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 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.
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Original Russian Text © B.M. Shumilov, 2017, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2017, Vol. 20, No. 1, pp. 107–120.
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Shumilov, B.M. Semi-orthogonal spline-wavelets with derivatives and the algorithm with splitting. Numer. Analys. Appl. 10, 90–100 (2017). https://doi.org/10.1134/S1995423917010098
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DOI: https://doi.org/10.1134/S1995423917010098