{"id":"https://openalex.org/W2136866714","doi":"https://doi.org/10.1137/0915025","title":"GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems","display_name":"GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2136866714","doi":"https://doi.org/10.1137/0915025","mag":"2136866714"},"language":"en","primary_location":{"id":"doi:10.1137/0915025","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915025","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/A5019550551","display_name":"Anne Greenbaum","orcid":"https://orcid.org/0000-0002-3783-3466"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anne Greenbaum","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065363123","display_name":"Lloyd N. Trefethen","orcid":"https://orcid.org/0000-0003-2504-1709"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lloyd N. Trefethen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019550551"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7822,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.91750981,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"2","first_page":"359","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980000257492065,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9958000183105469,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9719811677932739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8400968313217163},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.7764487266540527},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.7280789017677307},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6245174407958984},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5896390676498413},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.5404021143913269},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.536693274974823},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4292536675930023},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.42756569385528564},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21400564908981323},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.050599873065948486}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9719811677932739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8400968313217163},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.7764487266540527},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.7280789017677307},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6245174407958984},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5896390676498413},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.5404021143913269},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.536693274974823},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4292536675930023},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42756569385528564},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21400564908981323},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.050599873065948486},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":4,"locations":[{"id":"doi:10.1137/0915025","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915025","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.1786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.1786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/matrix_approx.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.5583","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.5583","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/trefethen/publication/PDF/1994_60.pdf","raw_type":"text"},{"id":"pmh:oai:ecommons.cornell.edu:1813/5473","is_oa":false,"landing_page_url":"https://hdl.handle.net/1813/5473","pdf_url":null,"source":{"id":"https://openalex.org/S4306400757","display_name":"eCommons (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"technical report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W8840247","https://openalex.org/W101236918","https://openalex.org/W201600687","https://openalex.org/W344307202","https://openalex.org/W1669374329","https://openalex.org/W1965720095","https://openalex.org/W1975795280","https://openalex.org/W1982602023","https://openalex.org/W1982604350","https://openalex.org/W1998366068","https://openalex.org/W2047151498","https://openalex.org/W2048659456","https://openalex.org/W2055342986","https://openalex.org/W2059363444","https://openalex.org/W2059586807","https://openalex.org/W2059987914","https://openalex.org/W2061887203","https://openalex.org/W2068395392","https://openalex.org/W2069766942","https://openalex.org/W2100384730","https://openalex.org/W2117366131","https://openalex.org/W2130860589","https://openalex.org/W2137029533","https://openalex.org/W2140153041","https://openalex.org/W2568342123","https://openalex.org/W3108043981","https://openalex.org/W4299000130"],"related_works":["https://openalex.org/W1964004266","https://openalex.org/W2028574017","https://openalex.org/W2053245975","https://openalex.org/W1996754067","https://openalex.org/W3166616159","https://openalex.org/W2385065544","https://openalex.org/W4285469404","https://openalex.org/W2079421048","https://openalex.org/W2136866714","https://openalex.org/W4287126381"],"abstract_inverted_index":{"Abstract.":[0],"The":[1,27],"GMRES":[2,38,47,80],"and":[3,11,39,49,63,71,82],"Arnoldi":[4,51,85],"algorithms,":[5],"which":[6],"reduce":[7],"to":[8],"the":[9,15,61,84],"CR":[10],"Lanczos":[12],"algorithms":[13],"in":[14],"symmetric":[16],"case,":[17],"both":[18],"minimize":[19],"p(A)b":[20],"over":[21],"polynomials":[22],"p":[23,31],"of":[24,68],"degree":[25],"n.":[26],"difference":[28],"is":[29,32],"that":[30],"normalized":[33],"at":[34,40],"z":[35,41],"0":[36],"for":[37,43],"x":[42],"Arnoldi.":[44],"Analogous":[45],""ideal":[46,50],""":[48,52],"problems":[53,74],"are":[54],"obtained":[55],"if":[56],"one":[57],"removes":[58],"b":[59],"from":[60],"discussion":[62],"minimizes":[64],"p(/l)II":[65],"instead.":[66],"Investigation":[67],"these":[69],"true":[70],"ideal":[72],"approximation":[73,96],"gives":[75],"insight":[76],"into":[77],"how":[78,83],"fast":[79],"converges":[81],"iteration":[86],"locates":[87],"eigenvalues.":[88],"Key":[89],"words.":[90],"GMRES,":[91],"CR,":[92],"Arnoldi,":[93],"Lanczos,":[94],"matrix":[95,99],"problem,":[97],"normal":[98]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}