{"id":"https://openalex.org/W1493972913","doi":"https://doi.org/10.1007/3-540-45988-x_10","title":"Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods","display_name":"Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1493972913","doi":"https://doi.org/10.1007/3-540-45988-x_10","mag":"1493972913"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45988-x_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45988-x_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5047541010","display_name":"Martine Ceberio","orcid":"https://orcid.org/0000-0001-5680-1155"},"institutions":[{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Martine Ceberio","raw_affiliation_strings":["IRIN - University of Nantes, 2, rue de la Houssini\u00e8re, B.P. 92208, F-44322, Nantes Cedex 3, France","IRIN \u2013 University of Nantes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIN - University of Nantes, 2, rue de la Houssini\u00e8re, B.P. 92208, F-44322, Nantes Cedex 3, France","institution_ids":["https://openalex.org/I97188460"]},{"raw_affiliation_string":"IRIN \u2013 University of Nantes","institution_ids":["https://openalex.org/I97188460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053935960","display_name":"Laurent Granvilliers","orcid":"https://orcid.org/0000-0003-3320-7502"},"institutions":[{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Granvilliers","raw_affiliation_strings":["IRIN - University of Nantes, 2, rue de la Houssini\u00e8re, B.P. 92208, F-44322, Nantes Cedex 3, France","IRIN \u2013 University of Nantes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIN - University of Nantes, 2, rue de la Houssini\u00e8re, B.P. 92208, F-44322, Nantes Cedex 3, France","institution_ids":["https://openalex.org/I97188460"]},{"raw_affiliation_string":"IRIN \u2013 University of Nantes","institution_ids":["https://openalex.org/I97188460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97188460"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.01196492,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"117","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9883999824523926,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9789000153541565,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/gaussian-elimination","display_name":"Gaussian elimination","score":0.7148129940032959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6901407241821289},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6523169279098511},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6005473732948303},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5996829271316528},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.5967510342597961},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5467544794082642},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49973320960998535},{"id":"https://openalex.org/keywords/local-consistency","display_name":"Local consistency","score":0.49910783767700195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4685455560684204},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4565216898918152},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.45333534479141235},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.45020216703414917},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3783974051475525},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.36870133876800537},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.30369511246681213},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.231784850358963},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.12003186345100403},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11829337477684021}],"concepts":[{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.7148129940032959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6901407241821289},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6523169279098511},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6005473732948303},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5996829271316528},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.5967510342597961},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5467544794082642},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49973320960998535},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.49910783767700195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4685455560684204},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4565216898918152},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.45333534479141235},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.45020216703414917},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3783974051475525},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.36870133876800537},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.30369511246681213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.231784850358963},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.12003186345100403},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11829337477684021},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-45988-x_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45988-x_10","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W56553795","https://openalex.org/W205862949","https://openalex.org/W1480778854","https://openalex.org/W1535419774","https://openalex.org/W1563516866","https://openalex.org/W1575568139","https://openalex.org/W1578819638","https://openalex.org/W1584569710","https://openalex.org/W1795557532","https://openalex.org/W1988879890","https://openalex.org/W1990426442","https://openalex.org/W1995621066","https://openalex.org/W2060498389","https://openalex.org/W2084965339","https://openalex.org/W2109714706","https://openalex.org/W2147795670","https://openalex.org/W2167206762","https://openalex.org/W4247032301","https://openalex.org/W6602279964","https://openalex.org/W6633808643"],"related_works":["https://openalex.org/W1486916474","https://openalex.org/W1984540483","https://openalex.org/W2569549435","https://openalex.org/W2328335329","https://openalex.org/W2091348864","https://openalex.org/W2784687883","https://openalex.org/W2737098235","https://openalex.org/W4303044088","https://openalex.org/W202947224","https://openalex.org/W1854665476"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
