A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization
Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational units perform better than...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/806945 |
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| _version_ | 1850173938894635008 |
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| author | Giorgio Gnecco |
| author_facet | Giorgio Gnecco |
| author_sort | Giorgio Gnecco |
| collection | DOAJ |
| description | Fixed-basis and variable-basis approximation schemes are compared for the problems of function
approximation and functional optimization (also known as infinite programming). Classes
of problems are investigated for which variable-basis schemes with sigmoidal computational
units perform better than fixed-basis ones, in terms of the minimum number of computational
units needed to achieve a desired error in function approximation or approximate optimization.
Previously known bounds on the accuracy are extended, with better rates, to families of d-variable functions whose actual dependence is on a subset of d′≪d variables, where the indices
of these d′ variables are not known a priori. |
| format | Article |
| id | doaj-art-c87fe3107a1b4eb3a8551d79ebd6b249 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c87fe3107a1b4eb3a8551d79ebd6b2492025-08-20T02:19:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/806945806945A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional OptimizationGiorgio Gnecco0Department of Communication, Computer and System Sciences (DIST), University of Genova, Via Opera Pia 13, 16145 Genova, ItalyFixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational units perform better than fixed-basis ones, in terms of the minimum number of computational units needed to achieve a desired error in function approximation or approximate optimization. Previously known bounds on the accuracy are extended, with better rates, to families of d-variable functions whose actual dependence is on a subset of d′≪d variables, where the indices of these d′ variables are not known a priori.http://dx.doi.org/10.1155/2012/806945 |
| spellingShingle | Giorgio Gnecco A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization Journal of Applied Mathematics |
| title | A Comparison between Fixed-Basis and Variable-Basis Schemes for
Function Approximation and Functional Optimization |
| title_full | A Comparison between Fixed-Basis and Variable-Basis Schemes for
Function Approximation and Functional Optimization |
| title_fullStr | A Comparison between Fixed-Basis and Variable-Basis Schemes for
Function Approximation and Functional Optimization |
| title_full_unstemmed | A Comparison between Fixed-Basis and Variable-Basis Schemes for
Function Approximation and Functional Optimization |
| title_short | A Comparison between Fixed-Basis and Variable-Basis Schemes for
Function Approximation and Functional Optimization |
| title_sort | comparison between fixed basis and variable basis schemes for function approximation and functional optimization |
| url | http://dx.doi.org/10.1155/2012/806945 |
| work_keys_str_mv | AT giorgiognecco acomparisonbetweenfixedbasisandvariablebasisschemesforfunctionapproximationandfunctionaloptimization AT giorgiognecco comparisonbetweenfixedbasisandvariablebasisschemesforfunctionapproximationandfunctionaloptimization |