An Algorithm with the Even-odd Splitting of the Wavelet Transform of Non-Hermitian Splines of the Seventh Degree, II

Abstract

In this study, the zeroing property of the first two moments is used to construct an algorithm for splitting spline wavelets of the seventh degree. The presentation is based on the system of basic spline wavelets of the seventh degree, constructed in the previous article, which implements the conditions of orthogonality to all polynomials of any degree. Then, using homogeneous Dirichlet boundary conditions, the system is adapted to orthogonality to all polynomials up to the first degree on a finite interval. Implicit finite relationships are obtained between the spline coefficients in the original scale, on the one hand, and the spline coefficients and wavelet coefficients in the nested scale, on the other hand. After eliminating the even rows of the system, the transformation matrix has seven diagonals instead of five, as in the previous case studied. The resulting system has been modified to ensure strict diagonal dominance and, hence, computational stability, in contrast to the fivediagonal case.