{"id":"https://openalex.org/W2054739190","doi":"https://doi.org/10.1109/ccece.2010.5575239","title":"PWL approximation of hyperbolic tangent and the first derivative for VLSI implementation","display_name":"PWL approximation of hyperbolic tangent and the first derivative for VLSI implementation","publication_year":2010,"publication_date":"2010-05-01","ids":{"openalex":"https://openalex.org/W2054739190","doi":"https://doi.org/10.1109/ccece.2010.5575239","mag":"2054739190"},"language":"en","primary_location":{"id":"doi:10.1109/ccece.2010.5575239","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccece.2010.5575239","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"CCECE 2010","raw_type":"proceedings-article"},"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/A5029446907","display_name":"Ehsan Rasekh","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ehsan Rasekh","raw_affiliation_strings":["University of Western Ontario, London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060012227","display_name":"Iman Rasekh","orcid":null},"institutions":[{"id":"https://openalex.org/I2801771032","display_name":"Islamic Azad University, Arak","ror":"https://ror.org/02558wk32","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I2801771032"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Iman Rasekh","raw_affiliation_strings":["Islamic Azad University, Arak, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Islamic Azad University, Arak, Iran","institution_ids":["https://openalex.org/I2801771032"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001681499","display_name":"Mohammad Eshghi","orcid":"https://orcid.org/0000-0003-3878-6363"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Eshghi","raw_affiliation_strings":["Shahid Beheshti University, Tehran, Iran","Shahid Beheshti University,Tehran,Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shahid Beheshti University, Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]},{"raw_affiliation_string":"Shahid Beheshti University,Tehran,Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"139","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.7659029960632324},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.7309789061546326},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.7296373844146729},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6830875873565674},{"id":"https://openalex.org/keywords/inverse-hyperbolic-function","display_name":"Inverse hyperbolic function","score":0.5931943655014038},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5476675033569336},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.5162489414215088},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.4876066744327545},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.47771477699279785},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45670366287231445},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.44223490357398987},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.43513697385787964},{"id":"https://openalex.org/keywords/tangent-stiffness-matrix","display_name":"Tangent stiffness matrix","score":0.4307510554790497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3656672537326813},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3569490909576416},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.19120758771896362},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18796053528785706},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.11984533071517944},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0753064751625061},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.07081335783004761}],"concepts":[{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.7659029960632324},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7309789061546326},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.7296373844146729},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6830875873565674},{"id":"https://openalex.org/C163016742","wikidata":"https://www.wikidata.org/wiki/Q640600","display_name":"Inverse hyperbolic function","level":4,"score":0.5931943655014038},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5476675033569336},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5162489414215088},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.4876066744327545},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.47771477699279785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45670366287231445},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.44223490357398987},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.43513697385787964},{"id":"https://openalex.org/C178295079","wikidata":"https://www.wikidata.org/wiki/Q919765","display_name":"Tangent stiffness matrix","level":4,"score":0.4307510554790497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3656672537326813},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3569490909576416},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.19120758771896362},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18796053528785706},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.11984533071517944},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0753064751625061},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.07081335783004761},{"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/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ccece.2010.5575239","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccece.2010.5575239","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"CCECE 2010","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1537384552","https://openalex.org/W1946342668","https://openalex.org/W1966859905","https://openalex.org/W1972425002","https://openalex.org/W1998379075","https://openalex.org/W2023745373","https://openalex.org/W2042148902","https://openalex.org/W2077463145","https://openalex.org/W2097694726","https://openalex.org/W2167425979"],"related_works":["https://openalex.org/W4255941220","https://openalex.org/W2623063456","https://openalex.org/W2130597259","https://openalex.org/W2980182494","https://openalex.org/W2379912139","https://openalex.org/W2564469544","https://openalex.org/W1974959254","https://openalex.org/W2167394514","https://openalex.org/W3181483149","https://openalex.org/W1998199163"],"abstract_inverted_index":{"Hyperbolic":[0,71],"tangent":[1,52,72,86],"function":[2],"is":[3,23,43,57,87,95],"approximated":[4,58,89],"using":[5,61,74,90],"piecewise":[6],"linear":[7,49],"approximation.":[8,70],"This":[9],"approximation":[10,73,114],"can":[11,104],"be":[12,105],"used":[13],"in":[14,112],"any":[15],"embedded":[16],"hardware":[17],"architecture":[18],"where":[19,39],"occupied":[20],"chip":[21],"space":[22],"a":[24,32,98],"challenging":[25],"factor.":[26],"The":[27],"presented":[28,47],"recursive":[29],"algorithm":[30],"makes":[31],"trade-off":[33],"between":[34],"circuit":[35],"delay":[36],"and":[37,53,59,64],"accuracy,":[38],"low":[40],"memory":[41],"consumption":[42],"required.":[44],"In":[45],"the":[46,69,81,113],"centered":[48],"approximation,":[50],"hyperbolic":[51,85,116],"its":[54],"first":[55,82],"derivative":[56,83],"optimized":[60],"maximum":[62,75],"error":[63,67,76,101],"mean":[65,91,99],"square":[66,92,100],"of":[68,84,102,110,115],"shows":[77],"better":[78,88],"results":[79],"while":[80],"error.":[93],"It":[94],"demonstrated":[96],"that":[97],"0.02":[103],"achieved":[106],"after":[107],"specific":[108],"number":[109],"iterations":[111],"tangent.":[117]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
