{"id":"https://openalex.org/W3180355713","doi":"https://doi.org/10.3390/a14070207","title":"Extended High Order Algorithms for Equations under the Same Set of Conditions","display_name":"Extended High Order Algorithms for Equations under the Same Set of Conditions","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3180355713","doi":"https://doi.org/10.3390/a14070207","mag":"3180355713"},"language":"en","primary_location":{"id":"doi:10.3390/a14070207","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14070207","pdf_url":"https://www.mdpi.com/1999-4893/14/7/207/pdf?version=1626150208","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/14/7/207/pdf?version=1626150208","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"],"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/A5007272221","display_name":"Debasis Sharma","orcid":"https://orcid.org/0000-0001-8456-6391"},"institutions":[{"id":"https://openalex.org/I4210097016","display_name":"International Institute of Information Technology","ror":"https://ror.org/00qryer39","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210097016"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Debasis Sharma","raw_affiliation_strings":["Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar 751003, Odisha, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar 751003, Odisha, India","institution_ids":["https://openalex.org/I4210097016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059808785","display_name":"Christopher I. Argyros","orcid":"https://orcid.org/0000-0002-7647-3571"},"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":"Christopher I. Argyros","raw_affiliation_strings":["Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA"],"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/A5039544015","display_name":"Sanjaya Kumar Parhi","orcid":"https://orcid.org/0000-0003-2489-4080"},"institutions":[{"id":"https://openalex.org/I108526665","display_name":"Fakir Mohan University","ror":"https://ror.org/00g0n6t22","country_code":"IN","type":"education","lineage":["https://openalex.org/I108526665"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sanjaya Kumar Parhi","raw_affiliation_strings":["Department of Mathematics, Fakir Mohan University, Balasore 756020, Odisha, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Fakir Mohan University, Balasore 756020, Odisha, India","institution_ids":["https://openalex.org/I108526665"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088480787","display_name":"Shanta Kumari Sunanda","orcid":"https://orcid.org/0000-0002-2912-9719"},"institutions":[{"id":"https://openalex.org/I4210097016","display_name":"International Institute of Information Technology","ror":"https://ror.org/00qryer39","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210097016"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shanta Kumari Sunanda","raw_affiliation_strings":["Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar 751003, Odisha, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar 751003, Odisha, India","institution_ids":["https://openalex.org/I4210097016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112700163","display_name":"Michael I. Argyros","orcid":null},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael I. Argyros","raw_affiliation_strings":["Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA","institution_ids":["https://openalex.org/I8692664"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5007272221","https://openalex.org/A5087674067"],"corresponding_institution_ids":["https://openalex.org/I113618177","https://openalex.org/I4210097016"],"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":1,"citation_normalized_percentile":{"value":0.13250802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"7","first_page":"207","last_page":"207"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9970999956130981,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9958000183105469,"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/algorithm","display_name":"Algorithm","score":0.7138190865516663},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6726555824279785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5729395747184753},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5599302649497986},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.552233874797821},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5480449795722961},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5271075963973999},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5229136347770691},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.462078332901001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4041805863380432},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.386687695980072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10044211149215698}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7138190865516663},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6726555824279785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5729395747184753},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5599302649497986},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.552233874797821},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5480449795722961},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5271075963973999},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5229136347770691},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.462078332901001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4041805863380432},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.386687695980072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10044211149215698},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a14070207","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14070207","pdf_url":"https://www.mdpi.com/1999-4893/14/7/207/pdf?version=1626150208","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5ff3d4b2c2f74d93930af8f0591b15ce","is_oa":true,"landing_page_url":"https://doaj.org/article/5ff3d4b2c2f74d93930af8f0591b15ce","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 14, Iss 7, p 207 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/14/7/207/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a14070207","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":"Algorithms; Volume 14; Issue 7; Pages: 207","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a14070207","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14070207","pdf_url":"https://www.mdpi.com/1999-4893/14/7/207/pdf?version=1626150208","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3180355713.pdf","grobid_xml":"https://content.openalex.org/works/W3180355713.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W576148093","https://openalex.org/W1129295489","https://openalex.org/W1969880706","https://openalex.org/W1971939073","https://openalex.org/W1988151191","https://openalex.org/W1993447371","https://openalex.org/W1998140106","https://openalex.org/W2011023522","https://openalex.org/W2025736591","https://openalex.org/W2033879466","https://openalex.org/W2038079975","https://openalex.org/W2040119000","https://openalex.org/W2083249868","https://openalex.org/W2212694602","https://openalex.org/W2395900292","https://openalex.org/W2483406971","https://openalex.org/W2535676826","https://openalex.org/W2596600094","https://openalex.org/W2623041482","https://openalex.org/W2895678269","https://openalex.org/W2923954579","https://openalex.org/W2956523656","https://openalex.org/W3136323413","https://openalex.org/W3156170434","https://openalex.org/W4233832035","https://openalex.org/W4289984654","https://openalex.org/W6627067467","https://openalex.org/W6642625135","https://openalex.org/W6656934079","https://openalex.org/W6688108382","https://openalex.org/W6712373834","https://openalex.org/W6755340119","https://openalex.org/W6761120517"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2366107444","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{"A":[0],"variety":[1],"of":[2,42,72,92],"strategies":[3],"are":[4,16,35,45],"used":[5,107],"to":[6,19,53,108],"construct":[7],"algorithms":[8,44,67,111],"for":[9,32,63],"solving":[10],"equations.":[11],"However,":[12],"higher":[13],"order":[14,66],"derivatives":[15],"usually":[17],"assumed":[18],"calculate":[20],"the":[21,33,40,50,60,69,90,115],"convergence":[22],"order.":[23],"More":[24],"importantly,":[25],"bounds":[26],"on":[27],"error":[28],"and":[29,58],"uniqueness":[30],"regions":[31],"solution":[34],"also":[36,105],"not":[37],"derived.":[38],"Therefore,":[39],"benefits":[41],"these":[43,56,83,93],"limited.":[46],"We":[47],"simply":[48],"use":[49],"first":[51],"derivative":[52],"tackle":[54],"all":[55],"issues":[57],"study":[59],"ball":[61,80],"analysis":[62],"two":[64],"sixth":[65],"under":[68],"same":[70,116],"set":[71],"conditions.":[73],"In":[74,85],"addition,":[75],"we":[76,88],"present":[77],"a":[78],"calculable":[79],"comparison":[81],"between":[82],"algorithms.":[84,94],"this":[86],"manner,":[87],"enhance":[89],"utility":[91],"Our":[95],"idea":[96],"is":[97,101],"very":[98],"general.":[99],"That":[100],"why":[102],"it":[103],"can":[104],"be":[106],"extend":[109],"other":[110],"as":[112],"well":[113],"in":[114],"way.":[117]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}