About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting
B.M. Shumilov
Tomsk State University of Architecture and Building, pl. Solyanaya, 2, Tomsk, 634003, Russia
Keywords: B-сплайны, вейвлеты, неявные соотношения разложения, B-splines, wavelets, implicit decomposition relations
Abstract
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.
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