  We explicitly demonstrate that current numerical relativity techniques are
able to accurately evolve black hole binaries with mass ratios of the order of
1000:1. This proof of principle is relevant for future third generation (3G)
gravitational wave detectors and space mission LISA, as by purely numerical
methods we would be able to accurately compute gravitational waves from the
last stages of black hole mergers, as directly predicted by general relativity.
We perform a sequence of simulations in the intermediate to small mass ratio
regime, $m_1^p/m_2^p = 1/7, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024$,
with the small hole starting from rest at a proper distance $D\approx13M$. We
compare these headon full numerical evolutions with the corresponding
semianalytic point particle perturbative results finding an impressive
agreement for the total gravitational radiated energy and linear momentum as
well as for the waveform spectra. We display numerical convergence of the
results and identify the minimal numerical resolutions required to accurately
solve for these very low amplitude gravitational waves. This work represents a
first step towards the considerable challenge of applying numerical-relativity
waveforms to interpreting gravitational-wave observations by LISA and
next-generation ground-based gravitational-wave detectors.
