  Ground state of the dissipative two-state system is investigated by means of
the Lanczos diagonalization method. We adopted the Hilbert-space-reduction
scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming
reservoir Hilbert space to being tractable in computers. Both the
implementation of the algorithm and the precision applied for the present
system are reported in detail. We evaluate the dynamical susceptibility
(resolvent) with the continued-fraction-expansion formula. Through analysing
the resolvent over a frequency range, whose range is often called `interesting'
frequency, we obtain the damping rate and the oscillation frequency. Our
results agree with those of a recent quantum Monte-Carlo study, which concludes
that the critical dissipation from oscillatory to over-damped behavior
decreases as the tunneling amplitude is strengthened.
