{"id":"https://openalex.org/W2053964895","doi":"https://doi.org/10.1007/bf01594934","title":"Convergence of quasi-Newton matrices generated by the symmetric rank one update","display_name":"Convergence of quasi-Newton matrices generated by the symmetric rank one update","publication_year":1991,"publication_date":"1991-03-01","ids":{"openalex":"https://openalex.org/W2053964895","doi":"https://doi.org/10.1007/bf01594934","mag":"2053964895"},"language":"en","primary_location":{"id":"doi:10.1007/bf01594934","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01594934","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5103149740","display_name":"Andrew R. Conn","orcid":"https://orcid.org/0000-0001-7470-1035"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. R. Conn","raw_affiliation_strings":["IBM T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA","IBM T. J Watson Research Center, Yorktown Heights, USA"],"affiliations":[{"raw_affiliation_string":"IBM T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"IBM T. J Watson Research Center, Yorktown Heights, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007869277","display_name":"Nicholas I. M. Gould","orcid":"https://orcid.org/0000-0002-1031-1588"},"institutions":[{"id":"https://openalex.org/I1286704778","display_name":"Rutherford Appleton Laboratory","ror":"https://ror.org/03gq8fr08","country_code":"GB","type":"facility","lineage":["https://openalex.org/I1286704778","https://openalex.org/I162524378","https://openalex.org/I4210087105"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"N. I. M. Gould","raw_affiliation_strings":["Rutherford Appleton Laboratory, Chilton, UK","Rutherford Appleton Laboratory Chilton, UK"],"affiliations":[{"raw_affiliation_string":"Rutherford Appleton Laboratory, Chilton, UK","institution_ids":["https://openalex.org/I1286704778"]},{"raw_affiliation_string":"Rutherford Appleton Laboratory Chilton, UK","institution_ids":["https://openalex.org/I1286704778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002913605","display_name":"Philippe L. Toint","orcid":"https://orcid.org/0000-0002-6166-1860"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Ph. L. Toint","raw_affiliation_strings":["Department of Mathematics, Facult\u00e9s Universitaires ND de la Paix, B-5000, Namur, Belgium","Department of Mathematics, Facult\u00e9s Universitaires ND de la Paix, Namur, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Facult\u00e9s Universitaires ND de la Paix, B-5000, Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]},{"raw_affiliation_string":"Department of Mathematics, Facult\u00e9s Universitaires ND de la Paix, Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103149740"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":9.0339,"has_fulltext":true,"cited_by_count":215,"citation_normalized_percentile":{"value":0.9839779,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"50","issue":"1-3","first_page":"177","last_page":"195"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9991000294685364,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9371514320373535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8365017771720886},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.7677266001701355},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.7601140737533569},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7331289649009705},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6534844040870667},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6265446543693542},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5843052268028259},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5757953524589539},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5741366744041443},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5136598944664001},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4386797547340393},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41661399602890015},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4066168963909149},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3014090359210968},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2130891978740692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07793834805488586}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9371514320373535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8365017771720886},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.7677266001701355},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.7601140737533569},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7331289649009705},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6534844040870667},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6265446543693542},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5843052268028259},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5757953524589539},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5741366744041443},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5136598944664001},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4386797547340393},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41661399602890015},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4066168963909149},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3014090359210968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2130891978740692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07793834805488586},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bf01594934","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01594934","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:pure.unamur.be:openaire_cris_publications/f95a6439-2929-43a1-b994-b7961181ff9a","is_oa":false,"landing_page_url":"https://researchportal.unamur.be/en/publications/f95a6439-2929-43a1-b994-b7961181ff9a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Conn, A, Gould, N & Toint, P 1991, 'Convergence of quasi-Newton matrices generated by the symmetric rank one update', Mathematical Programming, vol. 50, no. 1-3, pp. 177-195. https://doi.org/10.1007/BF01594934","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dial.uclouvain.be:boreal:100279","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.2/100279","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Programming, Vol. 50, no. 2, p. 177-195 (1991)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320330380","display_name":"Information Technology Research Centre","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1579664581","https://openalex.org/W1893275031","https://openalex.org/W1965776043","https://openalex.org/W1988591078","https://openalex.org/W2011253492","https://openalex.org/W2022313155","https://openalex.org/W2048221927","https://openalex.org/W2060217404","https://openalex.org/W2062294426","https://openalex.org/W2068484625","https://openalex.org/W2090963365","https://openalex.org/W2123019231","https://openalex.org/W2143573110","https://openalex.org/W2148589597","https://openalex.org/W2482182218","https://openalex.org/W4231015361","https://openalex.org/W4236316114","https://openalex.org/W4253845129","https://openalex.org/W4299512035","https://openalex.org/W6634665210"],"related_works":["https://openalex.org/W2034199493","https://openalex.org/W2070932288","https://openalex.org/W4221162014","https://openalex.org/W2996136316","https://openalex.org/W2053964895","https://openalex.org/W114133465","https://openalex.org/W2972343833","https://openalex.org/W2463007134","https://openalex.org/W2970432723","https://openalex.org/W2050698291"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-06-24T00:00:00"}