  White's density matrix renormalization group ({DMRG}) method has been applied
to the one-dimensional Ising model in a transverse field ({ITF}), in order to
study the accuracy of the numerical algorithm. Due to the exact solubility of
the {ITF} for any finite chain length, the errors introduced by the basis
truncation procedure could have been directly analysed. By computing different
properties, like the energies of the low-lying levels or the ground-state one-
and two-point correlation functions, we obtained a detailed picture, how these
errors behave as functions of the various model and algorithm parameters. Our
experience with the {ITF} contributes to a better understanding of the {DMRG}
method, and may facilitate its optimization in other applications.
