  We define truncated Mellin moments of parton distributions by restricting the
integration range over the Bjorken variable to the experimentally accessible
subset x_0 < x < 1 of the allowed kinematic range 0 < x < 1. We derive the
evolution equations satisfied by truncated moments in the general (singlet)
case in terms of an infinite triangular matrix of anomalous dimensions which
couple each truncated moment to all higher moments with orders differing by
integers. We show that the evolution of any moment can be determined to
arbitrarily good accuracy by truncating the system of coupled moments to a
sufficiently large but finite size, and show how the equations can be solved in
a way suitable for numerical applications. We discuss in detail the accuracy of
the method in view of applications to precision phenomenology.
