{"id":"https://openalex.org/W1520393398","doi":"https://doi.org/10.1007/bf02241698","title":"A comparison of methods for determining turning points of nonlinear equations","display_name":"A comparison of methods for determining turning points of nonlinear equations","publication_year":1982,"publication_date":"1982-09-01","ids":{"openalex":"https://openalex.org/W1520393398","doi":"https://doi.org/10.1007/bf02241698","mag":"1520393398"},"language":"en","primary_location":{"id":"doi:10.1007/bf02241698","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02241698","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","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/A5038997010","display_name":"Rami Melhem","orcid":"https://orcid.org/0000-0001-6403-5446"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. G. Melhem","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Pittsburgh, 15261, Pittsburgh, PA, USA","Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburgh, 15261, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040660746","display_name":"Werner C. Rheinboldt","orcid":null},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. C. Rheinboldt","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Pittsburgh, 15261, Pittsburgh, PA, USA","Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburgh, 15261, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, USA","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038997010"],"corresponding_institution_ids":["https://openalex.org/I170201317"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":13.7367,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.99690881,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"3","first_page":"201","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.964900016784668,"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":0.964900016784668,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9559000134468079,"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/computation","display_name":"Computation","score":0.6952875256538391},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6474458575248718},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6113817095756531},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.59999680519104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5890336632728577},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5850976705551147},{"id":"https://openalex.org/keywords/turning-point","display_name":"Turning point","score":0.5726221799850464},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4388737380504608},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30732351541519165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3016161322593689},{"id":"https://openalex.org/keywords/period","display_name":"Period (music)","score":0.07289105653762817}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6952875256538391},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6474458575248718},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6113817095756531},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.59999680519104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5890336632728577},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5850976705551147},{"id":"https://openalex.org/C3018122192","wikidata":"https://www.wikidata.org/wiki/Q569250","display_name":"Turning point","level":3,"score":0.5726221799850464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4388737380504608},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30732351541519165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3016161322593689},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.07289105653762817},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02241698","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02241698","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W278121284","https://openalex.org/W349593503","https://openalex.org/W427736150","https://openalex.org/W1597438796","https://openalex.org/W1976464801","https://openalex.org/W2002811134","https://openalex.org/W2015441000","https://openalex.org/W2033772586","https://openalex.org/W2035910846","https://openalex.org/W2067659237","https://openalex.org/W2068336910","https://openalex.org/W2078950386","https://openalex.org/W2083229135","https://openalex.org/W2087743687","https://openalex.org/W2100150950","https://openalex.org/W2137608537","https://openalex.org/W2144144582","https://openalex.org/W2150604642","https://openalex.org/W2165693293","https://openalex.org/W2250944347","https://openalex.org/W2754652376","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2078423466","https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W4213019146","https://openalex.org/W2484395025","https://openalex.org/W4244710238","https://openalex.org/W4210630282","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W3039678079"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}