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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/806945 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1110-757X 1687-0042 |