Initialization and inner product computations of wavelet transform by interpolatory subdivision scheme

1 Interpolatory basis function 2 (t) and its rst and second derivatives 0 2 (t) and 00 2 (t). 11 2 Interpolation of the function f(t) = e t sin(t); t = 0; 0:125; 0:25; :::; 10 (solid line) using the interpolatory subdivision scheme (dotted line) and the Shannon bases sinc(t) (shown using points). The interpolating points are taken at t = 0 Abstract The initialization of wavelet transforms and the inner product computations of wavelets with their derivatives are very important in many applications. In this correspondence, the interpolatory subdivision scheme (ISS) is proposed to solve these problems eeciently. We introduce a general procedure to compute the exact values of derivatives of the interpolatory fundamental function and then derive a fast recursive algorithm for the realization of the initialization and inner product evaluations. Error analysis of the algorithm and its comparison with other approaches are discussed. Numerical experiments demonstrate high performance of the algorithm.