{"id":"https://openalex.org/W2771426051","doi":"https://doi.org/10.1137/16m1105840","title":"Matrix Stabilization Using Differential Equations","display_name":"Matrix Stabilization Using Differential Equations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2771426051","doi":"https://doi.org/10.1137/16m1105840","mag":"2771426051"},"language":"en","primary_location":{"id":"doi:10.1137/16m1105840","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1105840","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Journal on Numerical Analysis","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/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030219464"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8169,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87257515,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"55","issue":"6","first_page":"3097","last_page":"3119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9966999888420105,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8300752639770508},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7541376352310181},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6454290151596069},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6232595443725586},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.5232985615730286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.515112578868866},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45320749282836914},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4508022964000702},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4455222487449646},{"id":"https://openalex.org/keywords/normal-matrix","display_name":"Normal matrix","score":0.4344017803668976},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33698296546936035},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10511142015457153}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300752639770508},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7541376352310181},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6454290151596069},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6232595443725586},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.5232985615730286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.515112578868866},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45320749282836914},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4508022964000702},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4455222487449646},{"id":"https://openalex.org/C175380299","wikidata":"https://www.wikidata.org/wiki/Q6852339","display_name":"Normal matrix","level":3,"score":0.4344017803668976},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33698296546936035},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10511142015457153},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political 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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1105840","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1105840","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1575147392","https://openalex.org/W1861644487","https://openalex.org/W1972112356","https://openalex.org/W1984560319","https://openalex.org/W2020884817","https://openalex.org/W2040306605","https://openalex.org/W2096434207","https://openalex.org/W2102688209","https://openalex.org/W2110657969","https://openalex.org/W2152279941","https://openalex.org/W2156291021","https://openalex.org/W2547028630","https://openalex.org/W2616614818"],"related_works":["https://openalex.org/W3174042135","https://openalex.org/W4297415474","https://openalex.org/W4226352068","https://openalex.org/W2048533143","https://openalex.org/W2127340547","https://openalex.org/W2358130123","https://openalex.org/W2079980032","https://openalex.org/W200613325","https://openalex.org/W1966353092","https://openalex.org/W3156788868"],"abstract_inverted_index":{"We":[0,63],"consider":[1],"the":[2,27,43,79,108,111,118,123,134],"problem":[3],"of":[4,11,81,107,110,126,129,136],"stabilizing":[5],"a":[6,9,15,46,53,59,67,95],"matrix":[7,17,29,83],"by":[8],"correction":[10,44],"minimal":[12],"norm:":[13],"Given":[14],"square":[16],"that":[18,42,117],"has":[19],"some":[20],"eigenvalues":[21],"with":[22,33],"positive":[23,34],"real":[24,35],"part,":[25],"find":[26],"nearest":[28],"having":[30],"no":[31],"eigenvalue":[32],"part.":[36],"It":[37,113],"can":[38],"be":[39,50],"further":[40,115],"required":[41],"have":[45,52,58],"prescribed":[47,54],"structure,":[48],"e.g.,":[49],"real,":[51],"sparsity":[55],"pattern,":[56],"or":[57],"given":[60],"maximal":[61],"rank.":[62],"propose":[64],"and":[65,73,132],"study":[66],"novel":[68],"approach":[69,119],"to":[70,89,122,133],"this":[71],"nonconvex":[72],"nonsmooth":[74],"optimization":[75],"problem,":[76],"based":[77],"on":[78],"solution":[80],"low-rank":[82],"differential":[84],"equations.":[85],"This":[86],"enables":[87],"us":[88],"compute":[90],"locally":[91],"optimal":[92],"solutions":[93],"in":[94],"fast":[96],"way,":[97],"also":[98],"for":[99],"higher-dimensional":[100],"problems.":[101],"Illustrative":[102],"numerical":[103],"experiments":[104],"provide":[105],"evidence":[106],"efficiency":[109],"method.":[112],"is":[114],"shown":[116],"applies":[120],"equally":[121],"related":[124],"problems":[125],"closed-loop":[127],"stabilization":[128,135],"control":[130],"systems":[131],"gyroscopic":[137],"systems.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
