{"id":"https://openalex.org/W2071440391","doi":"https://doi.org/10.1002/nla.1680020203","title":"Matrix shapes invariant under the symmetric QR algorithm","display_name":"Matrix shapes invariant under the symmetric QR algorithm","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2071440391","doi":"https://doi.org/10.1002/nla.1680020203","mag":"2071440391"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1680020203","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020203","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with 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/A5023391278","display_name":"Peter Arbenz","orcid":"https://orcid.org/0000-0002-1501-3176"},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Peter Arbenz","raw_affiliation_strings":["Eidgeno\u0308ssische Technische Hochschule, Institut fu\u0308r Wissenschaftliches Rechnen, CH-8092 Zu\u0308rich, Switzerland","Eidgen\u00f6ssische Technische Hochschule, Institut f\u00fcr Wissenschaftliches Rechnen, CH\u20108092 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Eidgeno\u0308ssische Technische Hochschule, Institut fu\u0308r Wissenschaftliches Rechnen, CH-8092 Zu\u0308rich, Switzerland","institution_ids":["https://openalex.org/I2799323385"]},{"raw_affiliation_string":"Eidgen\u00f6ssische Technische Hochschule, Institut f\u00fcr Wissenschaftliches Rechnen, CH\u20108092 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I2799323385"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gene H. Golub","raw_affiliation_strings":["Stanford University, Department of Computer Science, Stanford CA 94305-2140, USA","Stanford University, Department of Computer Science, Stanford CA 94305\u20102140, USA"],"affiliations":[{"raw_affiliation_string":"Stanford University, Department of Computer Science, Stanford CA 94305-2140, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University, Department of Computer Science, Stanford CA 94305\u20102140, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023391278"],"corresponding_institution_ids":["https://openalex.org/I2799323385"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":1.0564,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.77056445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"2","first_page":"87","last_page":"93"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9433000087738037,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9433000087738037,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.8221167325973511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.758230984210968},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5691649913787842},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5598143935203552},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5528969168663025},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.5009350776672363},{"id":"https://openalex.org/keywords/band-matrix","display_name":"Band matrix","score":0.495096355676651},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.48132073879241943},{"id":"https://openalex.org/keywords/cuthill\u2013mckee-algorithm","display_name":"Cuthill\u2013McKee algorithm","score":0.47537413239479065},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4708264172077179},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34194186329841614},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.2578497529029846},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24619603157043457}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.8221167325973511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.758230984210968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5691649913787842},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5598143935203552},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5528969168663025},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.5009350776672363},{"id":"https://openalex.org/C33343441","wikidata":"https://www.wikidata.org/wiki/Q806350","display_name":"Band matrix","level":5,"score":0.495096355676651},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.48132073879241943},{"id":"https://openalex.org/C118151440","wikidata":"https://www.wikidata.org/wiki/Q1146458","display_name":"Cuthill\u2013McKee algorithm","level":5,"score":0.47537413239479065},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4708264172077179},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34194186329841614},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2578497529029846},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24619603157043457},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nla.1680020203","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020203","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1981885118","https://openalex.org/W2023663671","https://openalex.org/W2035180740","https://openalex.org/W2059586807","https://openalex.org/W2065197309","https://openalex.org/W2568342123","https://openalex.org/W2753176400","https://openalex.org/W4249958171"],"related_works":["https://openalex.org/W2074908389","https://openalex.org/W2060901997","https://openalex.org/W2079120751","https://openalex.org/W4375816806","https://openalex.org/W2343519557","https://openalex.org/W2038377282","https://openalex.org/W2076299227","https://openalex.org/W2039525487","https://openalex.org/W2369254890","https://openalex.org/W1981810616"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"QR":[2,80],"algorithm":[3,7,23],"is":[4,19,24,47],"a":[5,35,38,56],"basic":[6],"for":[8],"computing":[9],"the":[10,22,28,50,79],"eigenvalues":[11],"of":[12,37,73],"dense":[13],"matrices.":[14],"For":[15],"efficiency":[16],"reasons":[17],"it":[18],"prerequisite":[20],"that":[21],"applied":[25],"only":[26],"after":[27],"original":[29],"matrix":[30,36,60],"has":[31],"been":[32],"reduced":[33],"to":[34,58],"particular":[39],"shape,":[40],"most":[41],"notably":[42],"Hessenberg":[43],"and":[44],"tridiagonal,":[45],"which":[46,70],"preserved":[48,77],"during":[49],"iterative":[51],"process.":[52],"In":[53,65],"certain":[54],"circumstances":[55],"reduction":[57],"another":[59],"shape":[61],"may":[62],"be":[63],"advantageous.":[64],"this":[66],"paper,":[67],"we":[68],"identify":[69],"zero":[71],"patterns":[72],"symmetric":[74],"matrices":[75],"are":[76],"under":[78],"algorithm.":[81]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
