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

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 efficiently. 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 the high performance of the algorithm.