{"id":"https://openalex.org/W4311779598","doi":"https://doi.org/10.1007/s11075-022-01474-w","title":"Dynamics of Newton-like root finding methods","display_name":"Dynamics of Newton-like root finding methods","publication_year":2022,"publication_date":"2022-12-15","ids":{"openalex":"https://openalex.org/W4311779598","doi":"https://doi.org/10.1007/s11075-022-01474-w"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01474-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01474-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01474-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01474-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051930849","display_name":"B. Campos","orcid":"https://orcid.org/0000-0001-9205-0256"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"B. Campos","raw_affiliation_strings":["Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005195683","display_name":"Jordi Canela","orcid":"https://orcid.org/0000-0001-7879-5438"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. Canela","raw_affiliation_strings":["Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038986038","display_name":"P. Vindel","orcid":"https://orcid.org/0000-0001-8422-4738"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"P. Vindel","raw_affiliation_strings":["Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1ticas y Aplicaciones de Castell\u00f3n, Universitat Jaume I, Castell\u00f3, Spain","institution_ids":["https://openalex.org/I10902133"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005195683","https://openalex.org/A5038986038","https://openalex.org/A5051930849"],"corresponding_institution_ids":["https://openalex.org/I10902133"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":5.57,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.97687861,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"93","issue":"4","first_page":"1453","last_page":"1480"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9923999905586243,"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/mathematics","display_name":"Mathematics","score":0.7933233976364136},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6534602046012878},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6466351747512817},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6430826187133789},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.599915087223053},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.5962579846382141},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5208768844604492},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.49790382385253906},{"id":"https://openalex.org/keywords/root-finding-algorithm","display_name":"Root-finding algorithm","score":0.48394420742988586},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.4758686423301697},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.46951931715011597},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4580494463443756},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.42667803168296814},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3816394507884979},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3449268341064453},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29161620140075684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14595192670822144},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08133414387702942}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7933233976364136},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6534602046012878},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6466351747512817},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6430826187133789},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.599915087223053},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5962579846382141},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5208768844604492},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.49790382385253906},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.48394420742988586},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.4758686423301697},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.46951931715011597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4580494463443756},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.42667803168296814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3816394507884979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3449268341064453},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29161620140075684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14595192670822144},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08133414387702942},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s11075-022-01474-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01474-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01474-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2501.04645","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.04645","pdf_url":"https://arxiv.org/pdf/2501.04645","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ddd.uab.cat:281986","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/281986","pdf_url":"https://ddd.uab.cat/pub/artpub/2023/281986/numalg_a2023m8v93n4p1453-1480.pdf","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":"Article"},{"id":"pmh:oai:repositori.uji.es:10234/201577","is_oa":true,"landing_page_url":"http://hdl.handle.net/10234/201577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400303","display_name":"Repositori UJI (Universitat Jaume I)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I10902133","host_organization_name":"Universitat Jaume I","host_organization_lineage":["https://openalex.org/I10902133"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11075-022-01474-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-022-01474-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-022-01474-w.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1855301596","display_name":null,"funder_award_id":"PGC2018-095896-B-C22","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G2078372972","display_name":null,"funder_award_id":"PID2020-118281GB- C32","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6728930308","display_name":null,"funder_award_id":"PGC 2018","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G6731524417","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320322926","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311779598.pdf","grobid_xml":"https://content.openalex.org/works/W4311779598.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W576148093","https://openalex.org/W2017369318","https://openalex.org/W2025159184","https://openalex.org/W2048193077","https://openalex.org/W2055308255","https://openalex.org/W2062985118","https://openalex.org/W2068381736","https://openalex.org/W2086281390","https://openalex.org/W2087134934","https://openalex.org/W2089373101","https://openalex.org/W2190816950","https://openalex.org/W2316549649","https://openalex.org/W2753620842","https://openalex.org/W2784209412","https://openalex.org/W2895267754","https://openalex.org/W3012654629","https://openalex.org/W3088549004","https://openalex.org/W3165209395"],"related_works":["https://openalex.org/W2557315028","https://openalex.org/W2369347388","https://openalex.org/W1985487460","https://openalex.org/W4297921956","https://openalex.org/W2123238992","https://openalex.org/W2951861326","https://openalex.org/W2276000398","https://openalex.org/W4388044523","https://openalex.org/W2126445604","https://openalex.org/W2377857862"],"abstract_inverted_index":{"Abstract":[0],"When":[1],"exploring":[2],"the":[3,10,20,28,53,56,88,102],"literature,":[4],"it":[5],"can":[6],"be":[7],"observed":[8],"that":[9],"operator":[11,105],"obtained":[12,58],"when":[13],"applying":[14,60],"Newton-like":[15,61,92],"root":[16],"finding":[17],"algorithms":[18,62],"to":[19,63,86],"quadratic":[21],"polynomials":[22,69],"z":[23,72,75],"2":[24],"\u2212":[25,77],"c":[26,78],"has":[27,35],"same":[29],"form":[30],"regardless":[31],"of":[32,55,66,90,101,110,113],"which":[33],"algorithm":[34],"been":[36],"used.":[37],"In":[38],"this":[39,44,111],"paper,":[40],"we":[41,81],"justify":[42],"why":[43],"expression":[45,89],"is":[46,49],"obtained.":[47],"This":[48],"done":[50],"by":[51],"studying":[52],"symmetries":[54],"operators":[57],"after":[59],"a":[64,98],"family":[65],"degree":[67],"d":[68,76],"p":[70],"(":[71],")":[73],"=":[74],".":[79],"Moreover,":[80],"provide":[82,107],"an":[83],"iterative":[84],"procedure":[85],"obtain":[87],"new":[91],"algorithms.":[93],"We":[94],"also":[95],"carry":[96],"out":[97],"dynamical":[99],"study":[100],"given":[103],"generic":[104],"and":[106],"general":[108],"conclusions":[109],"type":[112],"methods.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}