{"id":"https://openalex.org/W2016975329","doi":"https://doi.org/10.1145/1277500.1277514","title":"Numerical local rings and local solution of nonlinear systems","display_name":"Numerical local rings and local solution of nonlinear systems","publication_year":2007,"publication_date":"2007-07-25","ids":{"openalex":"https://openalex.org/W2016975329","doi":"https://doi.org/10.1145/1277500.1277514","mag":"2016975329"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277514","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5016209568","display_name":"Barry H. Dayton","orcid":null},"institutions":[{"id":"https://openalex.org/I27639287","display_name":"Northeastern Illinois University","ror":"https://ror.org/04edns687","country_code":"US","type":"education","lineage":["https://openalex.org/I27639287"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Barry H. Dayton","raw_affiliation_strings":["Northeastern Illinois University, Chicago, IL."],"affiliations":[{"raw_affiliation_string":"Northeastern Illinois University, Chicago, IL.","institution_ids":["https://openalex.org/I27639287"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016209568"],"corresponding_institution_ids":["https://openalex.org/I27639287"],"apc_list":null,"apc_paid":null,"fwci":0.875,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":9,"citation_normalized_percentile":{"value":0.742496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":82,"max":83},"biblio":{"volume":null,"issue":null,"first_page":"79","last_page":"86"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9914,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9748,"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/zero","display_name":"Zero (linguistics)","score":0.5801404},{"id":"https://openalex.org/keywords/representation","display_name":"Representation","score":0.4784772}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66589344},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6192809},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5801404},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.51065403},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5050474},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4784772},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4626423},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.42888921},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3499025},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33625805},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30345863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14833355},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.08258414},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08046085},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277514","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":20,"referenced_works":["https://openalex.org/W1483218536","https://openalex.org/W1529743226","https://openalex.org/W1570420806","https://openalex.org/W1992373021","https://openalex.org/W200316079","https://openalex.org/W2009126887","https://openalex.org/W2022825799","https://openalex.org/W2028576930","https://openalex.org/W2030143626","https://openalex.org/W2031453829","https://openalex.org/W2035953755","https://openalex.org/W2043938310","https://openalex.org/W2048961297","https://openalex.org/W2066181227","https://openalex.org/W2071860648","https://openalex.org/W2166309907","https://openalex.org/W2796914266","https://openalex.org/W4285719527","https://openalex.org/W4292096448","https://openalex.org/W609793669"],"related_works":["https://openalex.org/W4313491656","https://openalex.org/W4249605382","https://openalex.org/W3279617","https://openalex.org/W3013650182","https://openalex.org/W2989283631","https://openalex.org/W2800717388","https://openalex.org/W2250701745","https://openalex.org/W2146390824","https://openalex.org/W2053206769","https://openalex.org/W2044942888"],"abstract_inverted_index":{"Adapting":[0],"a":[1,9,20,54,60,73,93],"1915":[2],"method":[3],"of":[4,11,15,19,97,111],"Macaulay,":[5],"one":[6,52],"can":[7,77],"give":[8],"calculation":[10],"the":[12,69,82,85,98,108,112],"local":[13],"ring":[14],"an":[16,43],"isolated":[17],"zero":[18],"polynomial":[21,123],"system":[22],"{f1,":[23],"f2,":[24],".":[25,26,27,33,34,35],",":[28,36],"ft}":[29],"\u2286":[30],"C[x1,":[31],"x2,":[32],"xs]":[37],"using":[38],"oating":[39],"point":[40],"arithmetic.":[41],"Using":[42],"approximate":[44],"reverse":[45],"reduced":[46],"row":[47],"echelon":[48],"form":[49],"algorithm":[50],"(ARRREF)":[51],"gets":[53],"Gr\u00f6bner":[55],"basis":[56],"with":[57],"respect":[58],"to":[59,68,87,118],"global,":[61],"rather":[62],"than":[63],"local,":[64],"ordering":[65],"which":[66,103],"leads":[67],"usual":[70],"representation":[71],"as":[72,120,122],"matrix":[74],"algebra.":[75],"This":[76],"be":[78,105],"exploited":[79],"by":[80],"relaxing":[81],"tolerance":[83],"in":[84,92,107],"ARRREF":[86],"get":[88],"information":[89],"on":[90],"zeros":[91],"small":[94],"Euclidean":[95],"neighborhood":[96],"given":[99],"zero.":[100],"The":[101],"technique,":[102],"may":[104],"useful":[106],"endgame":[109],"stage":[110],"homotopy":[113],"continuation":[114],"method,":[115],"is":[116],"applied":[117],"analytic":[119],"well":[121],"systems.":[124]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2016975329","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2024-12-08T05:06:09.484150","created_date":"2016-06-24"}