A Boolean sum interpolation for multivariate functions of bounded variation - Prestin, Jürgen; Semenova, Yevgeniya V. (Frontiers in Applied Mathematics and Statistics, 2024)
In this paper we study the approximation error for trigonometric interpolation of multivariate functions with bounded variation. We employ the notation introduced in \cite{AIS_PAUS_SV_TIC_2017} for the so-called Hardy-Krause variation. In addition to the interpolation on the tensor product grid, we discuss in particular the $L_p$ error of the interpolation on sparse grids for such functions of bounded variation.