A comparison of two methods for accelerating the convergence of Fourier series

AbstractWe compare the epsilon algorithm of Wynn with a generalization of summation by parts for accelerating slowly convergent Fourier series. The series considered are ∑nn−p cos nθ(sin nθ), ∑nJo(ny)cos nθ(sin nθ) and four series that arise from the numerical inversion Summation by parts is shown to be advantageous in the acceleration of Fourier sine series. Both acceleration techniques are shown to lead to approximately the same accuracy in accelerating the series that come from the Laplace transform examples