{"id":"https://openalex.org/W1564234264","doi":"https://doi.org/10.1007/bfb0037424","title":"On the role of orthogonality in the GMRES method","display_name":"On the role of orthogonality in the GMRES method","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1564234264","doi":"https://doi.org/10.1007/bfb0037424","mag":"1564234264"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0037424","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0037424","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5047172374","display_name":"Miroslav Rozlo\u017e\u0144\u0131k","orcid":"https://orcid.org/0000-0002-4328-9970"},"institutions":[{"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/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"M. Rozlo\u017en\u00edk","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","Academy of Sciences of the Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Academy of Sciences of the Czech Republic","institution_ids":["https://openalex.org/I202391551"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067193132","display_name":"Zden\u011bk Strako\u0161","orcid":"https://orcid.org/0000-0002-7499-8761"},"institutions":[{"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/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Z. Strako\u0161","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","Academy of Sciences of the Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Academy of Sciences of the Czech Republic","institution_ids":["https://openalex.org/I202391551"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053422141","display_name":"Miroslav T\u016fma","orcid":"https://orcid.org/0000-0003-2808-6929"},"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"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"M. T\u016fma","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","Academy of Sciences of the Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07, Praha 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Academy of Sciences of the Czech Republic","institution_ids":["https://openalex.org/I202391551"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047172374"],"corresponding_institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210155092"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17443946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"409","last_page":"416"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9873999953269958,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9440779685974121},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.8903056979179382},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7753841876983643},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5838766098022461},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.5521860122680664},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5482316017150879},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5153741240501404},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5014674663543701},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.49984288215637207},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4793970584869385},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4756086468696594},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4547615945339203},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.45091328024864197},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.440424382686615},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.44031932950019836},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.439355731010437},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3476647138595581},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3271605372428894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.230977863073349},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.063361257314682}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9440779685974121},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.8903056979179382},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7753841876983643},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5838766098022461},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.5521860122680664},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5482316017150879},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5153741240501404},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5014674663543701},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.49984288215637207},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4793970584869385},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4756086468696594},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4547615945339203},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.45091328024864197},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.440424382686615},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.44031932950019836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.439355731010437},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3476647138595581},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3271605372428894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.230977863073349},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.063361257314682},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bfb0037424","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0037424","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.51.6726","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6726","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uivt.cas.cz/~tuma/ps/rst96.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"id":"https://metadata.un.org/sdg/2","display_name":"Zero hunger"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2037785139","https://openalex.org/W2041519450","https://openalex.org/W2100384730","https://openalex.org/W2140153041"],"related_works":["https://openalex.org/W1564234264","https://openalex.org/W2610002741","https://openalex.org/W2953862869","https://openalex.org/W1579526657","https://openalex.org/W2066215857","https://openalex.org/W4220970845","https://openalex.org/W2066998452","https://openalex.org/W2088138737","https://openalex.org/W2383813702","https://openalex.org/W2162876022"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}