On the functions generated by the general purpose analog computer
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/10083 |
Resumo: | Preprint |
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On the functions generated by the general purpose analog computerPreprintWe consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time. The GPAC generates as output univariate functions (i.e. functions f:R→R). In this paper we extend this model by: (i) allowing multivariate functions (i.e. functions f:Rn→Rm); (ii) introducing a notion of amount of resources (space) needed to generate a function, which allows the stratification of GPAC generable functions into proper subclasses. We also prove that a wide class of (continuous and discontinuous) functions can be uniformly approximated over their full domain. We prove a few stability properties of this model, mostly stability by arithmetic operations, composition and ODE solving, taking into account the amount of resources needed to perform each operation. We establish that generable functions are always analytic but that they can nonetheless (uniformly) approximate a wide range of nonanalytic functions. Our model and results extend some of the results from [19] to the multidimensional case, allow one to define classes of functions generated by GPACs which take into account bounded resources, and also strengthen the approximation result from [19] over a compact domain to a uniform approximation result over unbounded domains.ElsevierSapientiaOlivier, BournezDaniel, GraçaAmaury, Pouly20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/10083eng0890-5401AUT: DGR01772;https://doi.org/10.1016/j.ic.2017.09.015info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:21:38Zoai:sapientia.ualg.pt:10400.1/10083Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:01:50.785158Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the functions generated by the general purpose analog computer |
title |
On the functions generated by the general purpose analog computer |
spellingShingle |
On the functions generated by the general purpose analog computer Olivier, Bournez |
title_short |
On the functions generated by the general purpose analog computer |
title_full |
On the functions generated by the general purpose analog computer |
title_fullStr |
On the functions generated by the general purpose analog computer |
title_full_unstemmed |
On the functions generated by the general purpose analog computer |
title_sort |
On the functions generated by the general purpose analog computer |
author |
Olivier, Bournez |
author_facet |
Olivier, Bournez Daniel, Graça Amaury, Pouly |
author_role |
author |
author2 |
Daniel, Graça Amaury, Pouly |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Olivier, Bournez Daniel, Graça Amaury, Pouly |
description |
Preprint |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.1/10083 |
url |
http://hdl.handle.net/10400.1/10083 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0890-5401 AUT: DGR01772; https://doi.org/10.1016/j.ic.2017.09.015 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133249032683520 |