This work focuses on the partitioning of a given finite set. of data about a multivariate function at all nodes of a rectangular hypergrid, the position of its each node contains a small uncertainty. These uncertainties ire. reflected to weight function by Heaviside functions in univariate factors such that a parameter which is assumed to be quite small in comparison with the nominal value of the position of each node changes them to delta function when it vanishes. We use first, two terms of the expansion of each univariate factor in ascending powers of this parameter. The resulting formulae require the values of the partial derivatives of the multivariate function under consideration with respect to all independent variables at all nodes of the abovementioned hypergrid.