Applications of classical approximation theory to periodic basis function networks and computational harmonic analysisReport as inadecuate




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Bulletin of Mathematical Sciences

, Volume 3, Issue 3, pp 485–549

First Online: 09 July 2013Received: 22 January 2013Revised: 13 June 2013Accepted: 17 June 2013

Abstract

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.

Communicated by S.K. Jain.

The research of H.N. Mhaskar was supported, in part, by grant DMS-0908037 from the National Science Foundation and grant W911NF-09-1-0465 from the U.S. Army Research Office. The research of P. Nevai was supported by a KAU grant.

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Author: Hrushikesh N. Mhaskar - Paul Nevai - Eugene Shvarts

Source: https://link.springer.com/







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