  We propose a novel method to compute a finite difference stencil for Riesz
derivative for artibitrary speed of convergence. This method is based on
applying a pre-filter to the Gr\"unwald-Letnikov type central difference
stencil. The filter is obtained by solving for the inverse of a symmetric
Vandemonde matrix and exploiting the relationship between the Taylor's series
coefficients and fast Fourier transform. The filter costs O\left(N^{2}\right)
operations to evaluate for O\left(h^{N}\right) of convergence, where h is the
sampling distance. The higher convergence speed should more than offset the
overhead with the requirement of the number of nodal points for a desired error
tolerance significantly reduced. The benefit of progressive generation of the
stencil coefficients for adaptive grid size for dynamic problems with the
Gr\"unwald-Letnikov type difference scheme is also kept because of the
application of filtering. The higher convergence rate is verified through
numerical experiments.
