{"id":"https://openalex.org/W3046356091","doi":"https://doi.org/10.3390/computation8030069","title":"On the Solution of Equations by Extended Discretization","display_name":"On the Solution of Equations by Extended Discretization","publication_year":2020,"publication_date":"2020-07-31","ids":{"openalex":"https://openalex.org/W3046356091","doi":"https://doi.org/10.3390/computation8030069","mag":"3046356091"},"language":"en","primary_location":{"id":"doi:10.3390/computation8030069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation8030069","pdf_url":"https://www.mdpi.com/2079-3197/8/3/69/pdf?version=1596700665","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/8/3/69/pdf?version=1596700665","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017174213","display_name":"Gus Argyros","orcid":null},"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":"Gus I. Argyros","raw_affiliation_strings":["Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075553025","display_name":"Ioannis K. Argyros","orcid":"https://orcid.org/0000-0001-5733-0885"},"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":"Michael I. Argyros","raw_affiliation_strings":["Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068409818","display_name":"Samundra Regmi","orcid":"https://orcid.org/0000-0003-0035-1022"},"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":"Samundra Regmi","raw_affiliation_strings":["Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"],"raw_orcid":"https://orcid.org/0000-0003-0035-1022","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/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":"https://orcid.org/0000-0002-9189-9298","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"author_position":"last","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, Karnataka 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, Karnataka 575025, India","institution_ids":["https://openalex.org/I11880225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5087674067"],"corresponding_institution_ids":["https://openalex.org/I113618177"],"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":0.13785154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"3","first_page":"69","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987000226974487,"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":0.9980999827384949,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.9264211654663086},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.9037245512008667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7489586472511292},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7312370538711548},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.6274136304855347},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5608030557632446},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.5430338978767395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5396457314491272},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5295307040214539},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5088977813720703},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.5062205195426941},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5025098323822021},{"id":"https://openalex.org/keywords/discretization-of-continuous-features","display_name":"Discretization of continuous features","score":0.48002734780311584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47309473156929016},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"Modulus of continuity","score":0.4127247631549835},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.2531382441520691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16456368565559387},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.10762098431587219},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06958875060081482}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.9264211654663086},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.9037245512008667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7489586472511292},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7312370538711548},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.6274136304855347},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5608030557632446},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.5430338978767395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5396457314491272},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5295307040214539},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5088977813720703},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.5062205195426941},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5025098323822021},{"id":"https://openalex.org/C105427703","wikidata":"https://www.wikidata.org/wiki/Q665193","display_name":"Discretization of continuous features","level":4,"score":0.48002734780311584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47309473156929016},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.4127247631549835},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.2531382441520691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16456368565559387},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.10762098431587219},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06958875060081482},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation8030069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation8030069","pdf_url":"https://www.mdpi.com/2079-3197/8/3/69/pdf?version=1596700665","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:56959fe587b94b1bb38c2ee478d91694","is_oa":true,"landing_page_url":"https://doaj.org/article/56959fe587b94b1bb38c2ee478d91694","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":"Computation, Vol 8, Iss 3, p 69 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/8/3/69/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation8030069","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":"Computation; Volume 8; Issue 3; Pages: 69","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation8030069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation8030069","pdf_url":"https://www.mdpi.com/2079-3197/8/3/69/pdf?version=1596700665","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W68750926","https://openalex.org/W1129295489","https://openalex.org/W1555232731","https://openalex.org/W1971939073","https://openalex.org/W2002120595","https://openalex.org/W2037650572","https://openalex.org/W2050361884","https://openalex.org/W2065253292","https://openalex.org/W2072330702","https://openalex.org/W2076492844","https://openalex.org/W2081647667","https://openalex.org/W2141640731","https://openalex.org/W2143608864","https://openalex.org/W2553905176","https://openalex.org/W2799387372","https://openalex.org/W2887966033","https://openalex.org/W2966534858","https://openalex.org/W2986671393","https://openalex.org/W2997294501","https://openalex.org/W2999555005","https://openalex.org/W3169076552","https://openalex.org/W4289984654"],"related_works":["https://openalex.org/W2322326521","https://openalex.org/W2337518075","https://openalex.org/W1982747109","https://openalex.org/W1529605592","https://openalex.org/W2592900118","https://openalex.org/W3176239760","https://openalex.org/W2472678242","https://openalex.org/W2010171228","https://openalex.org/W2000161518","https://openalex.org/W3046356091"],"abstract_inverted_index":{"The":[0],"method":[1],"of":[2,41,51,76],"discretization":[3,53],"is":[4,28],"used":[5],"to":[6],"solve":[7],"nonlinear":[8],"equations":[9],"involving":[10],"Banach":[11],"space":[12],"valued":[13],"operators":[14],"using":[15,33],"Lipschitz":[16,77],"or":[17,78],"H\u00f6lder":[18,79],"constants.":[19],"But":[20],"these":[21],"constants":[22],"cannot":[23],"always":[24],"be":[25],"found.":[26],"That":[27],"why":[29],"we":[30,47,60],"present":[31],"results":[32,66],"\u03c9\u2212":[34,62],"continuity":[35,63],"conditions":[36],"on":[37,88],"the":[38,42,49,52,70,74,89],"Fr\u00e9chet":[39],"derivative":[40],"operator":[43],"involved.":[44,91],"This":[45],"way,":[46],"extend":[48],"applicability":[50],"technique.":[54],"It":[55],"turns":[56],"out":[57],"that":[58],"if":[59],"specialize":[61],"our":[64],"new":[65],"improve":[67],"those":[68],"in":[69,73],"literature":[71],"too":[72],"case":[75],"continuity.":[80],"Our":[81],"analysis":[82],"includes":[83],"tighter":[84],"upper":[85],"error":[86],"bounds":[87],"distances":[90]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-08-07T00:00:00"}
