AUTHOR=Prestin Jürgen , Semenova Yevgeniya V. TITLE=A Boolean sum interpolation for multivariate functions of bounded variation JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=Volume 10 - 2024 YEAR=2024 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1489137 DOI=10.3389/fams.2024.1489137 ISSN=2297-4687 ABSTRACT=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.