{"id":"https://openalex.org/W2042027180","doi":"https://doi.org/10.1080/00207160802684434","title":"On a third order family of methods for solving nonlinear equations","display_name":"On a third order family of methods for solving nonlinear equations","publication_year":2010,"publication_date":"2010-05-25","ids":{"openalex":"https://openalex.org/W2042027180","doi":"https://doi.org/10.1080/00207160802684434","mag":"2042027180"},"language":"en","primary_location":{"id":"doi:10.1080/00207160802684434","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802684434","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":null,"display_name":"Djordje Herceg","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Djordje Herceg","raw_affiliation_strings":["University of Novi Sad","Faculty of Science and Mathematics, Department of Mathematics and Informatics , University of Novi Sad , Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Novi Sad","institution_ids":["https://openalex.org/I170726198"]},{"raw_affiliation_string":"Faculty of Science and Mathematics, Department of Mathematics and Informatics , University of Novi Sad , Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Djordje Herceg","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Djordje Herceg","raw_affiliation_strings":["University of Novi Sad","Faculty of Science and Mathematics, Department of Mathematics and Informatics , University of Novi Sad , Novi Sad, Serbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Novi Sad","institution_ids":["https://openalex.org/I170726198"]},{"raw_affiliation_string":"Faculty of Science and Mathematics, Department of Mathematics and Informatics , University of Novi Sad , Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Dragoslav Herceg","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":true,"raw_author_name":"Dragoslav Herceg","raw_affiliation_strings":["University of Novi Sad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Novi Sad","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"last","author":{"id":null,"display_name":"Dragoslav Herceg","orcid":null},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Dragoslav Herceg","raw_affiliation_strings":["University of Novi Sad"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Novi Sad","institution_ids":["https://openalex.org/I170726198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170726198"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.1372594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"87","issue":"11","first_page":"2533","last_page":"2541"},"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":0.9860000014305115,"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/T12354","display_name":"Innovations in Educational Methods","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8666648268699646},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6924507021903992},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.59441077709198},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5726471543312073},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5287361145019531},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5051091313362122},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.49534979462623596},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4871637523174286},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4605748653411865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4045228362083435},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2095530927181244},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06728050112724304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8666648268699646},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6924507021903992},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.59441077709198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5726471543312073},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5287361145019531},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5051091313362122},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.49534979462623596},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4871637523174286},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4605748653411865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4045228362083435},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2095530927181244},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06728050112724304},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160802684434","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802684434","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1964637974","https://openalex.org/W2006869483","https://openalex.org/W2048632019","https://openalex.org/W2068484625","https://openalex.org/W2326297968","https://openalex.org/W4239096436"],"related_works":["https://openalex.org/W2350788688","https://openalex.org/W2358591430","https://openalex.org/W2103912232","https://openalex.org/W2031390949","https://openalex.org/W2026900827","https://openalex.org/W3094698614","https://openalex.org/W1964267519","https://openalex.org/W3180920337","https://openalex.org/W3140142921","https://openalex.org/W4308670056"],"abstract_inverted_index":{"In":[0],"this":[1,99],"article":[2],"we":[3],"present":[4],"a":[5],"third-order":[6],"family":[7,104],"of":[8,62,81,102],"methods":[9,16],"for":[10,21,89,98],"solving":[11],"nonlinear":[12,41],"equations.":[13],"Some":[14],"well-known":[15],"belong":[17],"to":[18,39],"our":[19,82],"family,":[20],"example":[22],"Halley's":[23],"method,":[24,66],"method":[25,38,53],"(24)":[26],"from":[27,54],"[M.":[28],"Basto,":[29],"V.":[30],"Semiao,":[31],"and":[32,50,57,119],"F.L.":[33],"Calheiros,":[34],"A":[35],"new":[36],"iterative":[37],"compute":[40],"equations,":[42],"Appl.":[43,67],"Math.":[44,68],"Comput.":[45,69],"173":[46],"(2006),":[47],"pp.":[48,72],"468\u2013483]":[49],"the":[51,78,90,103],"super-Halley":[52],"[J.M.":[55],"Gutierrez":[56],"M.A.":[58],"Hernandez,":[59],"An":[60],"acceleration":[61],"Newton's":[63],"method:":[64],"Super-Halley":[65],"117":[70],"(2001),":[71],"223\u2013239].":[73],"The":[74],"convergence":[75],"analysis":[76],"shows":[77,106],"third":[79],"order":[80],"family.":[83,100],"We":[84],"also":[85],"give":[86],"sufficient":[87],"conditions":[88],"stopping":[91],"inequality":[92],"|x":[93],"n+1\u2212\u03b1|\u2264|x":[94],"n+1\u2212x":[95],"n":[96],"|":[97],"Comparison":[101],"members":[105],"that":[107],"there":[108],"are":[109,117],"no":[110],"significant":[111],"differences":[112],"between":[113],"them.":[114],"Several":[115],"examples":[116],"presented":[118],"compared.":[120]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}