{"id":"https://openalex.org/W4294958998","doi":"https://doi.org/10.3390/sym14091881","title":"Optimal Derivative-Free One-Point Algorithms for Computing Multiple Zeros of Nonlinear Equations","display_name":"Optimal Derivative-Free One-Point Algorithms for Computing Multiple Zeros of Nonlinear Equations","publication_year":2022,"publication_date":"2022-09-08","ids":{"openalex":"https://openalex.org/W4294958998","doi":"https://doi.org/10.3390/sym14091881"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091881","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1881/pdf?version=1662630279","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/2073-8994/14/9/1881/pdf?version=1662630279","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004397459","display_name":"Sunil Kumar","orcid":"https://orcid.org/0000-0002-8471-5139"},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sunil Kumar","raw_affiliation_strings":["Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Channai 601103, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Channai 601103, India","institution_ids":["https://openalex.org/I81556334"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102704914","display_name":"Jai Bhagwan","orcid":"https://orcid.org/0000-0002-6941-1364"},"institutions":[{"id":"https://openalex.org/I4210107852","display_name":"Government Medical College","ror":"https://ror.org/01te4n153","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210107852"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jai Bhagwan","raw_affiliation_strings":["Department of Mathematics, Government Post Graduate College, Rohtak 124001, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government Post Graduate College, Rohtak 124001, India","institution_ids":["https://openalex.org/I4210107852"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006002266","display_name":"Lorentz J\u00e4ntschi","orcid":"https://orcid.org/0000-0001-8524-743X"},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]},{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Lorentz J\u00e4ntschi","raw_affiliation_strings":["Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania","Institute of Doctoral Studies, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I158333966"]},{"raw_affiliation_string":"Institute of Doctoral Studies, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004397459","https://openalex.org/A5006002266"],"corresponding_institution_ids":["https://openalex.org/I158333966","https://openalex.org/I3125347698","https://openalex.org/I81556334"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9141,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.8364532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"9","first_page":"1881","last_page":"1881"},"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/T12354","display_name":"Innovations in Educational Methods","score":0.9623000025749207,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9541000127792358,"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/convergence","display_name":"Convergence (economics)","score":0.7123302817344666},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6390765905380249},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5708902478218079},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5615841746330261},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5293182730674744},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5218676328659058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5170722603797913},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5073902010917664},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5064817667007446},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.5046583414077759},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4865919351577759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47069406509399414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13449522852897644}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7123302817344666},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6390765905380249},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5708902478218079},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5615841746330261},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5293182730674744},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5218676328659058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5170722603797913},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5073902010917664},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5064817667007446},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5046583414077759},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4865919351577759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47069406509399414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13449522852897644},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091881","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1881/pdf?version=1662630279","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:7c29e7a74c8e4ed386bf70b773e73d5c","is_oa":true,"landing_page_url":"https://doaj.org/article/7c29e7a74c8e4ed386bf70b773e73d5c","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 9, p 1881 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1881/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091881","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"}],"best_oa_location":{"id":"doi:10.3390/sym14091881","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091881","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1881/pdf?version=1662630279","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4294958998.pdf","grobid_xml":"https://content.openalex.org/works/W4294958998.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W19715789","https://openalex.org/W169252370","https://openalex.org/W1966366562","https://openalex.org/W1972417972","https://openalex.org/W1982246852","https://openalex.org/W1989809391","https://openalex.org/W1990096926","https://openalex.org/W2001436769","https://openalex.org/W2010034224","https://openalex.org/W2013195662","https://openalex.org/W2017299431","https://openalex.org/W2032105013","https://openalex.org/W2035380993","https://openalex.org/W2039381603","https://openalex.org/W2059815115","https://openalex.org/W2078749110","https://openalex.org/W2083764494","https://openalex.org/W2087815951","https://openalex.org/W2213022072","https://openalex.org/W2953692893","https://openalex.org/W2966120677","https://openalex.org/W2982961745","https://openalex.org/W2990474610","https://openalex.org/W2996250151","https://openalex.org/W3021906145","https://openalex.org/W3036761082","https://openalex.org/W3038757318","https://openalex.org/W3113176096","https://openalex.org/W3124563292","https://openalex.org/W3136289413","https://openalex.org/W3177655429","https://openalex.org/W3197964090","https://openalex.org/W4291289349","https://openalex.org/W4293071515","https://openalex.org/W6641880522","https://openalex.org/W6645806630","https://openalex.org/W6688545251"],"related_works":["https://openalex.org/W2395105737","https://openalex.org/W2369507325","https://openalex.org/W3208270790","https://openalex.org/W3135719690","https://openalex.org/W2368550193","https://openalex.org/W1985023705","https://openalex.org/W2061027733","https://openalex.org/W2387252559","https://openalex.org/W2384620691","https://openalex.org/W4401950215"],"abstract_inverted_index":{"In":[0],"this":[1,46,178],"paper,":[2],"we":[3,49,148],"describe":[4],"iterative":[5],"derivative-free":[6],"algorithms":[7,52,83],"for":[8,64],"multiple":[9,20,68],"roots":[10,21,69],"of":[11,22,32,67,101,161,177],"a":[12,23,73],"nonlinear":[13,24],"equation.":[14],"Many":[15],"researchers":[16],"have":[17,85],"evaluated":[18,95],"the":[19,27,36,55,78,81,110,140,151,158,166,174],"equation":[25],"using":[26,54,105],"first-":[28],"or":[29],"second-order":[30,51],"derivative":[31,38],"functions.":[33],"However,":[34],"calculating":[35],"function\u2019s":[37],"at":[39,96],"each":[40],"iteration":[41],"is":[42,60,103],"laborious.":[43],"So,":[44],"taking":[45],"as":[47],"motivation,":[48],"develop":[50],"without":[53],"derivatives.":[56],"The":[57,99],"convergence":[58,87,102],"analysis":[59],"first":[61],"carried":[62],"out":[63],"particular":[65],"values":[66],"before":[70],"coming":[71],"to":[72,77,93],"general":[74],"conclusion.":[75],"According":[76],"Kung\u2013Traub":[79],"hypothesis,":[80],"new":[82],"will":[84],"optimal":[86],"since":[88],"only":[89],"two":[90],"functions":[91],"need":[92],"be":[94],"every":[97],"step.":[98],"order":[100],"investigated":[104],"Taylor\u2019s":[106],"series":[107],"expansion.":[108],"Moreover,":[109],"applicability":[111],"and":[112,128,133,143],"comparisons":[113],"with":[114,165],"existing":[115],"methods":[116],"are":[117],"demonstrated":[118],"on":[119],"three":[120,134],"real-life":[121],"problems":[122,137],"(e.g.,":[123],"Kepler\u2019s,":[124],"Van":[125],"der":[126],"Waals,":[127],"continuous-stirred":[129],"tank":[130],"reactor":[131],"problems)":[132],"standard":[135],"academic":[136],"that":[138,154],"contain":[139],"root":[141,145],"clustering":[142],"complex":[144],"problems.":[146],"Finally,":[147],"see":[149],"from":[150],"computational":[152],"outcomes":[153],"our":[155],"approaches":[156],"use":[157],"least":[159],"amount":[160],"processing":[162],"time":[163],"compared":[164],"ones":[167],"already":[168],"in":[169],"use.":[170],"This":[171],"effectively":[172],"displays":[173],"theoretical":[175],"conclusions":[176],"study.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
