{"id":"https://openalex.org/W1969437942","doi":"https://doi.org/10.1137/s0036144599362406","title":"Matrix Exponentials---Another Approach","display_name":"Matrix Exponentials---Another Approach","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1969437942","doi":"https://doi.org/10.1137/s0036144599362406","mag":"1969437942"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144599362406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599362406","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5103566997","display_name":"William A. Harris","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William A. Harris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058371999","display_name":"Jay P. Fillmore","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jay P. Fillmore","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103560381","display_name":"Donald R. Smith","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Donald R. Smith","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0914,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.9338954,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"43","issue":"4","first_page":"694","last_page":"706"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.6287000179290771,"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":0.6287000179290771,"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/matrix-exponential","display_name":"Matrix exponential","score":0.5698954463005066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5321390628814697},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5087600350379944},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49011263251304626},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4160485565662384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14834189414978027},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.060675740242004395},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.05978557467460632}],"concepts":[{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.5698954463005066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5321390628814697},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5087600350379944},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49011263251304626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4160485565662384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14834189414978027},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.060675740242004395},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.05978557467460632},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144599362406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599362406","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/W194660281","https://openalex.org/W1634723628","https://openalex.org/W2066683261","https://openalex.org/W2067136705","https://openalex.org/W2091541526","https://openalex.org/W2097142169","https://openalex.org/W2318820498","https://openalex.org/W2949978140","https://openalex.org/W4238169414"],"related_works":["https://openalex.org/W2022992047","https://openalex.org/W2989687840","https://openalex.org/W1969390712","https://openalex.org/W1995516663","https://openalex.org/W1601910470","https://openalex.org/W2952997836","https://openalex.org/W2905395987","https://openalex.org/W2110769443","https://openalex.org/W1982019426","https://openalex.org/W3171470103"],"abstract_inverted_index":{"The":[0,28],"exponential":[1],"of":[2,9,21,30,45],"a":[3,10],"matrix":[4,11,23],"and":[5,24],"the":[6,19,22,25,31],"spectral":[7],"decomposition":[8],"can":[12],"be":[13,40],"computed":[14],"knowing":[15],"nothing":[16],"more":[17],"than":[18],"eigenvalues":[20],"Cayley--Hamilton":[26],"theorem.":[27],"arrangement":[29],"ideas":[32],"in":[33],"this":[34],"paper":[35],"is":[36],"simple":[37],"enough":[38],"to":[39,42],"taught":[41],"beginning":[43],"students":[44],"ODEs.":[46]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}