The randomizing FFT : an alternative to pivoting in

Recently, randomizing input transformations have been developed for streamlining Gaussian elimination. Multiplying by special sparse random matrices, these transformations produce an equivalent linear system which, with probability 1, Gaussian elimination can solve without any augmentation by pivoting. In this paper we study properties of the unitary Randomizing Discrete Fourier Transform (RDFT), which scales rows by random values from the complex unit circle and then applies the conventional DFT. When the problem size is a power of 2, the Randomizing Fast Fourier Transform (RFFT) algorithm can eeciently implement the RDFT, using existing FFT code, on the many parallel and vector machines whose architectures support FFT-like computations.