{"id":"https://openalex.org/W2964775560","doi":"https://doi.org/10.3390/sym11080981","title":"Extended Convergence Analysis of the Newton\u2013Hermitian and Skew\u2013Hermitian Splitting Method","display_name":"Extended Convergence Analysis of the Newton\u2013Hermitian and Skew\u2013Hermitian Splitting Method","publication_year":2019,"publication_date":"2019-08-02","ids":{"openalex":"https://openalex.org/W2964775560","doi":"https://doi.org/10.3390/sym11080981","mag":"2964775560"},"language":"en","primary_location":{"id":"doi:10.3390/sym11080981","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080981","pdf_url":"https://www.mdpi.com/2073-8994/11/8/981/pdf?version=1564729887","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/2073-8994/11/8/981/pdf?version=1564729887","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Ioannis K Argyros","raw_affiliation_strings":["Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"author_position":"middle","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":false,"raw_author_name":"Santhosh George","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka 575 025, 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 575 025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Chandhini Godavarma","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":"Chandhini Godavarma","raw_affiliation_strings":["Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka 575 025, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka 575 025, India","institution_ids":["https://openalex.org/I11880225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067260006","display_name":"\u00c1. Alberto Magre\u00f1\u00e1n","orcid":"https://orcid.org/0000-0002-6991-5706"},"institutions":[{"id":"https://openalex.org/I168974976","display_name":"Universidad de La Rioja","ror":"https://ror.org/0553yr311","country_code":"ES","type":"education","lineage":["https://openalex.org/I168974976"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alberto A Magre\u00f1\u00e1n","raw_affiliation_strings":["Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de la Rioja, 26006 Logro\u00f1o, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de la Rioja, 26006 Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I168974976"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087674067"],"corresponding_institution_ids":["https://openalex.org/I113618177"],"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":0.1303748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"8","first_page":"981","last_page":"981"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"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":0.6305500268936157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6283653378486633},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5855855941772461},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"Radius of convergence","score":0.49428772926330566},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.4914287328720093},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4893340468406677},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47593238949775696},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44130054116249084},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4388504922389984},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.41285470128059387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32094770669937134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14509403705596924},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12202036380767822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07540014386177063}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6305500268936157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6283653378486633},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5855855941772461},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.49428772926330566},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.4914287328720093},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4893340468406677},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47593238949775696},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44130054116249084},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4388504922389984},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.41285470128059387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32094770669937134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14509403705596924},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12202036380767822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07540014386177063},{"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/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11080981","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080981","pdf_url":"https://www.mdpi.com/2073-8994/11/8/981/pdf?version=1564729887","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:f2fd2ad4cf8c4799a5a5b637d159493d","is_oa":true,"landing_page_url":"https://doaj.org/article/f2fd2ad4cf8c4799a5a5b637d159493d","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":"Symmetry, Vol 11, Iss 8, p 981 (2019)","raw_type":"article"},{"id":"pmh:oai:portal.dialnet.es:doc/5d959e6e2999525d7e948459","is_oa":true,"landing_page_url":"https://investigacion.unirioja.es/documentos/5d959e6e2999525d7e948459","pdf_url":null,"source":{"id":"https://openalex.org/S4306402551","display_name":"RIUR (Universidad de La Rioja)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3032752892","host_organization_name":"Universidad Internacional de La Rioja","host_organization_lineage":["https://openalex.org/I3032752892"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym11080981","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080981","pdf_url":"https://www.mdpi.com/2073-8994/11/8/981/pdf?version=1564729887","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":[{"display_name":"Reduced inequalities","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W20141860","https://openalex.org/W176298991","https://openalex.org/W1971939073","https://openalex.org/W1974783314","https://openalex.org/W1988828340","https://openalex.org/W1993952196","https://openalex.org/W1995489291","https://openalex.org/W2002102128","https://openalex.org/W2048369486","https://openalex.org/W2056527665","https://openalex.org/W2075835091","https://openalex.org/W2090963365","https://openalex.org/W2104500275","https://openalex.org/W2107501462","https://openalex.org/W2620114959","https://openalex.org/W6703668766"],"related_works":["https://openalex.org/W3196977684","https://openalex.org/W3104367283","https://openalex.org/W4317464059","https://openalex.org/W4378757502","https://openalex.org/W4385248177","https://openalex.org/W2359656545","https://openalex.org/W2128408413","https://openalex.org/W3143080231","https://openalex.org/W151199910","https://openalex.org/W2029462152"],"abstract_inverted_index":{"Many":[0],"problems":[1],"in":[2,80],"diverse":[3],"disciplines":[4],"such":[5,48],"as":[6],"applied":[7],"mathematics,":[8],"mathematical":[9],"biology,":[10],"chemistry,":[11],"economics,":[12],"and":[13,121],"engineering,":[14],"to":[15,20,37,44],"mention":[16],"a":[17,22,26,39,45,63],"few,":[18],"reduce":[19],"solving":[21],"nonlinear":[23,29],"equation":[24],"or":[25],"system":[27],"of":[28,41,47,52,94,106,124,145],"equations.":[30],"Then":[31],"various":[32],"iterative":[33],"methods":[34],"are":[35],"considered":[36],"generate":[38],"sequence":[40],"approximations":[42],"converging":[43],"solution":[46],"problems.":[49],"The":[50],"goal":[51],"this":[53,112],"article":[54,127],"is":[55,88,114,116],"two-fold:":[56],"On":[57,131],"the":[58,73,77,92,100,104,107,122,125,132,138,155],"one":[59],"hand,":[60,134],"we":[61,135],"present":[62,126],"correct":[64],"convergence":[65,95,140],"criterion":[66,78,141],"for":[67,128],"Newton\u2013Hermitian":[68],"splitting":[69],"(NHSS)":[70],"method":[71],"under":[72,99],"Kantorovich":[74],"theory,":[75],"since":[76,103],"given":[79,101],"Numer.":[81],"Linear":[82],"Algebra":[83],"Appl.,":[84],"2011,":[85],"18,":[86],"299\u2013315":[87],"not":[89],"correct.":[90],"Indeed,":[91],"radius":[93,113],"cannot":[96],"be":[97],"defined":[98],"criterion,":[102],"discriminant":[105],"quadratic":[108],"polynomial":[109],"from":[110],"which":[111],"derived":[115],"negative":[117],"(See":[118],"Remark":[119],"1":[120],"conclusions":[123],"more":[129],"details).":[130],"other":[133],"have":[136],"extended":[137],"corrected":[139],"using":[142],"our":[143],"idea":[144],"recurrent":[146],"functions.":[147],"Numerical":[148],"examples":[149],"involving":[150],"convection\u2013diffusion":[151],"equations":[152],"further":[153],"validate":[154],"theoretical":[156],"results.":[157]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}