  Reverberation mapping probes the structure of the broad emission-line region
(BLR) in active galactic nuclei (AGN). The kinematics of the BLR gas can be
used to measure the mass of the central supermassive black hole. The main
uncertainty affecting black hole mass determinations is the structure of the
BLR. We present a new method for reverberation mapping based on regularized
linear inversion (RLI) that includes modelling of the AGN continuum light
curves. This enables fast calculation of velocity-resolved response maps to
constrain BLR structure. RLI allows for negative response, such as when some
areas of the BLR respond in inverse proportion to a change in ionizing
continuum luminosity. We present time delays, integrated response functions,
and velocity-delay maps for the $\rm{H}\,\beta$ broad emission line in five
nearby AGN, as well as for $\rm{H}\,\alpha$ and $\rm{H}\,\gamma$ in Arp 151,
using data from the Lick AGN Monitoring Project 2008. We find indications of
prompt response in three of the objects (Arp 151, NGC 5548 and SBS 1116+583A)
with additional prompt response in the red wing of $\rm{H}\,\beta$. In SBS
1116+583A we find evidence for a multimodal broad prompt response followed by a
second narrow response at 10 days. We find no clear indications of negative
response. The results are complementary to, and consistent with, other methods
such as cross correlation, maximum entropy and dynamical modelling. Regularized
linear inversion with continuum light curve modelling provides a fast,
complementary method for velocity-resolved reverberation mapping and is
suitable for use on large datasets.
