Accumulated error in iterative use of FFT

Abstract

The roundoff error accumulation in the iterative use of the fast Fourier transform (FFT) is discussed. By using numerical simulations of partial differential equations, we numerically show that the roundoff error in the iterative use of the FFT tends to be accumulated. To avoid a lack of precision, we present numerical simulations in which a quadruple precision floating point number is used, which ensures sufficient precision against the accumulation of the roundoff errors in the FFT.