Before revision:  In order to get a numerical stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, we in this paper  consider the condition number constrained covariance matrix approximation problem and present its explicit solution with respect to  Frobenius norm.
After revision:  In order to get a numerical stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, we in this paper consider the condition number constrained covariance matrix approximation problem and present its explicit solution with respect to the Frobenius norm.