{"id":"https://openalex.org/W2076492844","doi":"https://doi.org/10.1080/00207160412331284123","title":"On the local convergence of secant-type methods","display_name":"On the local convergence of secant-type methods","publication_year":2004,"publication_date":"2004-08-30","ids":{"openalex":"https://openalex.org/W2076492844","doi":"https://doi.org/10.1080/00207160412331284123","mag":"2076492844"},"language":"en","primary_location":{"id":"doi:10.1080/00207160412331284123","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160412331284123","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5067555613","display_name":"Sergio Amat","orcid":"https://orcid.org/0000-0002-9954-5240"},"institutions":[{"id":"https://openalex.org/I3123212020","display_name":"Universidad Polit\u00e9cnica de Cartagena","ror":"https://ror.org/02k5kx966","country_code":"ES","type":"education","lineage":["https://openalex.org/I3123212020"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. Amat *","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica , Universidad de Cartagena , Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica , Universidad de Cartagena , Spain","institution_ids":["https://openalex.org/I3123212020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089190023","display_name":"Sonia Busquier","orcid":null},"institutions":[{"id":"https://openalex.org/I3123212020","display_name":"Universidad Polit\u00e9cnica de Cartagena","ror":"https://ror.org/02k5kx966","country_code":"ES","type":"education","lineage":["https://openalex.org/I3123212020"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. Busquier \u2020","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica , Universidad de Cartagena , Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica , Universidad de Cartagena , Spain","institution_ids":["https://openalex.org/I3123212020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089932651","display_name":"J.M. Guti\u00e9rrez","orcid":"https://orcid.org/0000-0002-0434-7250"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. M. Guti\u00e9rrez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas y Computaci\u00f3n , Universidad de La Rioja , Spain","Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas y Computaci\u00f3n , Universidad de La Rioja , Spain","institution_ids":["https://openalex.org/I168974976"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Spain","institution_ids":["https://openalex.org/I168974976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089932651"],"corresponding_institution_ids":["https://openalex.org/I168974976"],"apc_list":null,"apc_paid":null,"fwci":3.0075,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.90012407,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"81","issue":"9","first_page":"1153","last_page":"1161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.996399998664856,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9807999730110168,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/convergence","display_name":"Convergence (economics)","score":0.7981570959091187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7904890775680542},{"id":"https://openalex.org/keywords/secant-method","display_name":"Secant method","score":0.782742440700531},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"Radius of convergence","score":0.6143811345100403},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5288192629814148},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5241339802742004},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.49580034613609314},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4877370297908783},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.4286857843399048},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34766751527786255},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.3244839012622833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26284095644950867},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.19382166862487793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17649811506271362},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.1358206868171692},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09747779369354248},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.05307421088218689},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.04711750149726868}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7981570959091187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904890775680542},{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.782742440700531},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.6143811345100403},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5288192629814148},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5241339802742004},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.49580034613609314},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4877370297908783},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.4286857843399048},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34766751527786255},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.3244839012622833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26284095644950867},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.19382166862487793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17649811506271362},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.1358206868171692},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09747779369354248},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.05307421088218689},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.04711750149726868},{"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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160412331284123","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160412331284123","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W25637881","https://openalex.org/W112273107","https://openalex.org/W140329123","https://openalex.org/W571836983","https://openalex.org/W1129295489","https://openalex.org/W1995043720","https://openalex.org/W1995091049","https://openalex.org/W2022296788","https://openalex.org/W2048658386","https://openalex.org/W2050361884","https://openalex.org/W2062008013"],"related_works":["https://openalex.org/W4297921956","https://openalex.org/W2951861326","https://openalex.org/W1985487460","https://openalex.org/W2740653611","https://openalex.org/W2762113365","https://openalex.org/W2142167470","https://openalex.org/W2350788688","https://openalex.org/W2379238906","https://openalex.org/W3143080231","https://openalex.org/W2029462152"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"carry":[4],"out":[5],"a":[6],"local":[7],"convergence":[8],"study":[9],"for":[10],"Secant-type":[11],"methods.":[12],"Our":[13],"goal":[14],"is":[15],"to":[16],"enlarge":[17],"the":[18,24],"radius":[19],"of":[20],"convergence,":[21],"without":[22],"increasing":[23],"necessary":[25],"hypothesis.":[26],"Finally,":[27],"some":[28],"numerical":[29],"tests":[30],"and":[31],"comparisons":[32],"with":[33],"early":[34],"results":[35],"are":[36],"analyzed.":[37]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
