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

Abstract

The article investigates an implicit method of decomposition of the 7th degree non-Hermitian splines into a series of wavelets with two zero moments. The system of linear algebraic equations connecting the coefficients of the spline expansion on the initial scale with the spline coefficients and wavelet coefficients on the embedded scale is obtained. The even-odd splitting of the wavelet decomposition algorithm into a solution of the half-size five-diagonal system of linear equations and some local averaging formulas are substantiated. The results of numerical experiments on accuracy on polynomials and compression of spline-wavelet decomposition are presented.