About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting

This paper deals with the use of a scalar product with derivatives for constructing semi-orthogonal spline-wavelets. The reduction of supports of such wavelets in comparison with classical semi-orthogonal wavelets is shown. For the splines of the 3rd degree, the algorithm of wavelet-transformation in the form of the solution to a three-diagonal system of the linear equations with strict diagonal prevalence has been obtained. The results of numerical experiments on the calculation of derivatives of a discretely set function are presented.