Geodesic
About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 107-120

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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. 
@article{SJVM_2017_20_1_a8,
     author = {B. M. Shumilov},
     title = {About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {107--120},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a8/}
}
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B. M. Shumilov. About semi-orthogonal spline-wavelets with derivatives, and the algorithm with splitting. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 107-120. http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a8/