TRANSFORMATIONS TO ACCELERATE THE CONVERGENCE OF FOURIER SERIES.

Abstract : The paper offers a comparative review of methods for accelerating the numerical convergence of Fourier series. The various reasons for which Fourier series either diverge or converge sufficiently slowly to render them useless for computation are discussed and where possible an appropriate convergence acceleration transformation is prescribed. Particular emphasis is placed upon the use of continued fractions, which appears at the same time to have the widest domain of application and to be the most powerful general method available. (Author)