{"id":"https://openalex.org/W4383955896","doi":"https://doi.org/10.1137/22m1498735","title":"Rank-1 Matrix Differential Equations for Structured Eigenvalue Optimization.","display_name":"Rank-1 Matrix Differential Equations for Structured Eigenvalue Optimization.","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383955896","doi":"https://doi.org/10.1137/22m1498735"},"language":"en","primary_location":{"id":"doi:10.1137/22m1498735","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1498735","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":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["Division of Mathematics, Gran Sasso Science Institute, L\u2019 Aquila, I-67100 Italy","Division of Mathematics, Gran Sasso Science Institute, L' Aquila, I-67100 Italy"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Gran Sasso Science Institute, L\u2019 Aquila, I-67100 Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Division of Mathematics, Gran Sasso Science Institute, L' Aquila, I-67100 Italy","institution_ids":["https://openalex.org/I4210150763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["Mathematisches Institut, Universit\u00e4t T\u00fcbingen, D\u201372076 T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, D\u201372076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027942366","display_name":"Stefano Sicilia","orcid":"https://orcid.org/0009-0001-0937-4469"},"institutions":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Sicilia","raw_affiliation_strings":["Division of Mathematics, Gran Sasso Science Institute, L\u2019 Aquila, I-67100 Italy","Division of Mathematics, Gran Sasso Science Institute, L' Aquila, I-67100 Italy"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Gran Sasso Science Institute, L\u2019 Aquila, I-67100 Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Division of Mathematics, Gran Sasso Science Institute, L' Aquila, I-67100 Italy","institution_ids":["https://openalex.org/I4210150763"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030219464"],"corresponding_institution_ids":["https://openalex.org/I4210150763"],"apc_list":null,"apc_paid":null,"fwci":1.8153,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87315434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"61","issue":"4","first_page":"1737","last_page":"1762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9959999918937683,"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/mathematics","display_name":"Mathematics","score":0.7887519598007202},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7151861190795898},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5909504890441895},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.5044988393783569},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46004819869995117},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.4542551040649414},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4429280459880829},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.41783416271209717},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3310236632823944},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2973005771636963},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20099610090255737}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7887519598007202},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7151861190795898},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5909504890441895},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.5044988393783569},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46004819869995117},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.4542551040649414},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4429280459880829},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.41783416271209717},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3310236632823944},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2973005771636963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20099610090255737},{"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1498735","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1498735","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":[{"id":"https://openalex.org/G6653824781","display_name":null,"funder_award_id":"PRIN-17","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W149522324","https://openalex.org/W1225265921","https://openalex.org/W1972112356","https://openalex.org/W2006017464","https://openalex.org/W2034169759","https://openalex.org/W2050649877","https://openalex.org/W2051601650","https://openalex.org/W2064404969","https://openalex.org/W2073955633","https://openalex.org/W2090832914","https://openalex.org/W2108754424","https://openalex.org/W2110657969","https://openalex.org/W2133776435","https://openalex.org/W2134332047","https://openalex.org/W2152279941","https://openalex.org/W2156291021","https://openalex.org/W2333929843","https://openalex.org/W2413150331","https://openalex.org/W2771426051","https://openalex.org/W3021961868","https://openalex.org/W4205293427","https://openalex.org/W4293244147"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2112835755","https://openalex.org/W2349674371","https://openalex.org/W4291951920","https://openalex.org/W2963262648","https://openalex.org/W2165749285","https://openalex.org/W2097495471","https://openalex.org/W1696545756","https://openalex.org/W4301867002","https://openalex.org/W2470850800"],"abstract_inverted_index":{".A":[0],"new":[1],"approach":[2,155],"to":[3,24,33,43,46,136,290],"solving":[4],"eigenvalue":[5,89,109],"optimization":[6,19,90,110],"problems":[7,20,37],"for":[8,91,191,212,314,323],"large":[9,68,315],"structured":[10,26,34,49,108],"matrices":[11,69,78,94,139,164,192,213,316,325],"is":[12,22,85,106,147,182,188,247,254,258,287],"proposed":[13],"and":[14,28,32,75,82,125,172,184,196,274,294,322,329],"studied.":[15],"The":[16,51,100,153,241],"class":[17],"of":[18,67,102,123,129,226,234,237,243,266,275],"considered":[21],"related":[23],"computing":[25,40],"pseudospectra":[27],"their":[29],"extremal":[30],"points,":[31],"matrix":[35,331],"nearness":[36,332],"such":[38],"as":[39,187],"the":[41,63,103,130,143,150,162,167,174,178,189,199,219,223,227,231,235,251,263,267,271,276,283,291,296,305,311],"distance":[42],"instability":[44],"or":[45],"singularity":[47],"under":[48],"perturbations.":[50],"perturbation":[52,77,324],"structure":[53,168,272],"can":[54,111],"be":[55,113,137],"a":[56,71,120,170,203,215,259,280,318],"general":[57],"linear":[58],"structure.":[59,145,252],"We":[60],"focus":[61],"on":[62,76,202,206,222,270],"practically":[64],"important":[65],"cases":[66,128],"with":[70,79,97,115,193,214,317,326],"given":[72,80,144,194,216,319,327],"sparsity":[73,217,320],"pattern":[74,321],"range":[81,195,328],"corange.":[83],"It":[84,253],"known":[86,183],"that":[87,107,256],"analogous":[88],"unstructured":[92],"complex":[93,238],"favorably":[95],"works":[96],"rank-1":[98,116,138,163,239,245,277,284,299],"matrices.":[99,240],"novelty":[101],"present":[104],"paper":[105],"still":[112],"performed":[114],"matrices,":[117],"which":[118],"yields":[119],"significant":[121],"reduction":[122],"storage":[124],"in":[126,149,157,210],"some":[127],"computational":[131],"cost.":[132],"Optimizers":[133],"are":[134],"shown":[135,255],"orthogonally":[140],"projected":[141,165,249,300],"onto":[142,166,177,230,250],"This":[146],"used":[148],"numerical":[151,154],"algorithms.":[152],"comes":[156],"two":[158,312],"different":[159],"versions.":[160],"If":[161],"form":[169],"manifold":[171,236],"if":[173],"orthogonal":[175,224],"projection":[176,225,286],"corresponding":[179],"tangent":[180,232,285],"spaces":[181],"computationally":[185,297],"inexpensive,":[186],"case":[190],"corange,":[197],"then":[198,248],"method":[200,220],"relies":[201,221],"gradient":[204,229,268,306],"system":[205,246,269,301],"this":[207,244],"manifold.":[208],"Otherwise,":[209],"particular":[211],"pattern,":[218],"free":[228],"space":[233,273],"solution":[242],"there":[257],"bijective":[260],"correspondence":[261],"between":[262],"stationary":[264],"points":[265],"system.":[278,307],"Near":[279],"local":[281],"minimizer":[282],"very":[288],"close":[289],"identity":[292],"map,":[293],"so":[295],"favorable":[298],"behaves":[302],"locally":[303],"like":[304],"Numerical":[308],"experiments":[309],"illustrate":[310],"approaches":[313],"corange.Keywordsstructured":[330],"problemsstructured":[333],"pseudospectrumpseudospectral":[334],"abscissapseudospectral":[335],"radiusrank-1":[336],"perturbationslow-rank":[337],"dynamicsgradient":[338],"systemMSC":[339],"codes15A1865F15":[340]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
