In this report we develop a method to derive finite difference approximations of linear operators in several space dimensions. The numerical schemes are obtained as solutions to optimization problems in a weighted L2-norm in the frequency domain. Then we show that this is closely related to the method of radial basis functions. It follows that different weights in the minimization problem lead to different basis functions. We apply the method to interpolation problems in one and two space dimensions. In one dimension, we also investigate how well an error indicator, which is derived from the minimization problem, can predict the real error in the interpolation.