{"id":"https://openalex.org/W1978242229","doi":"https://doi.org/10.1007/bf01219774","title":"The Lyapunov exponent and joint spectral radius of pairs of matrices are hard?when not impossible?to compute and to approximate","display_name":"The Lyapunov exponent and joint spectral radius of pairs of matrices are hard?when not impossible?to compute and to approximate","publication_year":1997,"publication_date":"1997-03-01","ids":{"openalex":"https://openalex.org/W1978242229","doi":"https://doi.org/10.1007/bf01219774","mag":"1978242229"},"language":"en","primary_location":{"id":"doi:10.1007/bf01219774","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01219774","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"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":"Mathematics of Control, Signals, and Systems","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/A5108523422","display_name":"John N. Tsitsiklis","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John N. Tsitsiklis","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA","Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, USA#TAB#","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073875709","display_name":"Vincent D. Blondel","orcid":null},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Vincent D. Blondel","raw_affiliation_strings":["Institute of Mathematics, University of Li\u00e9ge, B-4000, Li\u00e8ge, Belgium","Institute of Mathematics, University of Li\u00e9ge, Li\u00e8ge, Belgium"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Li\u00e9ge, B-4000, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]},{"raw_affiliation_string":"Institute of Mathematics, University of Li\u00e9ge, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108523422"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.7415,"has_fulltext":false,"cited_by_count":303,"citation_normalized_percentile":{"value":0.97660288,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"10","issue":"1","first_page":"31","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9926999807357788,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.8481149673461914},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7161790728569031},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.6935608983039856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6827150583267212},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6247571110725403},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.6236685514450073},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5123075246810913},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4878501892089844},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3790299594402313},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37802353501319885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27645087242126465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1241302490234375},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11477085947990417},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10847228765487671},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10496816039085388}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.8481149673461914},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7161790728569031},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.6935608983039856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6827150583267212},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6247571110725403},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6236685514450073},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5123075246810913},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4878501892089844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3790299594402313},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37802353501319885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27645087242126465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1241302490234375},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11477085947990417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10847228765487671},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10496816039085388},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/bf01219774","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01219774","pdf_url":null,"source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"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":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.15.4411","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.4411","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mit.edu/people/jnt/Papers/J064-97-vb-spectr-pre.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.15","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.15","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inma.ucl.ac.be/~blondel/publications/97BT-jsr.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.57.3762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.3762","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ulg.ac.be/mathsys/blondel/papers/TB97.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.62.6975","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.6975","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mit.edu/people/jnt/Papers/J064-97-vb-spectr.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W87950745","https://openalex.org/W204546099","https://openalex.org/W391578156","https://openalex.org/W1521579444","https://openalex.org/W1523273010","https://openalex.org/W1817451992","https://openalex.org/W1980368307","https://openalex.org/W1981798791","https://openalex.org/W2008442517","https://openalex.org/W2010002500","https://openalex.org/W2011039300","https://openalex.org/W2023729441","https://openalex.org/W2028886195","https://openalex.org/W2032100464","https://openalex.org/W2032326995","https://openalex.org/W2049236590","https://openalex.org/W2060886109","https://openalex.org/W2070972632","https://openalex.org/W2073446486","https://openalex.org/W2076566814","https://openalex.org/W2079227289","https://openalex.org/W2103966928","https://openalex.org/W2104292418","https://openalex.org/W2105265696","https://openalex.org/W2142324898","https://openalex.org/W2153130404","https://openalex.org/W2346714215","https://openalex.org/W2592184324","https://openalex.org/W2610857016","https://openalex.org/W3104847799","https://openalex.org/W3152126650","https://openalex.org/W3162365952","https://openalex.org/W3210839039","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979229270","https://openalex.org/W2374600121","https://openalex.org/W125502673","https://openalex.org/W2384948345","https://openalex.org/W2027784897","https://openalex.org/W2776265842","https://openalex.org/W2368364854","https://openalex.org/W2018408614","https://openalex.org/W2725952545","https://openalex.org/W2366108085"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":19}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
