{"id":"https://openalex.org/W2013346099","doi":"https://doi.org/10.1007/bf02140677","title":"A hyperbolic tangent identity and the geometry of Pad\u00e9 sign function iterations","display_name":"A hyperbolic tangent identity and the geometry of Pad\u00e9 sign function iterations","publication_year":1994,"publication_date":"1994-09-01","ids":{"openalex":"https://openalex.org/W2013346099","doi":"https://doi.org/10.1007/bf02140677","mag":"2013346099"},"language":"en","primary_location":{"id":"doi:10.1007/bf02140677","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02140677","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5024734235","display_name":"Charles Kenney","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. S. Kenney","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, 93106-9560, Santa Barbara, CA, USA","Department of Electrical and Computer Eng., University of California, Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, 93106-9560, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Eng., University of California, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078470824","display_name":"Alan J. Laub","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. J. Laub","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, 93106-9560, Santa Barbara, CA, USA","Department of Electrical and Computer Eng., University of California, Santa Barbara, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, 93106-9560, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Eng., University of California, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024734235"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.3896,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.86298569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":"2","first_page":"111","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9519000053405762,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.9032357931137085},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.5006332397460938},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.482708215713501},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46813616156578064},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4354860186576843},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.42890042066574097},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.42672866582870483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3817112445831299},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22314321994781494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13295575976371765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9032357931137085},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.5006332397460938},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.482708215713501},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46813616156578064},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4354860186576843},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.42890042066574097},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42672866582870483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3817112445831299},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22314321994781494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13295575976371765},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02140677","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02140677","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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":23,"referenced_works":["https://openalex.org/W1906034359","https://openalex.org/W1966280518","https://openalex.org/W1985242550","https://openalex.org/W1992110402","https://openalex.org/W1995258411","https://openalex.org/W2002086707","https://openalex.org/W2004254988","https://openalex.org/W2010855047","https://openalex.org/W2011398297","https://openalex.org/W2015001720","https://openalex.org/W2028617139","https://openalex.org/W2044991911","https://openalex.org/W2059998776","https://openalex.org/W2072386919","https://openalex.org/W2086748127","https://openalex.org/W2125922364","https://openalex.org/W2137634211","https://openalex.org/W2139794367","https://openalex.org/W2154627073","https://openalex.org/W4230598837","https://openalex.org/W4230959423","https://openalex.org/W4235059123","https://openalex.org/W4253458057"],"related_works":["https://openalex.org/W4318472270","https://openalex.org/W4378879993","https://openalex.org/W4377141943","https://openalex.org/W2110143569","https://openalex.org/W3122938442","https://openalex.org/W1946342668","https://openalex.org/W4280634131","https://openalex.org/W2366774435","https://openalex.org/W2360240017","https://openalex.org/W2525549133"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}