{"id":"https://openalex.org/W2082298889","doi":"https://doi.org/10.1137/s0895479897317077","title":"The BR Eigenvalue Algorithm","display_name":"The BR Eigenvalue Algorithm","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2082298889","doi":"https://doi.org/10.1137/s0895479897317077","mag":"2082298889"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479897317077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897317077","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/A5111726096","display_name":"G.A. Geist","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. A. Geist","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083325748","display_name":"Gary Howell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. W. Howell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006021673","display_name":"David S. Watkins","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. S. Watkins","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111726096"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4708,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.665008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"20","issue":"4","first_page":"1083","last_page":"1098"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.9008126258850098},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7184392809867859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7114900350570679},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.6951006054878235},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6807835102081299},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.5906471014022827},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.5901007056236267},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48824504017829895},{"id":"https://openalex.org/keywords/eigenvalue-algorithm","display_name":"Eigenvalue algorithm","score":0.41735729575157166},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3329944610595703},{"id":"https://openalex.org/keywords/hamiltonian-matrix","display_name":"Hamiltonian matrix","score":0.1406782567501068}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.9008126258850098},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7184392809867859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7114900350570679},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.6951006054878235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6807835102081299},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.5906471014022827},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.5901007056236267},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48824504017829895},{"id":"https://openalex.org/C109565186","wikidata":"https://www.wikidata.org/wiki/Q6766437","display_name":"Eigenvalue algorithm","level":5,"score":0.41735729575157166},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3329944610595703},{"id":"https://openalex.org/C135715101","wikidata":"https://www.wikidata.org/wiki/Q3299275","display_name":"Hamiltonian matrix","level":4,"score":0.1406782567501068},{"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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479897317077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479897317077","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1965366611","https://openalex.org/W1976676253","https://openalex.org/W1978321045","https://openalex.org/W2045712363","https://openalex.org/W2051410107","https://openalex.org/W2069842273","https://openalex.org/W2086351984","https://openalex.org/W4213230933","https://openalex.org/W4251074344"],"related_works":["https://openalex.org/W2156009096","https://openalex.org/W2075330145","https://openalex.org/W183203207","https://openalex.org/W2049166915","https://openalex.org/W1676602110","https://openalex.org/W1986034826","https://openalex.org/W2016499269","https://openalex.org/W2078767299","https://openalex.org/W2135737547","https://openalex.org/W4247066068"],"abstract_inverted_index":{"The":[0],"BR":[1,55,79],"algorithm,":[2,25,30],"a":[3,19,86,94],"new":[4],"method":[5],"for":[6],"calculating":[7],"the":[8,23,28,37,40,47,54,68,72,78,82],"eigenvalues":[9,38],"of":[10,39,88,96],"an":[11],"upper":[12],"Hessenberg":[13],"matrix,":[14],"is":[15,18,32],"introduced.":[16],"It":[17],"bulge-chasing":[20],"algorithm":[21,56,80,84],"like":[22],"QR":[24,29],"but,":[26],"unlike":[27],"it":[31,62],"well":[33,64],"adapted":[34],"to":[35],"computing":[36,91],"narrow-band,":[41],"nearly":[42],"tridiagonal":[43],"matrices":[44],"generated":[45],"by":[46,85],"look-ahead":[48],"Lanczos":[49,69],"process.":[50,70],"This":[51],"paper":[52],"describes":[53],"and":[57,93],"gives":[58],"numerical":[59],"evidence":[60],"that":[61],"works":[63],"in":[65,90,99],"conjunction":[66],"with":[67],"On":[71],"biggest":[73],"problems":[74],"run":[75],"so":[76],"far,":[77],"beats":[81],"$QR$":[83],"factor":[87,95],"30--60":[89],"time":[92],"over":[97],"100":[98],"matrix":[100],"storage":[101],"space.":[102]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}