{"id":"https://openalex.org/W4400417010","doi":"https://doi.org/10.3390/axioms13070458","title":"Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results","display_name":"Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results","publication_year":2024,"publication_date":"2024-07-07","ids":{"openalex":"https://openalex.org/W4400417010","doi":"https://doi.org/10.3390/axioms13070458"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13070458","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070458","pdf_url":"https://www.mdpi.com/2075-1680/13/7/458/pdf?version=1721123871","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/7/458/pdf?version=1721123871","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012052785","display_name":"Marlon Moscoso-Mart\u00ednez","orcid":"https://orcid.org/0000-0001-5182-3099"},"institutions":[{"id":"https://openalex.org/I4210116615","display_name":"Universidad Internacional De La Rioja","ror":"https://ror.org/029gnnp81","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210116615"]},{"id":"https://openalex.org/I4210137344","display_name":"Escuela Superior Polit\u00e9cnica del Chimborazo","ror":"https://ror.org/02zyw2q61","country_code":"EC","type":"education","lineage":["https://openalex.org/I4210137344"]},{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["EC","ES"],"is_corresponding":false,"raw_author_name":"Marlon Moscoso-Mart\u00ednez","raw_affiliation_strings":["Faculty of Sciences, Escuela Superior Polit\u00e9cnica de Chimborazo (ESPOCH), Panamericana Sur km 1 1/2, Riobamba 060106, Ecuador","Higher School of Engineering and Technology, Universidad Internacional de la Rioja (UNIR), Avda. de la Paz 137, 26006 Logro\u00f1o, Spain","Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-5182-3099","affiliations":[{"raw_affiliation_string":"Faculty of Sciences, Escuela Superior Polit\u00e9cnica de Chimborazo (ESPOCH), Panamericana Sur km 1 1/2, Riobamba 060106, Ecuador","institution_ids":["https://openalex.org/I4210137344"]},{"raw_affiliation_string":"Higher School of Engineering and Technology, Universidad Internacional de la Rioja (UNIR), Avda. de la Paz 137, 26006 Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I4210116615"]},{"raw_affiliation_string":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035204495","display_name":"Francisco I. Chicharro","orcid":"https://orcid.org/0000-0001-9116-2870"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco I. Chicharro","raw_affiliation_strings":["Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9116-2870","affiliations":[{"raw_affiliation_string":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085887256","display_name":"Alicia Cordero","orcid":"https://orcid.org/0000-0002-7462-9173"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Alicia Cordero","raw_affiliation_strings":["Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7462-9173","affiliations":[{"raw_affiliation_string":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049721976","display_name":"Juan R. Torregrosa","orcid":"https://orcid.org/0000-0002-9893-0761"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan R. Torregrosa","raw_affiliation_strings":["Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9893-0761","affiliations":[{"raw_affiliation_string":"Institute for Multidisciplinary Mathematics, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s/n, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092189370","display_name":"Gabriela Ure\u00f1a-Callay","orcid":"https://orcid.org/0009-0001-5842-7379"},"institutions":[{"id":"https://openalex.org/I4210116615","display_name":"Universidad Internacional De La Rioja","ror":"https://ror.org/029gnnp81","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210116615"]},{"id":"https://openalex.org/I4210137344","display_name":"Escuela Superior Polit\u00e9cnica del Chimborazo","ror":"https://ror.org/02zyw2q61","country_code":"EC","type":"education","lineage":["https://openalex.org/I4210137344"]}],"countries":["EC","ES"],"is_corresponding":false,"raw_author_name":"Gabriela Ure\u00f1a-Callay","raw_affiliation_strings":["Faculty of Sciences, Escuela Superior Polit\u00e9cnica de Chimborazo (ESPOCH), Panamericana Sur km 1 1/2, Riobamba 060106, Ecuador","Higher School of Engineering and Technology, Universidad Internacional de la Rioja (UNIR), Avda. de la Paz 137, 26006 Logro\u00f1o, Spain"],"raw_orcid":"https://orcid.org/0009-0001-5842-7379","affiliations":[{"raw_affiliation_string":"Faculty of Sciences, Escuela Superior Polit\u00e9cnica de Chimborazo (ESPOCH), Panamericana Sur km 1 1/2, Riobamba 060106, Ecuador","institution_ids":["https://openalex.org/I4210137344"]},{"raw_affiliation_string":"Higher School of Engineering and Technology, Universidad Internacional de la Rioja (UNIR), Avda. de la Paz 137, 26006 Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I4210116615"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5085887256"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.7165,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.95570949,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"13","issue":"7","first_page":"458","last_page":"458"},"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":0.9945999979972839,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.652662456035614},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6073111295700073},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6051554679870605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5675698518753052},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5571413636207581},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.556144654750824},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49793362617492676},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.49323147535324097},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4858691096305847},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4722774922847748},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4600207209587097},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4431456923484802},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4044952690601349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37920618057250977}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.652662456035614},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6073111295700073},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6051554679870605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5675698518753052},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5571413636207581},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.556144654750824},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49793362617492676},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49323147535324097},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4858691096305847},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4722774922847748},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4600207209587097},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4431456923484802},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4044952690601349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37920618057250977},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms13070458","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070458","pdf_url":"https://www.mdpi.com/2075-1680/13/7/458/pdf?version=1721123871","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:riunet.upv.es:10251/211510","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/211510","pdf_url":"https://riunet.upv.es/bitstreams/7e881f9e-b1b9-49f7-ad2d-498155b9617b/download","source":{"id":"https://openalex.org/S4306401500","display_name":"RiuNet (Politechnical University of Valencia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"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":null,"raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:59928e247ccf49fda3bc6cc109a53033","is_oa":true,"landing_page_url":"https://doaj.org/article/59928e247ccf49fda3bc6cc109a53033","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":"Axioms, Vol 13, Iss 7, p 458 (2024)","raw_type":"article"},{"id":"pmh:oai:reunir.unir.net:123456789/17948","is_oa":true,"landing_page_url":"https://reunir.unir.net/handle/123456789/17948","pdf_url":null,"source":{"id":"https://openalex.org/S4306400329","display_name":"Re-Unir (International University of La Rioja)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Articulo Revista Indexada"}],"best_oa_location":{"id":"doi:10.3390/axioms13070458","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070458","pdf_url":"https://www.mdpi.com/2075-1680/13/7/458/pdf?version=1721123871","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5578966692","display_name":null,"funder_award_id":"PAID-06-23","funder_id":"https://openalex.org/F4320334905","funder_display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia"}],"funders":[{"id":"https://openalex.org/F4320334905","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400417010.pdf"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W1499223973","https://openalex.org/W1560556759","https://openalex.org/W1966813653","https://openalex.org/W1971939073","https://openalex.org/W1972417972","https://openalex.org/W1977711281","https://openalex.org/W1982246852","https://openalex.org/W1988627280","https://openalex.org/W1998140106","https://openalex.org/W2026091072","https://openalex.org/W2026376036","https://openalex.org/W2034154257","https://openalex.org/W2043570811","https://openalex.org/W2049942793","https://openalex.org/W2054711601","https://openalex.org/W2055308255","https://openalex.org/W2060534108","https://openalex.org/W2062985118","https://openalex.org/W2067520338","https://openalex.org/W2068000066","https://openalex.org/W2072386919","https://openalex.org/W2082938873","https://openalex.org/W2086281390","https://openalex.org/W2147231378","https://openalex.org/W2165754740","https://openalex.org/W2337772616","https://openalex.org/W2483406971","https://openalex.org/W2526050422","https://openalex.org/W2563776347","https://openalex.org/W2792673560","https://openalex.org/W3005616585","https://openalex.org/W3083297350","https://openalex.org/W3138433766","https://openalex.org/W3179731331","https://openalex.org/W4213078570","https://openalex.org/W4283766831","https://openalex.org/W4283780942","https://openalex.org/W6629822898","https://openalex.org/W6641834252","https://openalex.org/W6645004281","https://openalex.org/W6645806630","https://openalex.org/W6647474764","https://openalex.org/W6656929869","https://openalex.org/W6659253634","https://openalex.org/W6661177502","https://openalex.org/W6667713290","https://openalex.org/W6684473933","https://openalex.org/W6728004239","https://openalex.org/W6773728631"],"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/W2351377961","https://openalex.org/W3140142921"],"abstract_inverted_index":{"In":[0],"this":[1,86,118,139],"manuscript,":[2],"we":[3,52,69],"introduce":[4],"a":[5,23,34,38,54,58,75,103,159],"novel":[6],"parametric":[7],"family":[8,19,152,188,233],"of":[9,66,85,89,105,117,123,138,144,150,186,189,204,230,234],"multistep":[10],"iterative":[11,90,190,235],"methods":[12,191],"designed":[13],"to":[14,73,199,201],"solve":[15],"nonlinear":[16],"equations.":[17],"This":[18,195],"is":[20],"derived":[21],"from":[22,209,214],"damped":[24],"Newton\u2019s":[25],"scheme":[26],"but":[27],"includes":[28,128],"an":[29],"additional":[30],"Newton":[31],"step":[32],"with":[33,57,158,172,192,221],"weight":[35],"function":[36],"and":[37,98,131,169,228],"\u201cfrozen\u201d":[39],"derivative,":[40],"that":[41,110],"is,":[42],"the":[43,48,71,82,121,135,148,187,202,215,226,231],"same":[44],"derivative":[45],"than":[46],"in":[47,120,175],"previous":[49],"step.":[50],"Initially,":[51],"develop":[53],"quad-parametric":[55],"class":[56,88],"first-order":[59],"convergence":[60,72,83,161],"rate.":[61],"Subsequently,":[62],"by":[63],"restricting":[64],"one":[65,113],"its":[67,93,100],"parameters,":[68],"accelerate":[70],"achieve":[74],"third-order":[76],"uni-parametric":[77],"family.":[78,140],"We":[79,108,217],"thoroughly":[80],"investigate":[81],"properties":[84],"final":[87],"methods,":[91],"assess":[92],"stability":[94,129,145],"through":[95],"dynamical":[96,132,178,182],"tools,":[97],"evaluate":[99],"performance":[101],"on":[102],"set":[104],"test":[106],"problems.":[107],"conclude":[109],"there":[111],"exists":[112],"optimal":[114],"fourth-order":[115],"member":[116],"class,":[119],"sense":[122],"Kung\u2013Traub\u2019s":[124],"conjecture.":[125],"Our":[126],"analysis":[127],"surfaces":[130,146],"planes,":[133],"revealing":[134],"intricate":[136],"nature":[137],"Notably,":[141],"our":[142,181,219],"exploration":[143],"enables":[147],"identification":[149],"specific":[151],"members":[153,185],"suitable":[154],"for":[155],"scalar":[156],"functions":[157],"challenging":[160],"behavior,":[162],"as":[163],"they":[164],"may":[165],"exhibit":[166],"periodical":[167],"orbits":[168],"fixed":[170],"points":[171],"attracting":[173],"behavior":[174],"their":[176],"corresponding":[177],"planes.":[179],"Furthermore,":[180],"study":[183],"finds":[184],"exceptional":[193],"stability.":[194],"property":[196],"allows":[197],"us":[198],"converge":[200],"solution":[203],"practical":[205],"problem-solving":[206],"applications":[207],"even":[208],"initial":[210],"estimations":[211],"very":[212],"far":[213],"solution.":[216],"confirm":[218],"findings":[220],"various":[222],"numerical":[223],"tests,":[224],"demonstrating":[225],"efficiency":[227],"reliability":[229],"presented":[232],"methods.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
