I want to decompose a square Hankel matrix $\bf {H}$, whose elements below the anti-diagonal are zeros. The decomposed factors should necessarily meet the following constraints: $$\begin{equation} \bf {H} = \bf {A}\bf {B}\end{equation},$$ where $\bf {A}$ is an anti-upper triangular matrix and $\bf {B}$ is a lower triangular matrix.
I have tried to use Kung's method (using SVD) to find the two factors, but I am not sure, how the Gaussian-elimination works to get the desired structures of $\bf {A}$ and $\bf {B}$. Can this be performed any other way?