On the functions generated by the general purpose analog computer

Detalhes bibliográficos
Autor(a) principal: Olivier, Bournez
Data de Publicação: 2017
Outros Autores: Daniel, Graça, Amaury, Pouly
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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spelling 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
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dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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