  We describe in detail full numerical and perturbative techniques to compute
the gravitational radiation from intermediate-mass-ratio black-hole-binary
inspirals and mergers. We perform a series of full numerical simulations of
nonspinning black holes with mass ratios q=1/10 and q=1/15 from different
initial separations and for different finite-difference resolutions. In order
to perform those full numerical runs, we adapt the gauge of the moving
punctures approach with a variable damping term for the shift. We also derive
an extrapolation (to infinite radius) formula for the waveform extracted at
finite radius. For the perturbative evolutions we use the full numerical
tracks, transformed into the Schwarzschild gauge, in the source terms of the
Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend
this perturbative formalism to take into account small intrinsic spins of the
large black hole, and validate it by computing the quasinormal mode
frequencies, where we find good agreement for spins |a/M|<0.3. Including the
final spins improves the overlap functions when comparing full numerical and
perturbative waveforms, reaching 99.5% for the leading (l,m)=(2,2) and (3,3)
modes, and 98.3% for the nonleading (2,1) mode in the q=1/10 case, which
includes 8 orbits before merger. For the q=1/15 case, we obtain overlaps near
99.7% for all three modes. We discuss the modeling of the full inspiral and
merger based on a combined matching of post-Newtonian, full numerical, and
geodesic trajectories.
