Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS
Volume 19, Issue 2, Pages 284-298Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2007.905851
Keywords
best approximation; existence; functions band-limited in frequency; Gaussian radial basis functions (RBFs); sampling theory; truncation; uniqueness
Ask authors/readers for more resources
This paper is aimed at exposing the reader to certain aspects in the design of the best approximants with Gaussian radial basis functions (RBFs). The class of functions to which this approach. applies consists of those compactly supported in frequency. The approximative properties of uniqueness and existence are restricted to this class. Functions which are smooth enough can be expanded in Gaussian series converging uniformly to the objective function. The uniqueness of these series is demonstrated by the context of the orthonormal basis in a Hilbert space. Furthermore, the best approximation to a given band-limited function from a truncated Gaussian series is analyzed by an energy-based argument. This analysis not only gives a theoretical proof concerned with the existence of best approximations but addresses the problems of architectural selection. Specifically, guidance for selecting the variance and the oversampling parameters is provided for practitioners.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available