{"id":"https://openalex.org/W2587874700","doi":"https://doi.org/10.1109/icece.2016.7853954","title":"Rational Krylov subspace method (RKSM) for solving the Lyapunov equations of index-1 descriptor systems and application to balancing based model reduction","display_name":"Rational Krylov subspace method (RKSM) for solving the Lyapunov equations of index-1 descriptor systems and application to balancing based model reduction","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2587874700","doi":"https://doi.org/10.1109/icece.2016.7853954","mag":"2587874700"},"language":"en","primary_location":{"id":"doi:10.1109/icece.2016.7853954","doi":"https://doi.org/10.1109/icece.2016.7853954","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icece.2016.7853954","pdf_url":null,"source":{"id":"https://openalex.org/S7407086530","display_name":"International Conference on Electrical and Computer Engineering (ICECE)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 9th International Conference on Electrical and Computer Engineering (ICECE)","raw_type":"proceedings-article"},"parent_works":[],"lineage":["https://openalex.org/W2587874700"],"child_works_count":0,"type":"conference-paper","is_traditional":true,"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/A5088467986","display_name":"M. Monir Uddin","orcid":"https://orcid.org/0000-0002-9817-6156","observed_orcids":["https://orcid.org/0000-0002-9817-6156","https://orcid.org/0000-0002-6526-9276"]},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"M. Monir Uddin","raw_affiliation_strings":["Department of Mathematics and Physics, North South University, Dhaka, Bangladesh","Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, North South University, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I183697816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077176345","display_name":"Md. Sumon Hossain","orcid":"https://orcid.org/0000-0002-6357-2300","observed_orcids":["https://orcid.org/0000-0002-6357-2300"]},"institutions":[{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"M. Sumon Hossain","raw_affiliation_strings":["Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I183697816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046346103","display_name":"Mohammed Forhad Uddin","orcid":"https://orcid.org/0000-0002-8717-2678","observed_orcids":["https://orcid.org/0000-0002-8717-2678"]},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Mohammad Forhad Uddin","raw_affiliation_strings":["Department of Mathematics and Physics, North South University, Dhaka, Bangladesh","Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, North South University, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh","institution_ids":["https://openalex.org/I183697816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8234,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.62843091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8916000127792358,"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":0.8916000127792358,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.040300000458955765,"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/T11081","display_name":"Advanced Control Systems Design","score":0.032600000500679016,"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-equation","display_name":"Lyapunov equation","score":0.9909999966621399},{"id":"https://openalex.org/keywords/iterative-solvers","display_name":"iterative solvers","score":0.5730000138282776}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8505769968032837},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.7957924604415894},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.624918520450592},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.61496502161026},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5861326456069946},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5549797415733337},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5189840197563171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5012238025665283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4932956099510193},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4837496280670166},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4695575535297394},{"id":"https://openalex.org/C143461762","wikidata":"https://www.wikidata.org/wiki/Q83587","display_name":"Controllability Gramian","level":3,"score":0.45416244864463806},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43413493037223816},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40374547243118286},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.39815276861190796},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.25211963057518005},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1227547824382782},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0973334014415741},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07591789960861206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07523533701896667},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.0657547116279602},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icece.2016.7853954","doi":"https://doi.org/10.1109/icece.2016.7853954","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icece.2016.7853954","pdf_url":null,"source":{"id":"https://openalex.org/S7407086530","display_name":"International Conference on Electrical and Computer Engineering (ICECE)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 9th International Conference on Electrical and Computer Engineering (ICECE)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W297328598","https://openalex.org/W1506342804","https://openalex.org/W1520511539","https://openalex.org/W1551480811","https://openalex.org/W1964400575","https://openalex.org/W2023322178","https://openalex.org/W2035969141","https://openalex.org/W2049154285","https://openalex.org/W2086590360","https://openalex.org/W2153132823","https://openalex.org/W2162144261","https://openalex.org/W2530901011","https://openalex.org/W4254671851","https://openalex.org/W6601037838"],"related_works":["https://openalex.org/W2911319329","https://openalex.org/W3152667721","https://openalex.org/W2944455231","https://openalex.org/W3156623494","https://openalex.org/W1999658804","https://openalex.org/W2944236610","https://openalex.org/W2160267228","https://openalex.org/W2621278735","https://openalex.org/W7096811539","https://openalex.org/W313722857"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,32],"the":[4,13,45,51,67,78,85,88,98,101],"iterative":[5],"method":[6,36,103],"for":[7,50,61],"solving":[8],"Lyapunov":[9,18],"equations":[10,19],"to":[11,65,77,83,96],"compute":[12,66],"low-rank":[14,68],"Gramian":[15,69,72],"factors.":[16,70],"Such":[17],"arise":[20],"from":[21],"large-scale":[22],"sparse":[23],"index-1":[24,62],"descriptor":[25,63],"system.":[26,90],"The":[27,71],"technique":[28,47],"is":[29,39,48],"mainly":[30],"based":[31,80],"rational":[33],"Krylov":[34],"subspace":[35],"(RKSM)":[37],"which":[38],"introduced":[40],"in":[41],"[1].":[42],"However,":[43],"there":[44],"proposed":[46,102],"applicable":[49],"standard":[52],"state":[53],"space":[54],"model.":[55],"Here,":[56],"we":[57],"extend":[58],"this":[59],"idea":[60],"system":[64],"factors":[73],"are":[74,94],"then":[75],"applied":[76],"balancing":[79],"model":[81],"reduction":[82],"reduce":[84],"complexity":[86],"of":[87,100],"underlying":[89],"Several":[91],"test":[92],"examples":[93],"considered":[95],"show":[97],"efficiency":[99],"numerically.":[104]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2017-02-24T00:00:00"}
