Kuduev A.Z.   Shumilov B.M.   Сулайманов З.М.  

Development of the theory of spline-wavelets and optimization of algorithms of processing of numerical information

Reporter: Kuduev A.Z.

In work the implicit method of decomposition of Hermite splines of the 7th degree on a series of "lazy" wavelets  with the displaced supports is investigated. Splitting of algorithm of wavelet-transformation on the parallel decision of four five-diagonal systems of the linear equations with strict diagonal predominance  is proved. Results of numerical experiments on exactness on polynomials and to compression of spline-wavelet-decompositions are presented. Ways of calculation of the derivatives necessary in wavelet-Hermite's transformation are discussed. The conclusion that the constructions using derivatives of high orders are applicable for the iterative solution of the nonlinear differential equations on the scheme of the  finite element method is drawn. Tasks of transfer of the implicit relations of decomposition offered in article are set on cases: a) "lazy" Hermite spline-wavelets of the 11th degree; b) wavelets of the 7th degree, semi-orthogonal with derivatives of the second order; c) wavelets of the 7th degree, orthogonal to polynomials, with the displaced supports; d) the minimal wavelets like Ryabenky-Demyanovich of the 3rd degree with the divided differences of the first order.

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