A Boolean sum interpolation for multivariate functions of bounded variation

This paper deals with the approximation error of trigonometric interpolation for multivariate functions of bounded variation in the sense of Hardy-Krause. We propose interpolation operators related to both the tensor product and sparse grids on the multivariate torus. For these interpolation processes, we investigate the corresponding error estimates in the L p norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches.