https://openalex.org/W2137029533","https://openalex.org/W2140153041","https://openalex.org/W2316564661","https://openalex.org/W4247112247"],"related_works":["https://openalex.org/W2094437101","https://openalex.org/W2077060636","https://openalex.org/W2364353629","https://openalex.org/W2478378501","https://openalex.org/W2018627399","https://openalex.org/W1971116595","https://openalex.org/W2362950008","https://openalex.org/W2497112068","https://openalex.org/W2158262334","https://openalex.org/W2047263139"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}