{"id":"https://openalex.org/W3109507353","doi":"https://doi.org/10.3390/sym12121947","title":"Generating Optimal Eighth Order Methods for Computing Multiple Roots","display_name":"Generating Optimal Eighth Order Methods for Computing Multiple Roots","publication_year":2020,"publication_date":"2020-11-25","ids":{"openalex":"https://openalex.org/W3109507353","doi":"https://doi.org/10.3390/sym12121947","mag":"3109507353"},"language":"en","primary_location":{"id":"doi:10.3390/sym12121947","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121947","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1947/pdf?version=1606312995","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/2073-8994/12/12/1947/pdf?version=1606312995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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, Gharuan, Mohali 140413, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, India","institution_ids":["https://openalex.org/I101407740"]}]},{"author_position":"middle","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/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/A5051902697","display_name":"Matteo D\u2019Amore","orcid":"https://orcid.org/0000-0002-2886-0032"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Matteo d\u2019Amore","raw_affiliation_strings":["Difarma, University of Salerno, Via Giovanni II, 132, 84084 Fisciano (SA), Italy"],"affiliations":[{"raw_affiliation_string":"Difarma, University of Salerno, Via Giovanni II, 132, 84084 Fisciano (SA), Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5051902697","https://openalex.org/A5080384699"],"corresponding_institution_ids":["https://openalex.org/I101407740","https://openalex.org/I131729948"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21880819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"12","first_page":"1947","last_page":"1947"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9861999750137329,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9757999777793884,"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":0.7596562504768372},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5904796719551086},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.579451322555542},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5502519607543945},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5399617552757263},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.539691686630249},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5373929738998413},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.5324332118034363},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5118653178215027},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5044280290603638},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4154747426509857},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10941839218139648}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7596562504768372},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5904796719551086},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.579451322555542},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5502519607543945},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5399617552757263},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.539691686630249},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5373929738998413},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5324332118034363},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5118653178215027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044280290603638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4154747426509857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10941839218139648},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12121947","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121947","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1947/pdf?version=1606312995","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:2a4f1ee24796414291e7ee8913c3a325","is_oa":true,"landing_page_url":"https://doaj.org/article/2a4f1ee24796414291e7ee8913c3a325","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 1947 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/12/1947/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12121947","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/sym12121947","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121947","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1947/pdf?version=1606312995","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/W3109507353.pdf","grobid_xml":"https://content.openalex.org/works/W3109507353.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W169252370","https://openalex.org/W232674853","https://openalex.org/W624935493","https://openalex.org/W961898562","https://openalex.org/W1966366562","https://openalex.org/W1972417972","https://openalex.org/W1974260008","https://openalex.org/W1975400766","https://openalex.org/W1976489082","https://openalex.org/W1983087877","https://openalex.org/W1988627280","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/W2039381603","https://openalex.org/W2048270647","https://openalex.org/W2048632019","https://openalex.org/W2050221432","https://openalex.org/W2054711601","https://openalex.org/W2067520338","https://openalex.org/W2078749110","https://openalex.org/W2213022072","https://openalex.org/W2293874761","https://openalex.org/W2628846632","https://openalex.org/W2762513771","https://openalex.org/W2768080874","https://openalex.org/W2784616802","https://openalex.org/W2789268375","https://openalex.org/W2905034405","https://openalex.org/W2970149159"],"related_works":["https://openalex.org/W2013332237","https://openalex.org/W1522259561","https://openalex.org/W2295517574","https://openalex.org/W2380221404","https://openalex.org/W2373248682","https://openalex.org/W1527746113","https://openalex.org/W2225738837","https://openalex.org/W944314213","https://openalex.org/W2156263007","https://openalex.org/W1968456887"],"abstract_inverted_index":{"There":[0],"are":[1,68,109],"a":[2,15,28,91],"few":[3],"optimal":[4,32],"eighth":[5,33],"order":[6,34],"methods":[7,36,44,74],"in":[8,19,75],"literature":[9],"for":[10,37],"computing":[11],"multiple":[12,38],"zeros":[13],"of":[14,31,42,77,90,96],"nonlinear":[16],"function.":[17],"Therefore,":[18],"this":[20],"work":[21],"our":[22],"main":[23],"focus":[24],"is":[25,45,61,85],"on":[26,47],"developing":[27],"new":[29],"family":[30],"iterative":[35],"zeros.":[39],"The":[40],"applicability":[41],"proposed":[43],"demonstrated":[46,87],"some":[48],"real":[49],"life":[50],"and":[51,81],"academic":[52],"problems":[53],"that":[54,63,98],"illustrate":[55],"the":[56,64,100,104],"efficient":[57],"convergence":[58,80],"behavior.":[59],"It":[60],"shown":[62],"newly":[65],"developed":[66],"schemes":[67],"able":[69],"to":[70],"compete":[71],"with":[72],"other":[73],"terms":[76],"numerical":[78],"error,":[79],"computational":[82],"time.":[83],"Stability":[84],"also":[86],"by":[88],"means":[89],"pictorial":[92],"tool,":[93],"namely,":[94],"basins":[95,108],"attraction":[97],"have":[99],"fractal-like":[101],"shapes":[102],"along":[103],"borders":[105],"through":[106],"which":[107],"symmetric.":[110]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
