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