How additive are the Fourier series in the sense of high dimensional model representation?

Abstract

The focus of this work is to investigate the quality of High Dimensional Model Representation (HDMR) to Fourier series. Towards this end, we experimantate with various Fourier series which are constructed for known univariate functions. Although the investigations are kept univariate, the extension that we obtain here to multivariate cases seems to be straightfor-ward. This is because we use the additivity measurers whose conceptual structures do not change from one multivariance to another. The additiviy measurers are certain well-ordered functionals mapping from a Hilbert space of multi or univariate functions to the interval [0, 1] and their close-to-one values mean certain level of additivity and therefore higher qualities of truncated HDMR approximants. Hence, those entities are evaluated for certain known cases.