Semi-orthogonal spline-wavelets with derivatives and the algorithm with splitting
Boris Shumilov · Numerical Analysis and Applications · 2017
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 the classical semi-orthogonal wavelets is shown. For splines of the third degree, the algorithm of wavelet-transformation in the formof the solution to a three-diagonal systemof linear equations with strict diagonal prevalence has been obtained. The results of numerical experiments on the calculation of derivatives of a discretely given function are presented.