{"id":"https://openalex.org/W2133083735","doi":"https://doi.org/10.1109/acc.2007.4282965","title":"On the Derivation of Higher Order Root-Finding Methods","display_name":"On the Derivation of Higher Order Root-Finding Methods","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2133083735","doi":"https://doi.org/10.1109/acc.2007.4282965","mag":"2133083735"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282965","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282965","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110208249","display_name":"Mohammed Abdulabbas Hasan","orcid":"https://orcid.org/0000-0002-5279-9200"},"institutions":[{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mohammed A. Hasan","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Minnesota, Duluth, USA","University of Minnesota, Duluth"],"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Minnesota, Duluth, USA","institution_ids":["https://openalex.org/I4210115145"]},{"raw_affiliation_string":"University of Minnesota, Duluth","institution_ids":["https://openalex.org/I4210115145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110208249"],"corresponding_institution_ids":["https://openalex.org/I4210115145"],"apc_list":null,"apc_paid":null,"fwci":1.2632,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78723404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":null,"first_page":"2328","last_page":"2333"},"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":0.9947999715805054,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.98580002784729,"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/newtons-method","display_name":"Newton's method","score":0.7084320187568665},{"id":"https://openalex.org/keywords/root-finding-algorithm","display_name":"Root-finding algorithm","score":0.6954307556152344},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6716954112052917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6701309680938721},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6610252857208252},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.6523019671440125},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6515581607818604},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6221145391464233},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.582177460193634},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5060543417930603},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46622729301452637},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.4522970914840698},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4265677034854889},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28515923023223877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21110981702804565},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17436042428016663}],"concepts":[{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7084320187568665},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.6954307556152344},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6716954112052917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6701309680938721},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6610252857208252},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.6523019671440125},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6515581607818604},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6221145391464233},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.582177460193634},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5060543417930603},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46622729301452637},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.4522970914840698},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4265677034854889},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28515923023223877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21110981702804565},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17436042428016663},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282965","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282965","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1550563201","https://openalex.org/W1568760617","https://openalex.org/W1608551107","https://openalex.org/W1832618622","https://openalex.org/W2006281261","https://openalex.org/W2014326812","https://openalex.org/W2017299431","https://openalex.org/W2023413246","https://openalex.org/W2041886034","https://openalex.org/W2150176466","https://openalex.org/W2162208935","https://openalex.org/W2330308866","https://openalex.org/W3194394486","https://openalex.org/W4233586510","https://openalex.org/W4234648522","https://openalex.org/W6632927565","https://openalex.org/W6634008307","https://openalex.org/W6800672827"],"related_works":["https://openalex.org/W2283569872","https://openalex.org/W2557315028","https://openalex.org/W2369347388","https://openalex.org/W1495632447","https://openalex.org/W1985487460","https://openalex.org/W2417247238","https://openalex.org/W4297921956","https://openalex.org/W2123238992","https://openalex.org/W2562964647","https://openalex.org/W2951861326"],"abstract_inverted_index":{"High":[0],"order":[1,18,36,54,62,102],"root-finding":[2],"algorithms":[3],"are":[4,51,81,95],"constructed":[5,82],"based":[6],"on":[7],"some":[8],"canonical":[9,24],"conditions":[10],"and":[11,41],"a":[12],"generalized":[13],"Taylor":[14],"series.":[15],"The":[16,26],"convergence":[17],"is":[19,45],"automatically":[20],"determined":[21],"using":[22],"these":[23],"conditions.":[25],"proposed":[27],"approaches":[28],"resulted":[29],"in":[30],"deriving":[31],"methods":[32,55,63,99],"of":[33,100,107],"any":[34],"desired":[35],"including":[37],"the":[38,76,85,90,105,108],"Newton,":[39],"Halley,":[40],"Ostrowski":[42],"iterations.":[43],"It":[44],"also":[46],"shown":[47],"that,":[48],"when":[49],"zeros":[50,74,106],"simple,":[52],"higher":[53,101],"may":[56],"be":[57],"obtained":[58],"by":[59],"applying":[60],"lower":[61],"such":[64],"as":[65,75],"Newton":[66],"Iteration":[67],"to":[68],"new":[69],"functions":[70,80],"which":[71],"have":[72],"same":[73],"original":[77],"function.":[78],"These":[79],"so":[83],"that":[84],"first":[86,91],"few":[87],"derivatives":[88],"beyond":[89],"vanish.":[92],"Several":[93],"examples":[94],"given":[96],"for":[97,103],"constructing":[98],"computing":[104],"entire":[109],"function":[110],"sin(z).":[111]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
