The evaluation of the conjugate function of a periodic spline on a uniform mesh

摘要

We present an O(N log N) algorithm for the simultaneous evaluation (at all N points of a uniform mesh) of a function conjugate to a periodic spline. The algorithm is based on the attenuation factor theory and makes use of the FFT. It can be applied to other function classes with known attenuation factors also. For the approximation by functions conjugate to splines of odd degree we state several optimality criterions and error bounds.