{"id":"https://openalex.org/W33492629","doi":null,"title":"An Algorithm for the Generalized Matrix Eigenvalue Problem Ax = Lambda Bx","display_name":"An Algorithm for the Generalized Matrix Eigenvalue Problem Ax = Lambda Bx","publication_year":1971,"publication_date":"1971-10-01","ids":{"openalex":"https://openalex.org/W33492629","mag":"33492629"},"language":"en","primary_location":{"id":"mag:33492629","doi":null,"is_oa":false,"landing_page_url":"https://apps.dtic.mil/dtic/tr/fulltext/u2/746896.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5109088963","display_name":"C Moler","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C Moler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103071563","display_name":"G. W. Stewart","orcid":"https://orcid.org/0009-0008-0586-9991","observed_orcids":["https://orcid.org/0009-0008-0586-9991"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. W. Stewart","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0008-0586-9991","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.00997506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":93},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11697","display_name":"Numerical Methods and Algorithms","score":9.999999747378752e-05,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.0,"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-eigenvalue-problem","display_name":"generalized eigenvalue problem","score":0.953000009059906},{"id":"https://openalex.org/keywords/qz-algorithm","display_name":"QZ algorithm","score":0.9710000157356262},{"id":"https://openalex.org/keywords/qr-algorithm","display_name":"QR algorithm","score":0.6940000057220459},{"id":"https://openalex.org/keywords/degeneracy","display_name":"degeneracy","score":0.5630000233650208},{"id":"https://openalex.org/keywords/matrix-eigenvalue-computation","display_name":"matrix eigenvalue computation","score":0.6800000071525574},{"id":"https://openalex.org/keywords/fortran-implementation","display_name":"FORTRAN implementation","score":0.7429999709129333}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.760233998298645},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7529809474945068},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.6651504039764404},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6362910866737366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5833980441093445},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5745190382003784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5512675046920776},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4566890001296997},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.43074941635131836},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4209015369415283},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3391905426979065},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19821476936340332},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13263845443725586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0883415937423706},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/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":"mag:33492629","doi":null,"is_oa":false,"landing_page_url":"https://apps.dtic.mil/dtic/tr/fulltext/u2/746896.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2042255949","https://openalex.org/W1968916337","https://openalex.org/W1980157308","https://openalex.org/W1984938247","https://openalex.org/W2047068450","https://openalex.org/W1986988066","https://openalex.org/W7095749468","https://openalex.org/W7009715542","https://openalex.org/W2099769673","https://openalex.org/W2032759960"],"abstract_inverted_index":{"Abstract":[0],":":[1],"A":[2,27,69],"new":[3],"method,":[4],"called":[5],"the":[6,12,15,35,58],"QZ":[7],"algorithm,":[8,60],"is":[9,32,41,54],"presented":[10],"for":[11],"solution":[13],"of":[14,45,57],"matrix":[16],"eigenvalue":[17],"problem":[18],"Ax":[19],"=":[20,67],"lambda":[21],"Bx":[22],"with":[23],"general":[24],"square":[25],"matrices":[26],"and":[28,61,72],"B.":[29],"Particular":[30],"attention":[31],"paid":[33],"to":[34,63],"degeneracies":[36],"which":[37],"result":[38],"when":[39,65],"B":[40,46,66],"singular.":[42],"No":[43],"inversions":[44],"or":[47],"its":[48],"submatrices":[49],"are":[50,76],"used.":[51],"The":[52],"algorithm":[53],"a":[55],"generalization":[56],"QR":[59],"reduces":[62],"it":[64],"I.":[68],"FORTRAN":[70],"program":[71],"some":[73],"illustrative":[74],"examples":[75],"included.":[77]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2016-06-24T00:00:00"}