{"id":"https://openalex.org/W2887556575","doi":"https://doi.org/10.1109/tcsii.2018.2864115","title":"Model Order Reduction of Linear Systems via the Cross Gramian and SVD","display_name":"Model Order Reduction of Linear Systems via the Cross Gramian and SVD","publication_year":2018,"publication_date":"2018-08-09","ids":{"openalex":"https://openalex.org/W2887556575","doi":"https://doi.org/10.1109/tcsii.2018.2864115","mag":"2887556575"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2018.2864115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2018.2864115","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems II: Express Briefs","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/A5034372090","display_name":"Yao\u2010Lin Jiang","orcid":"https://orcid.org/0000-0002-5541-1136"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao-Lin Jiang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-5541-1136","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065699512","display_name":"Zhen\u2010Zhong Qi","orcid":"https://orcid.org/0000-0002-6436-8037"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen-Zhong Qi","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100727437","display_name":"Ping Yang","orcid":"https://orcid.org/0000-0002-4655-9315"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Yang","raw_affiliation_strings":["College of Mathematics and System Sciences, Xinjiang University, Urumqi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1099,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92370558,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"66","issue":"3","first_page":"422","last_page":"426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9726999998092651,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gramian-matrix","display_name":"Gramian matrix","score":0.7968222498893738},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7220650315284729},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.661078929901123},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6559119820594788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6489190459251404},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6418771743774414},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.5386372208595276},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5361630320549011},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5102334022521973},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.5059825778007507},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4967857003211975},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48467639088630676},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43340036273002625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2654101848602295},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2299709916114807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2289237678050995},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.21689802408218384},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09979349374771118},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09763354063034058},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07822215557098389}],"concepts":[{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.7968222498893738},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7220650315284729},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.661078929901123},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6559119820594788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6489190459251404},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6418771743774414},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.5386372208595276},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5361630320549011},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5102334022521973},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.5059825778007507},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4967857003211975},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48467639088630676},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43340036273002625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2654101848602295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2299709916114807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2289237678050995},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.21689802408218384},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09979349374771118},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09763354063034058},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07822215557098389},{"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/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2018.2864115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2018.2864115","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8659213433","display_name":"\u63a7\u5236\u7cfb\u7edf\u7684\u5fae\u5206\u6d41\u5f62\u6700\u4f18\u5316\u964d\u9636\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61663043","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W185873980","https://openalex.org/W612821643","https://openalex.org/W1523281138","https://openalex.org/W1634732958","https://openalex.org/W1985927505","https://openalex.org/W1990877839","https://openalex.org/W2004851274","https://openalex.org/W2039401467","https://openalex.org/W2059308803","https://openalex.org/W2069748229","https://openalex.org/W2071576089","https://openalex.org/W2101706500","https://openalex.org/W2106165817","https://openalex.org/W2150809749","https://openalex.org/W2167434086","https://openalex.org/W2171422207","https://openalex.org/W2573372484","https://openalex.org/W2593777971","https://openalex.org/W3100658960","https://openalex.org/W3102707439","https://openalex.org/W3152462101","https://openalex.org/W6607620930","https://openalex.org/W7048927752"],"related_works":["https://openalex.org/W2610290447","https://openalex.org/W4392307167","https://openalex.org/W2016544089","https://openalex.org/W4312761325","https://openalex.org/W2194945047","https://openalex.org/W4323060099","https://openalex.org/W2147789090","https://openalex.org/W1971053378","https://openalex.org/W36455074","https://openalex.org/W3175148902"],"abstract_inverted_index":{"On":[0],"the":[1,4,8,23,26,30,35,39,49,64,69,73,84,88,100,104],"basis":[2],"of":[3,18,25,48,63,87,103],"cross":[5],"Gramian":[6],"and":[7,29,54,72],"singular":[9,66],"value":[10],"decomposition,":[11],"this":[12],"brief":[13],"investigates":[14],"model":[15],"order":[16],"reduction":[17],"linear":[19],"time-invariant":[20],"systems":[21],"in":[22,68],"view":[24],"symmetric":[27,89],"case":[28],"nonsymmetric":[31,40,105],"case.":[32],"It":[33],"guarantees":[34],"reduced":[36,50,85,101],"system":[37,41,51,86,90,102,106],"for":[38],"to":[42,93],"be":[43],"data-sparse.":[44],"The":[45,61],"asymptotical":[46],"stability":[47],"is":[52,59,77,91],"discussed":[53],"an":[55],"output":[56],"error":[57],"bound":[58],"provided.":[60],"correlation":[62],"Hankel":[65],"values":[67],"proposed":[70],"method":[71,76],"balanced":[74,97],"truncation":[75],"presented.":[78],"Finally,":[79],"numerical":[80],"results":[81],"indicate":[82],"that":[83,94],"equivalent":[92],"resulting":[95],"from":[96],"truncation,":[98],"while":[99],"has":[107],"a":[108],"good":[109],"performance.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}