{"id":"https://openalex.org/W2071271895","doi":"https://doi.org/10.1080/00207169908804892","title":"A new cubic method for computing a root","display_name":"A new cubic method for computing a root","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2071271895","doi":"https://doi.org/10.1080/00207169908804892","mag":"2071271895"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804892","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804892","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-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/A5108486368","display_name":"R.E. Shaw","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"R.E. Shaw","raw_affiliation_strings":["University of New Brunswick , P.O. Box 5050, Saint John, N.B, E2L 4L5, Canada","University of New Brunswick P.O. Box 5050 Saint John, N.B., E2L 4L5, Canada"],"affiliations":[{"raw_affiliation_string":"University of New Brunswick , P.O. Box 5050, Saint John, N.B, E2L 4L5, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"University of New Brunswick P.O. Box 5050 Saint John, N.B., E2L 4L5, Canada","institution_ids":["https://openalex.org/I106938459"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110219117","display_name":"L.E. Garey","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"L.E. Garey","raw_affiliation_strings":["University of New Brunswick , P.O. Box 5050, Saint John, N.B, E2L 4L5, Canada","University of New Brunswick P.O. Box 5050 Saint John, N.B., E2L 4L5, Canada"],"affiliations":[{"raw_affiliation_string":"University of New Brunswick , P.O. Box 5050, Saint John, N.B, E2L 4L5, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"University of New Brunswick P.O. Box 5050 Saint John, N.B., E2L 4L5, Canada","institution_ids":["https://openalex.org/I106938459"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108486368"],"corresponding_institution_ids":["https://openalex.org/I106938459"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22852512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"2","first_page":"243","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9990000128746033,"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":0.9990000128746033,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9610000252723694,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.957099974155426,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/root-finding-algorithm","display_name":"Root-finding algorithm","score":0.7932231426239014},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.763296365737915},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.7101336717605591},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6945416331291199},{"id":"https://openalex.org/keywords/secant-method","display_name":"Secant method","score":0.6761257648468018},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.6722644567489624},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6014668941497803},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.53180992603302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49431943893432617},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4851027727127075},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4835807681083679},{"id":"https://openalex.org/keywords/second-derivative","display_name":"Second derivative","score":0.45395559072494507},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4534963071346283},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41626495122909546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4052526652812958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3246407210826874},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15088915824890137},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14900708198547363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11364427208900452}],"concepts":[{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.7932231426239014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763296365737915},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.7101336717605591},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6945416331291199},{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.6761257648468018},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.6722644567489624},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6014668941497803},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.53180992603302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49431943893432617},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4851027727127075},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4835807681083679},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.45395559072494507},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4534963071346283},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41626495122909546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4052526652812958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3246407210826874},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15088915824890137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14900708198547363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11364427208900452},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804892","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804892","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2041939310","https://openalex.org/W2083577496","https://openalex.org/W2094640653","https://openalex.org/W2105737698"],"related_works":["https://openalex.org/W2557315028","https://openalex.org/W4280521361","https://openalex.org/W3188005714","https://openalex.org/W1985487460","https://openalex.org/W4297921956","https://openalex.org/W2951861326","https://openalex.org/W110954085","https://openalex.org/W2765266151","https://openalex.org/W1989048457","https://openalex.org/W2071271895"],"abstract_inverted_index":{"In":[0],"this":[1,114],"paper":[2],"a":[3,19,36,47,96,110],"new":[4,51],"cubic":[5,65,92],"order":[6],"root":[7,21,43,66],"finding":[8,44,67],"method":[9,34,45,63,68,93,98,102],"is":[10,31,35,69,121],"introduced.":[11],"The":[12,33,50],"algorithm":[13],"can":[14],"be":[15,104],"used":[16],"to":[17,123],"find":[18],"simple":[20],"in":[22],"an":[23],"interval":[24],"I":[25],"of":[26,61,79,113,118],"f(x)=0":[27],"where":[28],"the":[29,62,77,80,100,125],"function":[30,81],"convex.":[32],"hybrid":[37],"procedure":[38,52],"that":[39,94],"combines":[40,95],"Newton's":[41,64],"quadratic":[42],"with":[46,99,109],"superlinear":[48],"method.":[49],"requires":[53,76],"only":[54],"one":[55],"first":[56,84],"derivative":[57],"evaluation":[58,78],"per":[59],"application":[60],"also":[70],"described":[71],"for":[72],"comparison":[73],"purposes.":[74],"It":[75],"and":[82,85],"its":[83],"second":[86],"derivatives":[87],"at":[88],"each":[89],"iteration.":[90],"Another":[91],"Steffensen-type":[97],"secant":[101],"will":[103],"discussed":[105],"as":[106],"well":[107],"along":[108],"modified":[111],"version":[112],"procedure.":[115],"A":[116],"table":[117],"numerical":[119],"results":[120],"presented":[122],"compare":[124],"methods.":[126]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}