  The problem of decomposing a given covariance matrix as the sum of a positive
semi-definite matrix of given rank and a positive semi-definite diagonal
matrix, is considered. We present a projection-type algorithm to address this
problem. This algorithm appears to perform extremely well and is extremely fast
even when the given covariance matrix has a very large dimension. The
effectiveness of the algorithm is assessed through simulation studies and by
applications to three real datasets that are considered as benchmark for the
problem. A local convergence analysis of the algorithm is also presented.
