A Levin-type algorithm for accelerating the convergence of Fourier series
A nonlinear Levin-type algorithm is presented which is able to accelerate the convergence of Fourier series. The remainder is assumed to be the product of a remainder estimate and the sum of the first terms of two Poincaré-type expansions which are premultiplied by two different phase factors. This transformation is exact for Fourier series of the following type: \(\sum^ \infty_{n=0} q^ n (A\cos (nx)+ B\sin(nx))\) with \(0<| q|<1\). It is shown that this algorithm accelerates the convergence of Fourier series.
scientific article; zbMATH DE number 440289
scientific article