The Asymptotic Spectrum of Flipped Multilevel Toeplitz Matrices and of Certain Preconditionings

In this work, we perform a spectral analysis of flipped multilevel Toeplitz sequences, i.e., study the asymptotic behavior $\{Y_{{n}} T_{{n}} (f)\}_{{n}}$, where $T_{{n}}(f)$ is real, square matrix generated by function $f\in L^1([-\pi,\pi]^d)$ and $Y_n$ exchange matrix, which has 1's on main antidiagonal. line with what have shown for unilevel spectrum determined 2 x matrix-valued whose eigenvalues are $\pm |f|$. Furthermore, characterize eigenvalue distribution certain preconditioned sequences an that covers both circulant preconditioners. Finally, all our findings illustrated several numerical experiments.