  This paper is focuses on the computation of the positive moments of one-side
correlated random Gram matrices. Closed-form expressions for the moments can be
obtained easily, but numerical evaluation thereof is prone to numerical
stability, especially in high-dimensional settings. This letter provides a
numerically stable method that efficiently computes the positive moments in
closed-form. The developed expressions are more accurate and can lead to higher
accuracy levels when fed to moment based-approaches. As an application, we show
how the obtained moments can be used to approximate the marginal distribution
of the eigenvalues of random Gram matrices.
