{"id":"https://openalex.org/W2104481149","doi":"https://doi.org/10.1137/050624509","title":"A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix","display_name":"A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2104481149","doi":"https://doi.org/10.1137/050624509","mag":"2104481149"},"language":"en","primary_location":{"id":"doi:10.1137/050624509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624509","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Houduo Qi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029911976","display_name":"Defeng Sun","orcid":"https://orcid.org/0000-0003-0481-272X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Defeng Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112621269"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.7747,"has_fulltext":false,"cited_by_count":327,"citation_normalized_percentile":{"value":0.98576544,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"28","issue":"2","first_page":"360","last_page":"385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9957000017166138,"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":0.7836882472038269},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.7398160099983215},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.7115710377693176},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5378474593162537},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.515652060508728},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5106626152992249},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.501530647277832},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4985165596008301},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.47306904196739197},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.4539276957511902},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.43480929732322693},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43284353613853455},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4201127886772156},{"id":"https://openalex.org/keywords/matrix-function","display_name":"Matrix function","score":0.411722868680954},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.3768582344055176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3641064763069153},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.30907830595970154},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2474231719970703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21837252378463745},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.19860762357711792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1323162317276001},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07385808229446411}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7836882472038269},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.7398160099983215},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.7115710377693176},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5378474593162537},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.515652060508728},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5106626152992249},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.501530647277832},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4985165596008301},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.47306904196739197},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.4539276957511902},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.43480929732322693},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43284353613853455},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4201127886772156},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.411722868680954},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.3768582344055176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3641064763069153},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.30907830595970154},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2474231719970703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21837252378463745},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.19860762357711792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1323162317276001},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07385808229446411},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050624509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624509","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/102741","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/102741","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.101.2868","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.2868","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/~matsundf/Co_matrix_rev.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3906325352","display_name":null,"funder_award_id":"EP/D502535/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1480387038","https://openalex.org/W1491846897","https://openalex.org/W1497941563","https://openalex.org/W1534416612","https://openalex.org/W1551360398","https://openalex.org/W1577338488","https://openalex.org/W1966972652","https://openalex.org/W1979152443","https://openalex.org/W1980428414","https://openalex.org/W1982165727","https://openalex.org/W1992688650","https://openalex.org/W1999138341","https://openalex.org/W2004596681","https://openalex.org/W2007632272","https://openalex.org/W2015270939","https://openalex.org/W2017580271","https://openalex.org/W2019651381","https://openalex.org/W2020084878","https://openalex.org/W2021048962","https://openalex.org/W2046680696","https://openalex.org/W2047668748","https://openalex.org/W2050958540","https://openalex.org/W2061872779","https://openalex.org/W2067547116","https://openalex.org/W2068484625","https://openalex.org/W2070409288","https://openalex.org/W2072863821","https://openalex.org/W2075706482","https://openalex.org/W2077260542","https://openalex.org/W2079278943","https://openalex.org/W2082746403","https://openalex.org/W2087236370","https://openalex.org/W2090963365","https://openalex.org/W2091560152","https://openalex.org/W2094211749","https://openalex.org/W2119582979","https://openalex.org/W2127930751","https://openalex.org/W2148012411","https://openalex.org/W2152453276","https://openalex.org/W2165355250","https://openalex.org/W2246422272","https://openalex.org/W2316564661","https://openalex.org/W2478091498","https://openalex.org/W2583867411","https://openalex.org/W2610857016","https://openalex.org/W2798707604","https://openalex.org/W3029645440","https://openalex.org/W3118870036","https://openalex.org/W4245055410","https://openalex.org/W4249513058","https://openalex.org/W4255333822","https://openalex.org/W4293775970","https://openalex.org/W4293820388"],"related_works":["https://openalex.org/W2013605080","https://openalex.org/W2377470197","https://openalex.org/W4285316332","https://openalex.org/W1664950781","https://openalex.org/W2563719283","https://openalex.org/W2949437822","https://openalex.org/W3196363161","https://openalex.org/W2365346210","https://openalex.org/W3001734434","https://openalex.org/W2131847826"],"abstract_inverted_index":{"The":[0,23],"nearest":[1,86],"correlation":[2,9,87],"matrix":[3,10,18,88,97],"problem":[4,31],"is":[5,12,27,65],"to":[6,14,28,52],"find":[7],"a":[8,15,81],"which":[11],"closest":[13],"given":[16],"symmetric":[17],"in":[19,61],"the":[20,58,62,85,102,106,113,117,121],"Frobenius":[21],"norm.":[22],"well-studied":[24],"dual":[25,63],"approach":[26,64],"reformulate":[29],"this":[30,77],"as":[32,46],"an":[33],"unconstrained":[34],"continuously":[35,68],"differentiable":[36],"convex":[37],"optimization":[38],"problem.":[39,89],"Gradient":[40],"methods":[41,44,71],"and":[42,116],"quasi-Newton":[43],"such":[45],"BFGS":[47],"have":[48],"been":[49],"used":[50],"directly":[51],"obtain":[53],"globally":[54],"convergent":[55],"methods.":[56],"Since":[57],"objective":[59],"function":[60],"not":[66],"twice":[67],"differentiable,":[69],"these":[70],"converge":[72],"at":[73],"best":[74],"linearly.":[75],"In":[76],"paper,":[78],"we":[79,100],"investigate":[80],"Newton-type":[82],"method":[83],"for":[84],"Based":[90],"on":[91,94],"recent":[92],"developments":[93],"strongly":[95],"semismooth":[96],"valued":[98],"functions,":[99],"prove":[101],"quadratic":[103],"convergence":[104,115],"of":[105,120],"proposed":[107],"Newton":[108],"method.":[109,122],"Numerical":[110],"experiments":[111],"confirm":[112],"fast":[114],"high":[118],"efficiency":[119]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":32},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":34},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":13}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
