I have an optimization problem
$$\begin{array}{ll} \text{minimize} & Tr(X^TAX) \\ \text{subject to} & X^TX=I \end{array}$$
where $A\in R^{n \times n}$ and it is symmetric positive definite, $X \in {n \times k}$ and $k \ll n$
I need to compute the $XX^T$ efficiently.
We know the above optimization $X$ can be solve by find the $k$ eigenvectors of $A$. but eigenvalue-decomposition take expensive time. Is there any approximation algorithm since I only need $XX^T$.
