Title :
Geometric Upper Bounds on Rates of Variable-Basis Approximation
Author :
Vera Kurkova;Marcello Sanguineti
Author_Institution :
Inst. of Comput. Sci., Acad. of Sci. of the Czech Republic, Prague
Abstract :
In this paper, approximation by linear combinations of an increasing number n of computational units with adjustable parameters (such as perceptrons and radial basis functions) is investigated. Geometric upper bounds on rates of convergence of approximation errors are derived. The bounds depend on certain parameters specific for each function to be approximated. The results are illustrated by examples of values of such parameters in the case of approximation by linear combinations of orthonormal functions.
Keywords :
"Upper bound","Dictionaries","Computational modeling","Linear approximation","Neural networks","Polynomials","Pattern recognition","Optimization methods","Hilbert space","Convergence"
Journal_Title :
IEEE Transactions on Information Theory
DOI :
10.1109/TIT.2008.2006383