Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 806945, 17 pages.
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 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 -variable functions whose actual dependence is on a subset of variables, where the indices of these variables are not known a priori.
J. Appl. Math., Volume 2012 (2012), Article ID 806945, 17 pages.
First available in Project Euclid: 17 October 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Gnecco, Giorgio. A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization. J. Appl. Math. 2012 (2012), Article ID 806945, 17 pages. doi:10.1155/2012/806945. https://projecteuclid.org/euclid.jam/1350479408