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Mathematical modeling of technical objects is most frequently connected with mathematical processing of experimental data. The obtained pointlike dependencies of output variables on input ones are often strongly nonlinear, piecewise, and sometimes discontinuous. Approximation of these dependencies using polynomial resolution and spline-functions is problematic and may cause low accuracy. A radically new solution to this problem was suggested in a number of previous works. The method is based on partitioning of experimental dependencies into patches, approximation of each patch by analytic functions, multiplicative cutting of fragments from each function along the patch border and additive gluing of the fragments into a single function -- namely the model of approximated dependence. The analytic properties of this approximating glued function appear to be the major distinguishing feature and advantage of the method.