Floating point error analysis of two-dimensional, fast Fourier transform algorithms

Floating-point error is conducted for three algorithms commonly used for the calculation of two-dimensional fast Fourier transforms (FFTs), namely, the conventional row-column FFT, the vector-radix FFT, and the polynomial-transform FFT. The respective errors are determined both analytically and on the basis of computer simulation. Comparison shows that the vector-radix FFT and the polynomial-transform FFT, even though computationally more efficient than the row-column FFT, show approximately the same (and sometimes reduced) susceptibility to errors in floating-point arithmetic