{"id":"https://openalex.org/W4321375138","doi":"https://doi.org/10.3390/axioms12020215","title":"Stability Analysis of Simple Root Seeker for Nonlinear Equation","display_name":"Stability Analysis of Simple Root Seeker for Nonlinear Equation","publication_year":2023,"publication_date":"2023-02-18","ids":{"openalex":"https://openalex.org/W4321375138","doi":"https://doi.org/10.3390/axioms12020215"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12020215","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020215","pdf_url":"https://www.mdpi.com/2075-1680/12/2/215/pdf?version=1677143026","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/2075-1680/12/2/215/pdf?version=1677143026","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024989917","display_name":"Xiaofeng Wang","orcid":"https://orcid.org/0000-0001-8524-6488"},"institutions":[{"id":"https://openalex.org/I97009856","display_name":"Bohai University","ror":"https://ror.org/01kdzej58","country_code":"CN","type":"education","lineage":["https://openalex.org/I97009856"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaofeng Wang","raw_affiliation_strings":["School of Mathematical Sciences, Bohai University, Jinzhou 121013, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Bohai University, Jinzhou 121013, China","institution_ids":["https://openalex.org/I97009856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014474366","display_name":"Wenshuo Li","orcid":null},"institutions":[{"id":"https://openalex.org/I97009856","display_name":"Bohai University","ror":"https://ror.org/01kdzej58","country_code":"CN","type":"education","lineage":["https://openalex.org/I97009856"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenshuo Li","raw_affiliation_strings":["School of Mathematical Sciences, Bohai University, Jinzhou 121013, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Bohai University, Jinzhou 121013, China","institution_ids":["https://openalex.org/I97009856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024989917"],"corresponding_institution_ids":["https://openalex.org/I97009856"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.0594,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82805663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"12","issue":"2","first_page":"215","last_page":"215"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9839000105857849,"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/simple","display_name":"Simple (philosophy)","score":0.7120442986488342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7104288339614868},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6316666007041931},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6007367372512817},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5740855932235718},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.551113486289978},{"id":"https://openalex.org/keywords/riemann-sphere","display_name":"Riemann sphere","score":0.546334445476532},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.46596765518188477},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.46303069591522217},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45959529280662537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4271157383918762},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.4143463373184204},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19272056221961975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18443217873573303},{"id":"https://openalex.org/keywords/riemann-surface","display_name":"Riemann surface","score":0.14915567636489868},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11516532301902771},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.076883465051651}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7120442986488342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7104288339614868},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6316666007041931},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6007367372512817},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5740855932235718},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.551113486289978},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.546334445476532},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.46596765518188477},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.46303069591522217},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45959529280662537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4271157383918762},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.4143463373184204},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19272056221961975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18443217873573303},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.14915567636489868},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11516532301902771},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.076883465051651},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12020215","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020215","pdf_url":"https://www.mdpi.com/2075-1680/12/2/215/pdf?version=1677143026","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:doaj.org/article:1673eea469c4436589f41fd8cb3627a4","is_oa":true,"landing_page_url":"https://doaj.org/article/1673eea469c4436589f41fd8cb3627a4","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 2, p 215 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/2/215/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12020215","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12020215","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12020215","pdf_url":"https://www.mdpi.com/2075-1680/12/2/215/pdf?version=1677143026","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/G3001212766","display_name":null,"funder_award_id":"2022-MS-371","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G3596841339","display_name":null,"funder_award_id":"61976027","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323086","display_name":"Natural Science Foundation of Liaoning Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4321375138.pdf","grobid_xml":"https://content.openalex.org/works/W4321375138.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1967800406","https://openalex.org/W1972417972","https://openalex.org/W2001934194","https://openalex.org/W2008789565","https://openalex.org/W2027751126","https://openalex.org/W2044645814","https://openalex.org/W2047475327","https://openalex.org/W2048366372","https://openalex.org/W2072379969","https://openalex.org/W2094884079","https://openalex.org/W2260711816","https://openalex.org/W2306328142","https://openalex.org/W2886609366","https://openalex.org/W2944352255","https://openalex.org/W3138433766","https://openalex.org/W4210373614","https://openalex.org/W4210724393","https://openalex.org/W4210770178","https://openalex.org/W4283259256","https://openalex.org/W4283780942","https://openalex.org/W4284666099","https://openalex.org/W4295137662","https://openalex.org/W4307117562","https://openalex.org/W4313461378"],"related_works":["https://openalex.org/W2083364117","https://openalex.org/W4389790939","https://openalex.org/W2461127211","https://openalex.org/W2018878125","https://openalex.org/W2502019951","https://openalex.org/W2073648170","https://openalex.org/W2186171019","https://openalex.org/W2104352226","https://openalex.org/W2126137023","https://openalex.org/W4321499576"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,32,38,43,52,59,64,68,75,86,107],"stability":[4,53],"of":[5,8,19,42,54,74],"a":[6,96],"class":[7],"Liu\u2013Wang\u2019s":[9],"optimal":[10,87],"eighth-order":[11],"single-parameter":[12],"iterative":[13,44],"methods":[14],"for":[15],"solving":[16],"simple":[17],"roots":[18],"nonlinear":[20],"equations":[21],"was":[22,46,93],"studied":[23],"by":[24,48],"applying":[25],"them":[26],"to":[27,105],"arbitrary":[28],"quadratic":[29],"polynomials.":[30],"Under":[31],"Riemann":[33],"sphere":[34],"and":[35,58,79,85,99],"scaling":[36],"theorem,":[37],"complex":[39],"dynamic":[40],"behavior":[41,82,92],"method":[45],"analyzed":[47],"fractals.":[49],"We":[50],"discuss":[51],"all":[55],"fixed":[56],"points":[57,66],"parameter":[60,88],"spaces":[61],"starting":[62],"from":[63],"critical":[65],"with":[67,77,90],"Mathematica":[69],"software.":[70],"The":[71],"dynamical":[72,81],"planes":[73],"elements":[76],"good":[78],"bad":[80],"are":[83],"given,":[84],"element":[89],"stable":[91],"obtained.":[94],"Finally,":[95],"numerical":[97],"experiment":[98],"practical":[100],"application":[101],"were":[102],"carried":[103],"out":[104],"prove":[106],"conclusion.":[108]},"counts_by_year":[{"year":2023,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
