{"id":"https://openalex.org/W2091611891","doi":"https://doi.org/10.1155/2012/568740","title":"A Class of Three\u2010Step Derivative\u2010Free Root Solvers with Optimal Convergence Order","display_name":"A Class of Three\u2010Step Derivative\u2010Free Root Solvers with Optimal Convergence Order","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2091611891","doi":"https://doi.org/10.1155/2012/568740","mag":"2091611891"},"language":"en","primary_location":{"id":"doi:10.1155/2012/568740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/568740","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/568740.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/568740.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042799498","display_name":"Fazlollah Soleymani","orcid":"https://orcid.org/0000-0002-6905-8951"},"institutions":[{"id":"https://openalex.org/I4210103813","display_name":"Islamic Azad University, Zahedan Branch","ror":"https://ror.org/01am3pw68","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210103813"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"F. Soleymani","raw_affiliation_strings":["Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, Iran","Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan"],"affiliations":[{"raw_affiliation_string":"Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, Iran","institution_ids":["https://openalex.org/I4210103813"]},{"raw_affiliation_string":"Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan","institution_ids":["https://openalex.org/I4210103813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076884195","display_name":"S. Karimi Vanani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103813","display_name":"Islamic Azad University, Zahedan Branch","ror":"https://ror.org/01am3pw68","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210103813"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"S. Karimi Vanani","raw_affiliation_strings":["Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran","Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran","institution_ids":["https://openalex.org/I4210103813"]},{"raw_affiliation_string":"Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan","institution_ids":["https://openalex.org/I4210103813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040662402","display_name":"M. Jamali Paghaleh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103813","display_name":"Islamic Azad University, Zahedan Branch","ror":"https://ror.org/01am3pw68","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210103813"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. Jamali Paghaleh","raw_affiliation_strings":["Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, Iran","Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan"],"affiliations":[{"raw_affiliation_string":"Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan, Iran","institution_ids":["https://openalex.org/I4210103813"]},{"raw_affiliation_string":"Young Researchers Club, Islamic Azad University, Zahedan Branch, Zahedan","institution_ids":["https://openalex.org/I4210103813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042799498"],"corresponding_institution_ids":["https://openalex.org/I4210103813"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":7.1711,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.97853156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.9944999814033508,"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/class","display_name":"Class (philosophy)","score":0.7048444747924805},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6668435335159302},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.6587991714477539},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6338326930999756},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5941166877746582},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5038928389549255},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4769150912761688},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44806942343711853},{"id":"https://openalex.org/keywords/root-finding-algorithm","display_name":"Root-finding algorithm","score":0.4391981065273285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34764915704727173},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12739083170890808},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.048002809286117554}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7048444747924805},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6668435335159302},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.6587991714477539},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6338326930999756},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5941166877746582},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5038928389549255},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4769150912761688},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44806942343711853},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.4391981065273285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34764915704727173},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12739083170890808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.048002809286117554},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2012/568740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/568740","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/568740.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1357180263","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1357180263","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:568740","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/568740.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:4175491eb84c4d7b8744a7c81fc34cf3","is_oa":true,"landing_page_url":"https://doaj.org/article/4175491eb84c4d7b8744a7c81fc34cf3","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/568740","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/568740","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/568740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/568740","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/568740.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2091611891.pdf","grobid_xml":"https://content.openalex.org/works/W2091611891.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1972417972","https://openalex.org/W1990882954","https://openalex.org/W2025936812","https://openalex.org/W2031275499","https://openalex.org/W2033248762","https://openalex.org/W2035972127","https://openalex.org/W2038714395","https://openalex.org/W2041651819","https://openalex.org/W2044645814","https://openalex.org/W2048632019","https://openalex.org/W2053048023","https://openalex.org/W2055607857","https://openalex.org/W2056333052","https://openalex.org/W2063158840","https://openalex.org/W2069375119","https://openalex.org/W2075659701","https://openalex.org/W2118066179","https://openalex.org/W2166523047","https://openalex.org/W2170515392","https://openalex.org/W2258114693","https://openalex.org/W2271644272","https://openalex.org/W2284116559","https://openalex.org/W2289758233","https://openalex.org/W2333123932","https://openalex.org/W2607588096","https://openalex.org/W6695871624"],"related_works":["https://openalex.org/W1563175402","https://openalex.org/W3169616122","https://openalex.org/W3198881649","https://openalex.org/W1988566873","https://openalex.org/W4287325063","https://openalex.org/W2069686407","https://openalex.org/W3215882190","https://openalex.org/W2377857862","https://openalex.org/W2041939310","https://openalex.org/W2011848867"],"abstract_inverted_index":{"A":[0],"class":[1,34,53,72,100],"of":[2,26,32,70,90,101,110],"three\u2010step":[3,28],"eighth\u2010order":[4],"root":[5],"solvers":[6],"is":[7,14,54,63,73,104],"constructed":[8],"in":[9,22,65,114],"this":[10],"study.":[11],"Our":[12],"aim":[13],"fulfilled":[15],"by":[16],"using":[17],"an":[18],"interpolatory":[19],"rational":[20],"function":[21],"the":[23,33,36,42,52,71,78,82,98,107,111,115],"third":[24],"step":[25],"a":[27,88],"cycle.":[29],"Each":[30],"method":[31,69],"reaches":[35],"optimal":[37],"efficiency":[38],"index":[39],"according":[40],"to":[41,87],"Kung\u2010Traub":[43],"conjecture":[44],"concerning":[45],"multipoint":[46],"iterative":[47],"methods":[48,80,103,109],"without":[49],"memory.":[50],"Moreover,":[51],"free":[55],"from":[56,81],"derivative":[57],"calculation":[58],"per":[59],"full":[60],"iteration,":[61],"which":[62],"important":[64],"engineering":[66],"problems.":[67],"One":[68],"established":[74],"analytically.":[75],"To":[76],"test":[77],"derived":[79],"class,":[83],"we":[84],"apply":[85],"them":[86],"lot":[89],"nonlinear":[91],"scalar":[92],"equations.":[93],"Numerical":[94],"examples":[95],"suggest":[96],"that":[97],"novel":[99],"derivative\u2010free":[102],"better":[105],"than":[106],"existing":[108],"same":[112],"type":[113],"literature.":[116]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}