{"id":"https://openalex.org/W2912693630","doi":"https://doi.org/10.1137/060659909","title":"Approximate Diagonalization","display_name":"Approximate Diagonalization","publication_year":2007,"publication_date":"2007-11-02","ids":{"openalex":"https://openalex.org/W2912693630","doi":"https://doi.org/10.1137/060659909","mag":"2912693630"},"language":"en","primary_location":{"id":"doi:10.1137/060659909","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659909","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/A5112763739","display_name":"E. B. Davies","orcid":"https://orcid.org/0009-0002-7693-0530"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"E. B. Davies","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112763739"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7471,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.76065942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"4","first_page":"1051","last_page":"1064"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.996999979019165,"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/T11476","display_name":"Graph theory and applications","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/conjecture","display_name":"Conjecture","score":0.7756439447402954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7610839605331421},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5213831067085266},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42676854133605957},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3993677794933319},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27846866846084595},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2218134105205536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13078796863555908}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7756439447402954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7610839605331421},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5213831067085266},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42676854133605957},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3993677794933319},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27846866846084595},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2218134105205536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13078796863555908}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060659909","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659909","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.363.201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mth.kcl.ac.uk/staff/eb_davies/PDFfiles/198.pdf","raw_type":"text"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/d348405b-c1a1-4b8c-93ba-a2f1d1127977","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/d348405b-c1a1-4b8c-93ba-a2f1d1127977","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Davies, E B 2006, 'Approximate diagonalization', SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, vol. 29, no. 4, pp. 1051 - 1064. https://doi.org/10.1137/060659909","raw_type":"info:eu-repo/semantics/publishedVersion"}],"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/W38816153","https://openalex.org/W166129609","https://openalex.org/W175988912","https://openalex.org/W1981576702","https://openalex.org/W2036182269","https://openalex.org/W2078675418","https://openalex.org/W2079989873","https://openalex.org/W2081587879","https://openalex.org/W2082465767"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W4285308861"],"abstract_inverted_index":{"We":[0,19,38],"describe":[1],"a":[2,21],"new":[3],"method":[4,41],"of":[5,8,16,35,47],"computing":[6],"functions":[7],"highly":[9,48],"nonnormal":[10,49],"matrices":[11],"by":[12],"using":[13],"the":[14,36,40],"concept":[15],"approximate":[17],"diagonalization.":[18],"formulate":[20],"conjecture":[22],"about":[23],"its":[24],"efficiency":[25],"and":[26,30],"provide":[27],"both":[28],"theoretical":[29],"numerical":[31],"evidence":[32],"in":[33],"support":[34],"conjecture.":[37],"apply":[39],"to":[42],"compute":[43],"arbitrary":[44],"real":[45],"powers":[46],"matrices.":[50]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
