{"id":"https://openalex.org/W1969169294","doi":"https://doi.org/10.1007/s00211-003-0515-4","title":"On necessary and sufficient conditions for numerical verification of double turning points","display_name":"On necessary and sufficient conditions for numerical verification of double turning points","publication_year":2004,"publication_date":"2004-05-01","ids":{"openalex":"https://openalex.org/W1969169294","doi":"https://doi.org/10.1007/s00211-003-0515-4","mag":"1969169294"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-003-0515-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-003-0515-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5028278086","display_name":"Ken\u2019ichiro Tanaka","orcid":"https://orcid.org/0000-0003-0359-0969"},"institutions":[{"id":"https://openalex.org/I4210165074","display_name":"Information and Mathematical Science and Bioinformatics (Japan)","ror":"https://ror.org/05rgpb984","country_code":"JP","type":"company","lineage":["https://openalex.org/I4210165074"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ken?ichiro Tanaka","raw_affiliation_strings":["Department of Mathematical Informatics, Graduate School of Information Science and Technology, the University of Tokyo, Tokyo, 113-8656, Japan","Graduate School of Information Science and Technology, Department of Mathematical Informatics, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Informatics, Graduate School of Information Science and Technology, the University of Tokyo, Tokyo, 113-8656, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Graduate School of Information Science and Technology, Department of Mathematical Informatics, Japan#TAB#","institution_ids":["https://openalex.org/I4210165074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047106719","display_name":"Sunao Murashige","orcid":"https://orcid.org/0000-0002-8393-9739"},"institutions":[{"id":"https://openalex.org/I3133035077","display_name":"Ube Frontier University","ror":"https://ror.org/03sgcr744","country_code":"JP","type":"education","lineage":["https://openalex.org/I3133035077"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sunao Murashige","raw_affiliation_strings":["Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, the University of Tokyo, Chiba 277-8561, Japan","Graduate School of Frontier Sciences, Department of Complexity Science and Engineering, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, the University of Tokyo, Chiba 277-8561, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Graduate School of Frontier Sciences, Department of Complexity Science and Engineering, Japan#TAB#","institution_ids":["https://openalex.org/I3133035077"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109927229","display_name":"Shin Ichi Oishi","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shin?ichi Oishi","raw_affiliation_strings":["Department of Computer Science, School of Science and Engineering, Waseda University, Tokyo, 169-8555, Japan","School of Science and Engineering, Department of Computer Science, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, School of Science and Engineering, Waseda University, Tokyo, 169-8555, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"School of Science and Engineering, Department of Computer Science, Japan#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5028278086"],"corresponding_institution_ids":["https://openalex.org/I4210165074","https://openalex.org/I74801974"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.3435,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.60225746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"97","issue":"3","first_page":"537","last_page":"554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9728999733924866,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9728999733924866,"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/T12810","display_name":"Real-time simulation and control systems","score":0.9624999761581421,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T13935","display_name":"Mathematical Control Systems and Analysis","score":0.9559999704360962,"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/mathematics","display_name":"Mathematics","score":0.7689167261123657},{"id":"https://openalex.org/keywords/turning-point","display_name":"Turning point","score":0.7088699340820312},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.666681170463562},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6521600484848022},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5389737486839294},{"id":"https://openalex.org/keywords/banach-fixed-point-theorem","display_name":"Banach fixed-point theorem","score":0.5273830890655518},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5152847766876221},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4193337559700012},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41061410307884216},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34062591195106506},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11594590544700623},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05320391058921814}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7689167261123657},{"id":"https://openalex.org/C3018122192","wikidata":"https://www.wikidata.org/wiki/Q569250","display_name":"Turning point","level":3,"score":0.7088699340820312},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.666681170463562},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6521600484848022},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5389737486839294},{"id":"https://openalex.org/C2780549194","wikidata":"https://www.wikidata.org/wiki/Q220680","display_name":"Banach fixed-point theorem","level":3,"score":0.5273830890655518},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5152847766876221},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4193337559700012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41061410307884216},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34062591195106506},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11594590544700623},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05320391058921814},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-003-0515-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-003-0515-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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":8,"referenced_works":["https://openalex.org/W112023339","https://openalex.org/W160832363","https://openalex.org/W306160993","https://openalex.org/W429946928","https://openalex.org/W1596321532","https://openalex.org/W2005045093","https://openalex.org/W2039695994","https://openalex.org/W2165148137"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W4362508682"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
