{"id":"https://openalex.org/W2070989815","doi":"https://doi.org/10.1007/s10107-005-0695-z","title":"Convergence rate of Newton's method for L 2 spectral estimation","display_name":"Convergence rate of Newton's method for L 2 spectral estimation","publication_year":2005,"publication_date":"2005-12-30","ids":{"openalex":"https://openalex.org/W2070989815","doi":"https://doi.org/10.1007/s10107-005-0695-z","mag":"2070989815"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-005-0695-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-005-0695-z","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5113599408","display_name":"Hongxia Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongxia Yin","raw_affiliation_strings":["Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing, 100049, China","Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, 100049, Beijing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing, 100049, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, 100049, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101911108","display_name":"Chen Ling","orcid":"https://orcid.org/0000-0001-6314-2223"},"institutions":[{"id":"https://openalex.org/I90727586","display_name":"Zhejiang University of Finance and Economics","ror":"https://ror.org/055vj5234","country_code":"CN","type":"education","lineage":["https://openalex.org/I90727586"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Ling","raw_affiliation_strings":["School of Information, Zhejiang University of Finance and Economics, Hangzhou, 310012, China","School of Information, Zhejiang University of Finance and Economics, 310012, Hangzhou, China and Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Information, Zhejiang University of Finance and Economics, Hangzhou, 310012, China","institution_ids":["https://openalex.org/I90727586"]},{"raw_affiliation_string":"School of Information, Zhejiang University of Finance and Economics, 310012, Hangzhou, China and Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong#TAB#","institution_ids":["https://openalex.org/I90727586"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113599408"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.11088814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"107","issue":"3","first_page":"539","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9987000226974487,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9939000010490417,"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":0.8514125347137451},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6704328060150146},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6520962715148926},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6308144330978394},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5978376269340515},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5549394488334656},{"id":"https://openalex.org/keywords/steffensens-method","display_name":"Steffensen's method","score":0.5484592914581299},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.5350182056427002},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4921085238456726},{"id":"https://openalex.org/keywords/newton-fractal","display_name":"Newton fractal","score":0.4780578911304474},{"id":"https://openalex.org/keywords/secant-method","display_name":"Secant method","score":0.43213921785354614},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.42527562379837036},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.36988013982772827},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.350523442029953},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.34640049934387207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3301651179790497},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.23451226949691772},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11437642574310303},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07386612892150879}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8514125347137451},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6704328060150146},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6520962715148926},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6308144330978394},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5978376269340515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5549394488334656},{"id":"https://openalex.org/C173443657","wikidata":"https://www.wikidata.org/wiki/Q7606635","display_name":"Steffensen's method","level":5,"score":0.5484592914581299},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.5350182056427002},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4921085238456726},{"id":"https://openalex.org/C194342247","wikidata":"https://www.wikidata.org/wiki/Q1151001","display_name":"Newton fractal","level":4,"score":0.4780578911304474},{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.43213921785354614},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.42527562379837036},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.36988013982772827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.350523442029953},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.34640049934387207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3301651179790497},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.23451226949691772},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11437642574310303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07386612892150879},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-005-0695-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-005-0695-z","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/26984","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/26984","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W112339387","https://openalex.org/W1491846897","https://openalex.org/W1966698348","https://openalex.org/W1970295817","https://openalex.org/W1973198704","https://openalex.org/W1988518818","https://openalex.org/W1992688650","https://openalex.org/W1999503666","https://openalex.org/W2006115473","https://openalex.org/W2015270939","https://openalex.org/W2020084878","https://openalex.org/W2053643774","https://openalex.org/W2061263754","https://openalex.org/W2061872779","https://openalex.org/W2067547116","https://openalex.org/W2070409288","https://openalex.org/W2080537549","https://openalex.org/W2082746403","https://openalex.org/W2090963365","https://openalex.org/W2113734366","https://openalex.org/W2125829984","https://openalex.org/W2137507407","https://openalex.org/W2170060163","https://openalex.org/W2591416401","https://openalex.org/W2894073805"],"related_works":["https://openalex.org/W4297921956","https://openalex.org/W2951861326","https://openalex.org/W1985487460","https://openalex.org/W2356844075","https://openalex.org/W2196356369","https://openalex.org/W2124368230","https://openalex.org/W2986655728","https://openalex.org/W2349605439","https://openalex.org/W2731844756","https://openalex.org/W1592546441"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}