Methods of approximate reconstruction of functions defined on chaotic lattices

In this article we consider methods of reconstructing functions of $n$ variables from their values at the points of a chaotic lattice providing an error of the best order in the approximation of functions $f$ and their derivatives of order $l$ in $L_q(\Omega)$ in the class $\mathscr W=\{f\in W_p^k(\Omega):\|D^kf\|_{L_p(\Omega )}\leqslant 1\}$ and classes of $h$-lattices us well as in $\mathscr W$ for a fixed lattice. We obtain methods of interpolation by means of smooth piecewise polynomial functions having the specified properties. The order of computational complexity is estimated for these methods.