On Computation of Battle{Lemari e's Wavelets

We propose a matrix approach to the computation of Battle-Lemari e's wavelets. Since the Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a b-spline of order m. The polynomial is the symbol of an bi-innnite matrix B associated with b-spline of order 2m. We approximate B 2m by its nite section A N , a square matrix of nite order. We use A N to compute an approximation x N of F(x). We show that x N converges to x pointwise exponentially fast. This gives a feasible method to compute the scaling function for any given tolerance. Similarly, this method can be used to compute the wavelets.