On Two Algorithms of Wavelet Decomposition for Spaces of Linear Splines

Abstract

The purpose of this paper is to construct new types of wavelets for minimal splines on an irregular grid. The approach applied to construct spline-wavelet decompositions uses approximation relations as an initial structure for constructing the spaces of minimal splines. The advantages of this approach are the possibilities of using irregular grids and sufficiently arbitrary nonpolynomial spline-wavelets.