  We introduce a new non-perturbative method to tune the parameters of the
Columbia formulation of an anisotropic, clover-improved relativistic
heavy-quark (RHQ) action. By making use of suitable observables which can be
computed at a sequence of heavy-quark mass values, employing an $O(a)$-improved
discretized action with domain-wall chiral fermion, and safely interpolated
between the accessible heavy-quark mass region and the static point predicted
by heavy-quark effective theory, we are able to precisely determine the unknown
coefficients of the RHQ action. In this proof-of-principle study we benefit
from the RBC/UKQCD Iwasaki gauge configurations with $2+1$ flavors of dynamical
quarks, at three values of the lattice spacing varying from $0.11$ to $0.062$
fm. Preliminary results and applications to bottom spectroscopy are also
presented.
