{"id":"https://openalex.org/W2972300129","doi":"https://doi.org/10.3390/sym11091106","title":"A Convex Combination Approach for Mean-Based Variants of Newton\u2019s Method","display_name":"A Convex Combination Approach for Mean-Based Variants of Newton\u2019s Method","publication_year":2019,"publication_date":"2019-09-02","ids":{"openalex":"https://openalex.org/W2972300129","doi":"https://doi.org/10.3390/sym11091106","mag":"2972300129"},"language":"en","primary_location":{"id":"doi:10.3390/sym11091106","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11091106","pdf_url":"https://www.mdpi.com/2073-8994/11/9/1106/pdf?version=1567764696","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/9/1106/pdf?version=1567764696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085887256","display_name":"Alicia Cordero","orcid":"https://orcid.org/0000-0002-7462-9173"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alicia Cordero","raw_affiliation_strings":["Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7462-9173","affiliations":[{"raw_affiliation_string":"Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018731631","display_name":"Jonathan Franceschi","orcid":"https://orcid.org/0000-0002-0370-6346"},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES","IT"],"is_corresponding":true,"raw_author_name":"Jonathan Franceschi","raw_affiliation_strings":["Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","Universit\u00e1 di Ferrara, via Ludovico Ariosto, 35, 44121 Ferrara, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Universit\u00e1 di Ferrara, via Ludovico Ariosto, 35, 44121 Ferrara, Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049721976","display_name":"Juan R. Torregrosa","orcid":"https://orcid.org/0000-0002-9893-0761"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan R. Torregrosa","raw_affiliation_strings":["Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9893-0761","affiliations":[{"raw_affiliation_string":"Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023311908","display_name":"Anna Chiara Zagati","orcid":"https://orcid.org/0000-0002-4551-8415"},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES","IT"],"is_corresponding":false,"raw_author_name":"Anna C. Zagati","raw_affiliation_strings":["Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","Universit\u00e1 di Ferrara, via Ludovico Ariosto, 35, 44121 Ferrara, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera, s/n, 46022-Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Universit\u00e1 di Ferrara, via Ludovico Ariosto, 35, 44121 Ferrara, Italy","institution_ids":["https://openalex.org/I201324441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018731631"],"corresponding_institution_ids":["https://openalex.org/I201324441","https://openalex.org/I60053951"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6226,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82754656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"9","first_page":"1106","last_page":"1106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":1.0,"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":1.0,"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":0.9890999794006348,"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":0.9746999740600586,"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":0.6389650702476501},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6274036169052124},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5545227527618408},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.553193211555481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.541445791721344},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5304350852966309},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5094664692878723},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49124521017074585},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4436286687850952},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4266868829727173},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.42108774185180664},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4139694273471832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3377097249031067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3028751611709595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14299806952476501},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1293327808380127}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6389650702476501},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6274036169052124},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5545227527618408},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.553193211555481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.541445791721344},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5304350852966309},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5094664692878723},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49124521017074585},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4436286687850952},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4266868829727173},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.42108774185180664},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4139694273471832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3377097249031067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3028751611709595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14299806952476501},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1293327808380127},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11091106","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11091106","pdf_url":"https://www.mdpi.com/2073-8994/11/9/1106/pdf?version=1567764696","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6615bbe80bb747ca8cb9d0e926586d84","is_oa":true,"landing_page_url":"https://doaj.org/article/6615bbe80bb747ca8cb9d0e926586d84","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 9, p 1106 (2019)","raw_type":"article"},{"id":"pmh:oai:riunet.upv.es:10251/144084","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/144084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400639","display_name":"RiuNet (Universitat Polit\u00e8cnica de Val\u00e8ncia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.3390/sym11091106","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11091106","pdf_url":"https://www.mdpi.com/2073-8994/11/9/1106/pdf?version=1567764696","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1855301596","display_name":null,"funder_award_id":"PGC2018-095896-B-C22","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G6725151701","display_name":null,"funder_award_id":"PROMETEO 2016/089","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320321864","display_name":"Generalitat Valenciana","ror":"https://ror.org/0097mvx21"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2972300129.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W576148093","https://openalex.org/W1982246852","https://openalex.org/W2030284983","https://openalex.org/W2042383140","https://openalex.org/W2054711601","https://openalex.org/W2091326168","https://openalex.org/W2259043954","https://openalex.org/W2483406971","https://openalex.org/W2485731081","https://openalex.org/W2526050422","https://openalex.org/W2776018879","https://openalex.org/W6645806630","https://openalex.org/W6692019627"],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W3150973936","https://openalex.org/W4287263863","https://openalex.org/W3048353388","https://openalex.org/W3136821146","https://openalex.org/W2381473119"],"abstract_inverted_index":{"Several":[0],"authors":[1],"have":[2],"designed":[3],"variants":[4,34],"of":[5,35,44,46,58,60,66,94,117],"Newton\u2019s":[6,36],"method":[7,37],"for":[8],"solving":[9],"nonlinear":[10],"equations":[11,100],"by":[12],"using":[13],"different":[14,88],"means.":[15],"This":[16],"technique":[17],"involves":[18],"a":[19,64],"symmetry":[20,126],"in":[21,127],"the":[22,42,56,67,80,87,95,104,108,115,128],"corresponding":[23],"fixed-point":[24],"operator.":[25],"In":[26],"this":[27],"paper,":[28],"some":[29],"known":[30],"results":[31,82],"about":[32],"mean-based":[33],"(MBN)":[38],"are":[39,76,101],"re-analyzed":[40],"from":[41],"point":[43],"view":[45],"convex":[47],"combinations.":[48],"A":[49],"new":[50],"test":[51],"is":[52,70],"developed":[53],"to":[54,78,85,113],"study":[55],"order":[57],"convergence":[59,122],"general":[61],"MBN.":[62],"Furthermore,":[63],"generalization":[65],"Lehmer":[68],"mean":[69],"proposed":[71],"and":[72,84,123],"discussed.":[73],"Numerical":[74],"tests":[75],"provided":[77],"support":[79],"theoretical":[81],"obtained":[83],"compare":[86],"methods":[89,97],"employed.":[90],"Some":[91],"dynamical":[92],"planes":[93],"analyzed":[96],"on":[98],"several":[99],"presented,":[102],"revealing":[103],"great":[105],"difference":[106],"between":[107],"MBN":[109],"when":[110],"it":[111],"comes":[112],"determining":[114],"set":[116],"starting":[118],"points":[119],"that":[120],"ensure":[121],"observing":[124],"their":[125],"complex":[129],"plane.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
