Splitting algorithm for cubic spline-wavelets with two vanishing moments on the interval

This paper deals with the use of the first two vanishing moments for constructing cubic spline-wavelets meeting orthogonality conditions to polynomials of the first degree. A decrease in the supports of these wavelets is shown in comparison with the classical semiorthogonal wavelets. For splines with homogeneous Dirichlet boundary conditions of the first order, an algorithm of the shifted wavelet transform is obtained in the form of a solution of tridiagonal systems of linear algebraic equations with a strict diagonal dominance. Results of numerical experiments on data processing are presented.