Approximation of high-dimensional periodic functions with Fourier-based methods

Understand

In this paper we propose an approximation method for high-dimensional $1$-periodic functions based on the multivariate ANOVA decomposition.

• We provide an analysis on the classical ANOVA decomposition on the torus and prove some important properties such as the inheritance of smoothness for Sobolev type spaces and the weighted Wiener algebra.
• We exploit special kinds of sparsity in the ANOVA decomposition with the aim to approximate a function in a scattered data or black-box approximation scenario.
• This method allows us to simultaneously achieve an importance ranking on dimensions and dimension interactions which is referred to as attribute ranking in some applications.