Applications of classical approximation theory to periodic basis function networks and computational harmonic analysis

By Hrushikesh Narhar Mhaskar, Paul Nevai, Eugene Shvarts. 2013

10 citations recorded by the source corpus.

In this paper, we describe a novel approach to classical approximation theory of periodic univariate and multivariate functions by trigonometric polynomials. While classical wisdom holds that such approximation is too sensitive to the lack of smoothness of the target functions at isolated points, our constructions show how to overcome this problem. We describe applications to approximation by periodic basis function networks, and indicate further research in the direction of Jacobi expansion and approximation on the Euclidean sphere. While the paper is mainly intended to be a survey of our recent research in these directions, several results are proved for the first time here.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

Citations in the corpus

• Minimax Estimation of the $L_1$ Distance (2017, unknown): “In practice, uK and vK can be replaced by the efficiently implementable lowpass filtered Chebyshev expansion [19], which achieves the same uniform error rate as the best polynomial approximation.”