Integrals Involving Product of Polynomials and Daubechies Scale Functions

Abstract

In this paper, we will introduce an algorithm for obtaining integrals of the form ∫x0 tm φ(t)dt, m ∈ N ∪ {0}, where φ is the scaling functions of Daubechies wavelet. In order to obtain these integrals in dyadic points for x’s, we have to solve a linear system. We will investigate, sparseness, well-conditioning and strictly diagonal dominant of matrices of these systems.

Keywords

• daubechies wavelets
• scaling functions
• dyadic points
• diagonal dominant
• well-condition