{"id":"https://openalex.org/W2159755572","doi":"https://doi.org/10.1080/00207169808804700","title":"On the solution of the covariance matrix differential equation for singular systems","display_name":"On the solution of the covariance matrix differential equation for singular systems","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2159755572","doi":"https://doi.org/10.1080/00207169808804700","mag":"2159755572"},"language":"en","primary_location":{"id":"doi:10.1080/00207169808804700","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804700","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5027273282","display_name":"Masoud Shafiee","orcid":"https://orcid.org/0000-0002-1290-2226"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Masoud Shafiee","raw_affiliation_strings":["Department of Electrical Engineering, Amirkabir University, Tehran, Iran","Department of Electrical Engineering , Amirkabir University , Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Amirkabir University, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Department of Electrical Engineering , Amirkabir University , Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027384845","display_name":"Mohsen Razzaghi","orcid":"https://orcid.org/0000-0002-2189-0802"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]},{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["IR","US"],"is_corresponding":false,"raw_author_name":"Mohsen Razzaghi","raw_affiliation_strings":["Department of Mathematics and Statistics, Mississippi State University, Ms, 39762, USA ; Department of Mathematics, Amirkabir University, Tehran, Iran","Department of Mathematics , Amirkabir University , Tehran, Iran","Department of Mathematics and Statistics , Mississippi State University , Ms, 39762, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Mississippi State University, Ms, 39762, USA ; Department of Mathematics, Amirkabir University, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Department of Mathematics , Amirkabir University , Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , Mississippi State University , Ms, 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.2127749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"68","issue":"3-4","first_page":"337","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9659000039100647,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9659000039100647,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.933899998664856,"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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9312999844551086,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/kronecker-product","display_name":"Kronecker product","score":0.8425559997558594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.78806072473526},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5960093140602112},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.589381754398346},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5798363089561462},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5459120273590088},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.535096287727356},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5237329602241516},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.515466034412384},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49638086557388306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43344345688819885},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.43168455362319946},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14250299334526062},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06720724701881409}],"concepts":[{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.8425559997558594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.78806072473526},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5960093140602112},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.589381754398346},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5798363089561462},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5459120273590088},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.535096287727356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5237329602241516},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.515466034412384},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49638086557388306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43344345688819885},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.43168455362319946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14250299334526062},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06720724701881409},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169808804700","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804700","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":6,"referenced_works":["https://openalex.org/W2013348732","https://openalex.org/W2016848415","https://openalex.org/W2022483586","https://openalex.org/W2070623399","https://openalex.org/W2105317464","https://openalex.org/W2118039425"],"related_works":["https://openalex.org/W123417539","https://openalex.org/W2079407403","https://openalex.org/W2060299328","https://openalex.org/W4375957393","https://openalex.org/W4233239985","https://openalex.org/W2117336295","https://openalex.org/W2073634779","https://openalex.org/W3102722572","https://openalex.org/W2090103374","https://openalex.org/W1564288589"],"abstract_inverted_index":{"State":[0],"space":[1],"formulation":[2],"for":[3,22],"singular":[4],"linear":[5],"stationary":[6],"random":[7],"inputs":[8],"are":[9],"presented.":[10],"A":[11],"covariance":[12],"matrix":[13],"differential":[14],"equation":[15,25],"is":[16,29,33],"derived":[17],"and":[18],"a":[19],"new":[20],"technique":[21],"solving":[23],"this":[24],"using":[26],"Kronecker":[27],"product":[28],"included.":[30],"An":[31],"example":[32],"provided":[34],"to":[35],"illustrate":[36],"the":[37,40],"applicability":[38],"of":[39],"proposed":[41],"method.":[42]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}