A splitting algorithm for wavelet transforms of the Hermite splines of the seventh degree

In this paper, an implicit method of decomposition of $7$-th degree Hermite splines to a series of “lazy” wavelets with displaced supports is investigated. A splitting algorithm for wavelet transforms of solving four five-diagonal systems of linear equations with a strict diagonal dominance in parallel is justified. Results of numerical experiments on exactness for polynomials and on compression of spline-wavelet decomposition are presented.