{"id":"https://openalex.org/W2811368158","doi":"https://doi.org/10.13164/ma.2018.04","title":"Sizing up the regions of unique minima in the least squares nonlinear regression","display_name":"Sizing up the regions of unique minima in the least squares nonlinear regression","publication_year":2018,"publication_date":"2018-06-28","ids":{"openalex":"https://openalex.org/W2811368158","doi":"https://doi.org/10.13164/ma.2018.04","mag":"2811368158"},"language":"en","primary_location":{"id":"doi:10.13164/ma.2018.04","doi":"https://doi.org/10.13164/ma.2018.04","is_oa":true,"landing_page_url":"https://doi.org/10.13164/ma.2018.04","pdf_url":"https://doi.org/10.13164/ma.2018.04","source":{"id":"https://openalex.org/S4210210029","display_name":"Mathematics for Applications","issn_l":"1805-3610","issn":["1805-3610","1805-3629"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310314413","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/P4310314413"],"host_organization_lineage_names":["Brno University of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics for Application","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.13164/ma.2018.04","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084331618","display_name":"Leonid A. Khinkis","orcid":"https://orcid.org/0000-0002-0325-7202","observed_orcids":["https://orcid.org/0000-0002-0325-7202"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leonid Khinkis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076751471","display_name":"Milburn Crotzer","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Milburn Crotzer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028660561","display_name":"Adina Oprisan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adina Oprisan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.706,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.67439214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"7","issue":"1","first_page":"41","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.6074000000953674,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.6074000000953674,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.32010000944137573,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.03359999880194664,"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/nonlinear-least-squares","display_name":"nonlinear least squares","score":0.6549999713897705},{"id":"https://openalex.org/keywords/multiple-local-minima","display_name":"multiple local minima","score":0.875},{"id":"https://openalex.org/keywords/global-minimum","display_name":"global minimum","score":0.7799999713897705},{"id":"https://openalex.org/keywords/residual-sum-of-squares","display_name":"residual sum of squares","score":0.9210000038146973},{"id":"https://openalex.org/keywords/global-optimization","display_name":"global optimization","score":0.3569999933242798}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7592975497245789},{"id":"https://openalex.org/C46889948","wikidata":"https://www.wikidata.org/wiki/Q2755024","display_name":"Nonlinear regression","level":3,"score":0.7285929322242737},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.5689989328384399},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5482323169708252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5204905867576599},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5111330151557922},{"id":"https://openalex.org/C2777767291","wikidata":"https://www.wikidata.org/wiki/Q1080291","display_name":"Sizing","level":2,"score":0.5011661052703857},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4938989281654358},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4622400104999542},{"id":"https://openalex.org/C22354355","wikidata":"https://www.wikidata.org/wiki/Q422009","display_name":"Partial least squares regression","level":2,"score":0.42646270990371704},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.3687412738800049},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.36455219984054565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3373386859893799},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32644569873809814},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1404748558998108},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13311520218849182},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12474986910820007},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.13164/ma.2018.04","doi":"https://doi.org/10.13164/ma.2018.04","is_oa":true,"landing_page_url":"https://doi.org/10.13164/ma.2018.04","pdf_url":"https://doi.org/10.13164/ma.2018.04","source":{"id":"https://openalex.org/S4210210029","display_name":"Mathematics for Applications","issn_l":"1805-3610","issn":["1805-3610","1805-3629"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310314413","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/P4310314413"],"host_organization_lineage_names":["Brno University of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics for Application","raw_type":"journal-article"},{"id":"pmh:oai:https://dspace.vut.cz:11012/137267","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11012/137267","pdf_url":"http://hdl.handle.net/11012/137267","source":{"id":"https://openalex.org/S4306400317","display_name":"Brno University of Technology Digital Library (Brno University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I60587646","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/I60587646"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.13164/ma.2018.04","doi":"https://doi.org/10.13164/ma.2018.04","is_oa":true,"landing_page_url":"https://doi.org/10.13164/ma.2018.04","pdf_url":"https://doi.org/10.13164/ma.2018.04","source":{"id":"https://openalex.org/S4210210029","display_name":"Mathematics for Applications","issn_l":"1805-3610","issn":["1805-3610","1805-3629"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310314413","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/P4310314413"],"host_organization_lineage_names":["Brno University of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics for Application","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2811368158.pdf","grobid_xml":"https://content.openalex.org/works/W2811368158.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W155102939","https://openalex.org/W199310666","https://openalex.org/W200101083","https://openalex.org/W2029344049","https://openalex.org/W2132242633","https://openalex.org/W2440222624","https://openalex.org/W4233536583","https://openalex.org/W4241315756"],"related_works":["https://openalex.org/W1520338190","https://openalex.org/W200101083","https://openalex.org/W2058869626","https://openalex.org/W1991217434","https://openalex.org/W3010831251","https://openalex.org/W2134630840","https://openalex.org/W2364160632","https://openalex.org/W2123913166","https://openalex.org/W155994129","https://openalex.org/W1565959718"],"abstract_inverted_index":{"In":[0],"nonlinear":[1],"regression":[2],"analysis,":[3],"the":[4,16,24,31,50,59],"residual":[5],"sum":[6],"of":[7,23,33,42,63],"squares":[8],"may":[9],"possess":[10],"multiple":[11],"local":[12],"minima.This":[13],"complicates":[14],"finding":[15],"global":[17,37],"minimum":[18,38],"and":[19,28,45],"adversely":[20],"affects":[21],"reliability":[22],"relevant":[25],"statistical":[26],"methods.Identifying":[27],"sizing":[29],"up":[30],"regions":[32],"a":[34],"readily":[35],"identifiable":[36],"(RIGM)":[39],"is":[40],"therefore":[41],"both":[43],"theoretical":[44],"practical":[46],"interest.This":[47],"paper":[48],"addresses":[49],"issue":[51],"by":[52,58],"using":[53],"equidistant":[54],"function":[55],"previously":[56],"introduced":[57],"first":[60],"two":[61],"co-authors":[62],"this":[64],"paper.":[65],"MSC":[66],"(2010):":[67],"primary":[68],"62J02,":[69],"62K05,":[70],"62P10.":[71]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
