{"id":"https://openalex.org/W4412995820","doi":"https://doi.org/10.3390/a18080483","title":"An Improved Convergence Analysis of a Multi-Step Method with High-Efficiency Indices","display_name":"An Improved Convergence Analysis of a Multi-Step Method with High-Efficiency Indices","publication_year":2025,"publication_date":"2025-08-04","ids":{"openalex":"https://openalex.org/W4412995820","doi":"https://doi.org/10.3390/a18080483"},"language":"en","primary_location":{"id":"doi:10.3390/a18080483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18080483","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/a18080483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086323665","display_name":"Santhosh George","orcid":"https://orcid.org/0000-0002-3530-5539"},"institutions":[{"id":"https://openalex.org/I11880225","display_name":"National Institute of Technology Karnataka","ror":"https://ror.org/01hz4v948","country_code":"IN","type":"education","lineage":["https://openalex.org/I11880225"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Santhosh George","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India"],"raw_orcid":"https://orcid.org/0000-0002-3530-5539","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115027677","display_name":"Manjusree Gopal","orcid":"https://orcid.org/0009-0007-1093-4404"},"institutions":[{"id":"https://openalex.org/I11880225","display_name":"National Institute of Technology Karnataka","ror":"https://ror.org/01hz4v948","country_code":"IN","type":"education","lineage":["https://openalex.org/I11880225"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Manjusree Gopal","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India"],"raw_orcid":"https://orcid.org/0009-0007-1093-4404","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113193465","display_name":"S. R. Bhide","orcid":null},"institutions":[{"id":"https://openalex.org/I11880225","display_name":"National Institute of Technology Karnataka","ror":"https://ror.org/01hz4v948","country_code":"IN","type":"education","lineage":["https://openalex.org/I11880225"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Samhitha Bhide","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India"],"raw_orcid":"https://orcid.org/0009-0005-7170-6670","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087674067","display_name":"Ioannis K. Argyros","orcid":"https://orcid.org/0000-0002-9189-9298"},"institutions":[{"id":"https://openalex.org/I113618177","display_name":"Cameron University","ror":"https://ror.org/00rgv0036","country_code":"US","type":"education","lineage":["https://openalex.org/I113618177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ioannis K. Argyros","raw_affiliation_strings":["Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":"https://orcid.org/0000-0002-9189-9298","affiliations":[{"raw_affiliation_string":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5086323665"],"corresponding_institution_ids":["https://openalex.org/I11880225"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27368421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"8","first_page":"483","last_page":"483"},"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":0.995199978351593,"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":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6898458003997803},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5059444308280945},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3953762948513031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3908529281616211},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3777841031551361},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33121800422668457},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09176471829414368}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6898458003997803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5059444308280945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3953762948513031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3908529281616211},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3777841031551361},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33121800422668457},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09176471829414368},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a18080483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18080483","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:be3cd5510a724bf3856325bb5f585258","is_oa":true,"landing_page_url":"https://doaj.org/article/be3cd5510a724bf3856325bb5f585258","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 8, p 483 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18080483","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18080483","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1499223973","https://openalex.org/W1982246852","https://openalex.org/W2011023522","https://openalex.org/W2038079975","https://openalex.org/W2068720794","https://openalex.org/W2090963365","https://openalex.org/W2099981000","https://openalex.org/W2115499189","https://openalex.org/W2792673560","https://openalex.org/W2803622222","https://openalex.org/W3189312561","https://openalex.org/W3215555820","https://openalex.org/W4205246695","https://openalex.org/W4381051931","https://openalex.org/W4385838074","https://openalex.org/W4390790686","https://openalex.org/W4400614859","https://openalex.org/W4408345079","https://openalex.org/W6629822898","https://openalex.org/W6645806630","https://openalex.org/W6667569269","https://openalex.org/W6751879640","https://openalex.org/W6877728366"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298"],"abstract_inverted_index":{"A":[0],"multi-step":[1],"method":[2,26,120],"introduced":[3],"by":[4],"Raziyeh":[5],"and":[6,110,121],"Masoud":[7],"for":[8,107],"solving":[9],"nonlinear":[10],"systems":[11],"with":[12],"convergence":[13,23,44,65,112],"order":[14],"five":[15],"has":[16],"been":[17],"considered":[18],"in":[19,63,70,86,90],"this":[20],"paper.":[21],"The":[22],"of":[24,57,96,105,118],"the":[25,35,50,55,102,116,119],"was":[27,83],"studied":[28],"using":[29],"Taylor":[30,51],"series":[31],"expansion,":[32],"which":[33,67,82],"requires":[34],"function":[36],"to":[37,60,127],"be":[38],"six":[39],"times":[40],"differentiable.":[41],"However,":[42],"our":[43,64],"study":[45],"does":[46],"not":[47,84],"depend":[48],"on":[49],"series.":[52],"We":[53,114],"use":[54],"derivative":[56],"F":[58],"up":[59],"two":[61,94],"only":[62],"analysis,":[66],"is":[68,79],"presented":[69],"a":[71],"more":[72],"general":[73],"Banach":[74],"space":[75],"setting.":[76],"Semi-local":[77],"analysis":[78,109],"also":[80,122],"discussed,":[81],"given":[85],"earlier":[87,91],"studies.":[88],"Unlike":[89],"studies":[92],"(where":[93],"sets":[95],"assumptions":[97,106],"were":[98],"used),":[99],"we":[100],"used":[101],"same":[103],"set":[104],"semi-local":[108],"local":[111],"analysis.":[113],"discussed":[115],"dynamics":[117],"gave":[123],"some":[124],"numerical":[125],"examples":[126],"illustrate":[128],"theoretical":[129],"findings.":[130]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}