A Boolean sum interpolation for multivariate functions of bounded variation

Abstract

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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 Lp norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches.

Keywords

• Boolean sum operator
• multivariate function of bounded variation
• interpolation problem
• sparse grid
• tensor product grid
• hyperbolic cross