{"id":"https://openalex.org/W2978382295","doi":"https://doi.org/10.1177/0142331219875273","title":"Partially doubly symmetric solutions of general Sylvester matrix equations","display_name":"Partially doubly symmetric solutions of general Sylvester matrix equations","publication_year":2019,"publication_date":"2019-09-30","ids":{"openalex":"https://openalex.org/W2978382295","doi":"https://doi.org/10.1177/0142331219875273","mag":"2978382295"},"language":"en","primary_location":{"id":"doi:10.1177/0142331219875273","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331219875273","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","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/A5072708675","display_name":"Masoud Hajarian","orcid":"https://orcid.org/0000-0002-5549-9270"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Masoud Hajarian","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072708675"],"corresponding_institution_ids":["https://openalex.org/I48379061"],"apc_list":null,"apc_paid":null,"fwci":0.388,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64629594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"42","issue":"3","first_page":"503","last_page":"517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9986000061035156,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/sylvester-matrix","display_name":"Sylvester matrix","score":0.8740079402923584},{"id":"https://openalex.org/keywords/sylvester-equation","display_name":"Sylvester equation","score":0.7677497267723083},{"id":"https://openalex.org/keywords/sylvesters-law-of-inertia","display_name":"Sylvester's law of inertia","score":0.708468496799469},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6112704873085022},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5718639492988586},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5164461135864258},{"id":"https://openalex.org/keywords/biconjugate-gradient-method","display_name":"Biconjugate gradient method","score":0.491373211145401},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4826974868774414},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.4328973889350891},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42053431272506714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2418646514415741},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23555904626846313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20668208599090576},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.13766804337501526},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.0927751362323761},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07444453239440918}],"concepts":[{"id":"https://openalex.org/C20160815","wikidata":"https://www.wikidata.org/wiki/Q1482452","display_name":"Sylvester matrix","level":5,"score":0.8740079402923584},{"id":"https://openalex.org/C100468782","wikidata":"https://www.wikidata.org/wiki/Q3730848","display_name":"Sylvester equation","level":3,"score":0.7677497267723083},{"id":"https://openalex.org/C56828936","wikidata":"https://www.wikidata.org/wiki/Q1752621","display_name":"Sylvester's law of inertia","level":4,"score":0.708468496799469},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6112704873085022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5718639492988586},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5164461135864258},{"id":"https://openalex.org/C89408827","wikidata":"https://www.wikidata.org/wiki/Q855169","display_name":"Biconjugate gradient method","level":5,"score":0.491373211145401},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4826974868774414},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.4328973889350891},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42053431272506714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2418646514415741},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23555904626846313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20668208599090576},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.13766804337501526},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.0927751362323761},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07444453239440918},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","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},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.0},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/0142331219875273","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331219875273","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1964309134","https://openalex.org/W1964556214","https://openalex.org/W1964844604","https://openalex.org/W1971628002","https://openalex.org/W1979278406","https://openalex.org/W1980549954","https://openalex.org/W1983412111","https://openalex.org/W1984481129","https://openalex.org/W1987294157","https://openalex.org/W1990368370","https://openalex.org/W1990619741","https://openalex.org/W1991746142","https://openalex.org/W1991820316","https://openalex.org/W1996513997","https://openalex.org/W2006583233","https://openalex.org/W2020100362","https://openalex.org/W2020376719","https://openalex.org/W2022423405","https://openalex.org/W2022953228","https://openalex.org/W2023686904","https://openalex.org/W2026991672","https://openalex.org/W2033353732","https://openalex.org/W2033987350","https://openalex.org/W2039408173","https://openalex.org/W2040369882","https://openalex.org/W2049871086","https://openalex.org/W2050716149","https://openalex.org/W2051749898","https://openalex.org/W2055204337","https://openalex.org/W2058903283","https://openalex.org/W2072281876","https://openalex.org/W2075226287","https://openalex.org/W2085167487","https://openalex.org/W2092942375","https://openalex.org/W2117200692","https://openalex.org/W2138844572","https://openalex.org/W2160914386","https://openalex.org/W2282074372","https://openalex.org/W2327403873","https://openalex.org/W2480611454","https://openalex.org/W2535315411","https://openalex.org/W2544081764","https://openalex.org/W2547663684","https://openalex.org/W2735415958","https://openalex.org/W2763013132","https://openalex.org/W2773586218","https://openalex.org/W2782841119","https://openalex.org/W2805730876","https://openalex.org/W2884718586","https://openalex.org/W2891378268","https://openalex.org/W4245421955"],"related_works":["https://openalex.org/W2087190655","https://openalex.org/W1597114477","https://openalex.org/W1973485705","https://openalex.org/W1993763611","https://openalex.org/W144747989","https://openalex.org/W3141082938","https://openalex.org/W2036701498","https://openalex.org/W2073638342","https://openalex.org/W2566476448","https://openalex.org/W2978382295"],"abstract_inverted_index":{"The":[0],"study":[1],"of":[2,31,49,73],"linear":[3],"matrix":[4,53],"equations":[5,54],"is":[6],"extremely":[7],"important":[8],"in":[9,69],"many":[10],"scientific":[11],"fields":[12],"such":[13],"as":[14],"control":[15],"systems":[16],"and":[17],"stability":[18],"analysis.":[19],"In":[20],"this":[21],"work,":[22],"we":[23],"aim":[24],"to":[25,82],"design":[26],"the":[27,38,50,65,79],"Hestenes-Stiefel":[28],"(HS)":[29],"version":[30],"biconjugate":[32],"residual":[33],"(Bi-CR)":[34],"algorithm":[35,67,81],"for":[36,58],"computing":[37],"(least":[39],"Frobenius":[40],"norm)":[41],"partially":[42],"doubly":[43],"symmetric":[44],"solution":[45],"[Formula:":[46,55,59],"see":[47,56,60],"text]":[48,57],"general":[51],"Sylvester":[52],"text].":[61],"We":[62],"show":[63],"that":[64],"proposed":[66,80],"converges":[68],"a":[70],"finite":[71],"number":[72],"iterations.":[74],"Finally,":[75],"numerical":[76],"results":[77],"compare":[78],"alternative":[83],"algorithms.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}