I have a covariance matrix $Q$ and need to find $Q^{-1}$. Here, $Q$ is a Toeplitz matrix. I want to calculate the inverse of the matrix with FFT-based methods rather than the conventional ones like the Cholesky, QR or eigenvalue decompositions, or other Toeplitz inversion methods like Levinson-Trench or Berlekamp-Massey.
Can anyone tell me how can I do that please? Is there any established method which I can follow?