Realization of the spline-wavelet decomposition of the first order

The paper considers the discrete spline-wavelet decomposition of the first order based on a nonclassical approach to constructing wavelet decompositions. All the constructions only use mesh functions (flows); the finite-dimensional spaces of original flows, wavelet flows, and principal flows are introduced. These spaces are associated with an original and a coarsened meshes, respectively. As a result, simple decomposition and reconstruction formulas are obtained, and a basis of the wavelet space is provided by the simplest collection of unit coordinate vectors of the Euclidean space. An estimate for the time of realizing the decomposition with account for properties of the communication media of a computing system is presented.