An efficient numerical method for condition number constrained covariance matrix approximation

In the high-dimensional data setting, sample covariance matrix is singular. order to get a numerically stable and positive definite modification of in this paper we consider condition number constrained approximation problem present its explicit solution with respect Frobenius norm. The constraint guarantees numerical stability definiteness form simultaneously. By exploiting special structure also propose some new algorithms based on efficient decomposition techniques. Numerical experiments are given show computational efficiency proposed algorithms.