{"id":"https://openalex.org/W3106944038","doi":"https://doi.org/10.3390/sym12121969","title":"A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots","display_name":"A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots","publication_year":2020,"publication_date":"2020-11-28","ids":{"openalex":"https://openalex.org/W3106944038","doi":"https://doi.org/10.3390/sym12121969","mag":"3106944038"},"language":"en","primary_location":{"id":"doi:10.3390/sym12121969","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121969","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1969/pdf?version=1606885664","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/2073-8994/12/12/1969/pdf?version=1606885664","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/I63568130","display_name":"Sant Longowal Institute of Engineering and Technology","ror":"https://ror.org/01n15vy71","country_code":"IN","type":"education","lineage":["https://openalex.org/I63568130"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sunil Kumar","raw_affiliation_strings":["Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India","institution_ids":["https://openalex.org/I63568130"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080384699","display_name":"Deepak Kumar","orcid":"https://orcid.org/0000-0003-3500-3087"},"institutions":[{"id":"https://openalex.org/I101407740","display_name":"Chandigarh University","ror":"https://ror.org/05t4pvx35","country_code":"IN","type":"education","lineage":["https://openalex.org/I101407740"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Deepak Kumar","raw_affiliation_strings":["Department of Mathematics, Chandigarh University, 140413, Mohali, NH-95 Chandigarh-Ludhiana Highway, Punjab 140413, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chandigarh University, 140413, Mohali, NH-95 Chandigarh-Ludhiana Highway, Punjab 140413, India","institution_ids":["https://openalex.org/I101407740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029076054","display_name":"Janak Raj Sharma","orcid":"https://orcid.org/0000-0002-4627-2795"},"institutions":[{"id":"https://openalex.org/I63568130","display_name":"Sant Longowal Institute of Engineering and Technology","ror":"https://ror.org/01n15vy71","country_code":"IN","type":"education","lineage":["https://openalex.org/I63568130"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Janak Raj Sharma","raw_affiliation_strings":["Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India","institution_ids":["https://openalex.org/I63568130"]}]},{"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":4,"corresponding_author_ids":["https://openalex.org/A5006002266","https://openalex.org/A5080384699"],"corresponding_institution_ids":["https://openalex.org/I101407740","https://openalex.org/I158333966","https://openalex.org/I3125347698"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.0704,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87127561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"12","first_page":"1969","last_page":"1969"},"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":0.9740999937057495,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9560999870300293,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.7070488333702087},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6323828101158142},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.624938428401947},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6227589249610901},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6012986302375793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5183318853378296},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.49376043677330017},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48644161224365234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4807600677013397},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46254631876945496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0872148871421814}],"concepts":[{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.7070488333702087},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6323828101158142},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.624938428401947},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6227589249610901},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6012986302375793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5183318853378296},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.49376043677330017},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48644161224365234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4807600677013397},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46254631876945496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0872148871421814},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/sym12121969","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121969","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1969/pdf?version=1606885664","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:fddf103455c94896b47af0de88b36eac","is_oa":true,"landing_page_url":"https://doaj.org/article/fddf103455c94896b47af0de88b36eac","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":"Symmetry, Vol 12, Iss 12, p 1969 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/12/1969/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12121969","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/sym12121969","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121969","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1969/pdf?version=1606885664","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3106944038.pdf","grobid_xml":"https://content.openalex.org/works/W3106944038.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W169252370","https://openalex.org/W644048992","https://openalex.org/W1495800631","https://openalex.org/W1521233584","https://openalex.org/W1966366562","https://openalex.org/W1972417972","https://openalex.org/W1989809391","https://openalex.org/W2001436769","https://openalex.org/W2004914005","https://openalex.org/W2013195662","https://openalex.org/W2017299431","https://openalex.org/W2032105013","https://openalex.org/W2035380993","https://openalex.org/W2039381603","https://openalex.org/W2047067568","https://openalex.org/W2048632019","https://openalex.org/W2054711601","https://openalex.org/W2078749110","https://openalex.org/W2213022072","https://openalex.org/W2784616802","https://openalex.org/W2953692893","https://openalex.org/W2990474610","https://openalex.org/W3021906145","https://openalex.org/W3033021776","https://openalex.org/W3036761082","https://openalex.org/W3038757318","https://openalex.org/W3093067222"],"related_works":["https://openalex.org/W4378765297","https://openalex.org/W4230581126","https://openalex.org/W2761548024","https://openalex.org/W2016521071","https://openalex.org/W2001367988","https://openalex.org/W2069384021","https://openalex.org/W4394867213","https://openalex.org/W1990308498","https://openalex.org/W1986629578","https://openalex.org/W3196781293"],"abstract_inverted_index":{"Many":[0],"optimal":[1,21,42],"order":[2,22,44],"multiple":[3,25,49],"root":[4,26],"techniques,":[5],"which":[6],"use":[7],"derivatives":[8],"in":[9,15,70],"the":[10,55,57,84,87,99,104,115,122,127],"algorithm,":[11],"have":[12],"been":[13],"proposed":[14],"literature.":[16],"But":[17],"contrarily,":[18],"derivative":[19],"free":[20],"techniques":[23,46],"for":[24,47,62],"are":[27],"almost":[28],"nonexistent.":[29],"By":[30],"this":[31,135],"as":[32,80,119],"an":[33],"inspirational":[34],"factor,":[35],"here":[36],"we":[37,108],"present":[38],"a":[39,131],"family":[40],"of":[41,51,65,83,103,134],"fourth":[43],"derivative-free":[45,76],"computing":[48],"roots":[50],"nonlinear":[52,95],"equations.":[53],"At":[54],"beginning":[56],"convergence":[58],"analysis":[59],"is":[60,78,91],"executed":[61],"particular":[63],"values":[64],"multiplicity":[66],"afterwards":[67],"it":[68],"concludes":[69],"general":[71],"form.":[72],"Behl":[73],"et.":[74],"al":[75],"method":[77],"seen":[79],"special":[81],"case":[82],"family.":[85],"Moreover,":[86],"applicability":[88],"and":[89],"comparison":[90],"demonstrated":[92],"on":[93],"different":[94],"problems":[96],"that":[97,110],"certifies":[98],"efficient":[100],"convergent":[101],"nature":[102],"new":[105,112],"methods.":[106],"Finally,":[107],"conclude":[109],"our":[111],"methods":[113],"consume":[114],"lowest":[116],"CPU":[117],"time":[118],"compared":[120],"to":[121,130],"existing":[123],"ones.":[124],"This":[125],"illuminates":[126],"theoretical":[128],"outcomes":[129],"great":[132],"extent":[133],"study.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}