  We study purely dissipative relaxational dynamics in the three-dimensional
Ising universality class. To this end, we simulate the improved Blume-Capel
model on the simple cubic lattice by using local algorithms. We perform a
finite size scaling analysis of the integrated autocorrelation time of the
magnetic susceptibility in equilibrium at the critical point. We obtain
$z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully
magnetized configurations are suddenly quenched to the critical temperature,
giving consistent results for the dynamic critical exponent. Furthermore, our
estimate of $z$ is fully consistent with recent field theoretic results.
