An efficient algorithm for evaluation of derivatives of refinable scale functions

We present here an efficient algorithm for computing derivatives of refinable functions of compact support appearing in the bases of multiscale approximation of functions in \(L^2({\mathbb {R}})\) $L^2(\mathbb{R})$ . The scheme presented here provides values of admissible derivatives of refinable functions at dyadic rationals within their support. Results are demonstrated for the admissible derivatives of a variety of refinable functions often used for obtaining highly accurate approximate solution of physical problems.