{"id":"https://openalex.org/W3163667524","doi":"https://doi.org/10.3390/sym13050884","title":"A General Optimal Iterative Scheme with Arbitrary Order of Convergence","display_name":"A General Optimal Iterative Scheme with Arbitrary Order of Convergence","publication_year":2021,"publication_date":"2021-05-16","ids":{"openalex":"https://openalex.org/W3163667524","doi":"https://doi.org/10.3390/sym13050884","mag":"3163667524"},"language":"en","primary_location":{"id":"doi:10.3390/sym13050884","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13050884","pdf_url":"https://www.mdpi.com/2073-8994/13/5/884/pdf?version=1621330635","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/2073-8994/13/5/884/pdf?version=1621330635","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":["Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7462-9173","affiliations":[{"raw_affiliation_string":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"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":true,"raw_author_name":"Juan R. Torregrosa","raw_affiliation_strings":["Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9893-0761","affiliations":[{"raw_affiliation_string":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022707392","display_name":"Paula Triguero\u2010Navarro","orcid":"https://orcid.org/0000-0002-7319-9992"},"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":"Paula Triguero-Navarro","raw_affiliation_strings":["Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7319-9992","affiliations":[{"raw_affiliation_string":"Multidisciplinary Institute of Mathematics, Universitat Polit\u00e8nica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049721976"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.7493,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.92916201,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"5","first_page":"884","last_page":"884"},"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":0.9958999752998352,"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":0.9799000024795532,"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":0.7075349688529968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6404489874839783},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.600780725479126},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5608974695205688},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5365844368934631},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5116506218910217},{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.5014805793762207},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.46555784344673157},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.46253207325935364},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.44767558574676514},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3204463720321655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2861926555633545},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14388641715049744},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10549458861351013}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7075349688529968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6404489874839783},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.600780725479126},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5608974695205688},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5365844368934631},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5116506218910217},{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.5014805793762207},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.46555784344673157},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.46253207325935364},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.44767558574676514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3204463720321655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2861926555633545},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14388641715049744},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10549458861351013},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13050884","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13050884","pdf_url":"https://www.mdpi.com/2073-8994/13/5/884/pdf?version=1621330635","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:1dba5d1cb93045c9a0bc973268376518","is_oa":true,"landing_page_url":"https://doaj.org/article/1dba5d1cb93045c9a0bc973268376518","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 13, Iss 5, p 884 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/5/884/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13050884","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"},{"id":"pmh:oai:riunet.upv.es:10251/180472","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/180472","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/sym13050884","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13050884","pdf_url":"https://www.mdpi.com/2073-8994/13/5/884/pdf?version=1621330635","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/G5404829777","display_name":null,"funder_award_id":"PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE)","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G8063416118","display_name":null,"funder_award_id":"PGC2018","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3163667524.pdf","grobid_xml":"https://content.openalex.org/works/W3163667524.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W576148093","https://openalex.org/W1487444668","https://openalex.org/W1920232494","https://openalex.org/W1972417972","https://openalex.org/W1982246852","https://openalex.org/W2048193077","https://openalex.org/W2055308255","https://openalex.org/W2062985118","https://openalex.org/W2090963365","https://openalex.org/W2091326168","https://openalex.org/W2483406971","https://openalex.org/W2511950701","https://openalex.org/W2526050422","https://openalex.org/W2806752501","https://openalex.org/W2890864075","https://openalex.org/W2902485869","https://openalex.org/W2921216878","https://openalex.org/W2948405577","https://openalex.org/W2991347988","https://openalex.org/W3012002890","https://openalex.org/W3080565797","https://openalex.org/W3135229758","https://openalex.org/W3138433766","https://openalex.org/W4301621763","https://openalex.org/W6640177152","https://openalex.org/W6645806630"],"related_works":["https://openalex.org/W2378562963","https://openalex.org/W2350788688","https://openalex.org/W2353579944","https://openalex.org/W2089967807","https://openalex.org/W2078306205","https://openalex.org/W2033997865","https://openalex.org/W2031390949","https://openalex.org/W4378376763","https://openalex.org/W1964706674","https://openalex.org/W2103912232"],"abstract_inverted_index":{"A":[0],"general":[1],"optimal":[2],"iterative":[3],"method,":[4],"for":[5],"approximating":[6],"the":[7,38,50,60,64],"solution":[8],"of":[9,12,18,35,37,63,66,68,77],"nonlinear":[10],"equations,":[11],"(n+1)":[13],"steps":[14],"with":[15,49],"2n+1":[16],"order":[17],"convergence":[19],"is":[20,84],"presented.":[21,74],"Cases":[22],"n=0":[23],"and":[24,29,47,70],"n=1":[25],"correspond":[26],"to":[27,52],"Newton\u2019s":[28],"Ostrowski\u2019s":[30],"schemes,":[31],"respectively.":[32],"The":[33,56,75],"basins":[34,65],"attraction":[36,67],"proposed":[39],"schemes":[40],"on":[41,80],"different":[42,61,78],"test":[43,82],"functions":[44,83],"are":[45,73],"analyzed":[46],"compared":[48],"corresponding":[51],"other":[53],"known":[54,71],"methods.":[55],"dynamical":[57],"planes":[58],"showing":[59],"symmetries":[62],"new":[69],"methods":[72,79],"performance":[76],"some":[81],"shown.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}