The scheme for constructing wavelets based on approximation relations are described, the conditions for embedding spaces of local functions are presented, and a wavelet decomposition is constructed. The coefficient in the linear dependence of the computational complexity on the amount of input data is estimated in terms of approximation order. The results show that for a covering family with certain equipment, there exists a unique system of functions satisfying almost everywhere the approximation relations. For certain equipment and a vector function with linearly independent components on corresponding cells, the systems of functions are linearly independent. On the assumption of point functionals, the basic flow is found in at most some multiplicative operations and at most additive operations in the decomposition.