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Classes\nof problems are investigated for which variable\u2010basis schemes with sigmoidal computational\nunits perform better than fixed\u2010basis ones, in terms of the minimum number of computational\nunits needed to achieve a desired error in function approximation or approximate optimization. \nPreviously known bounds on the accuracy are extended, with better rates, to families of <jats:italic>d<\/jats:italic>\u2010variable functions whose actual dependence is on a subset of <jats:italic>d<\/jats:italic><jats:sup>\u2032<\/jats:sup> \u226a <jats:italic>d<\/jats:italic> variables, where the indices\nof these <jats:italic>d<\/jats:italic><jats:sup>\u2032<\/jats:sup> variables are not known a priori.<\/jats:p>","DOI":"10.1155\/2012\/806945","type":"journal-article","created":{"date-parts":[[2012,1,12]],"date-time":"2012-01-12T21:03:57Z","timestamp":1326402237000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Comparison between Fixed\u2010Basis and Variable\u2010Basis Schemes forFunction Approximation and Functional Optimization"],"prefix":"10.1155","volume":"2012","author":[{"given":"Giorgio","family":"Gnecco","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,1,12]]},"reference":[{"volume-title":"Calculus of Variations","year":"1963","author":"Gelfand I. 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