  The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with
controlled numerical errors by a conjugate gradient (CG) method. This CG
algorithm is accelerated by alternating it with exact diagonalisations in the
subspace spanned by the numerically computed eigenvectors. We study this
combined algorithm in case of the Dirac operator with (dynamical) Wilson
fermions in four-dimensional $\SUtwo$ gauge fields. The algorithm is
numerically very stable and can be parallelized in an efficient way. On
lattices of sizes $4^4-16^4$ an acceleration of the pure CG method by a factor
of~$4-8$ is found.
