  We show how to extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element
$\vert V_{cb} \vert$ from exclusive semileptonic $B \to D^{(*)}$ decays by
using the Dispersive Matrix (DM) method. It is a new approach which allows to
determine in a full non-perturbative way the hadronic form factors (FFs) in the
whole kinematical range, without making any assumption on their dependence on
the momentum transfer. We investigate also the issue of Lepton Flavor
Universality (LFU) by computing a pure theoretical estimate of the ratio
$R(D^{(*)})$. Our approach is applied to the preliminary LQCD computations of
the FFs, published by the FNAL/MILC [1] and the JLQCD [2] Collaborations, for
the $B \to D^*$ decays and to the final ones, computed by FNAL/MILC [3], for
the $B \to D$ transitions . Since the FNAL/MILC Collaborations have recently
published the final results of their LQCD computations of the FFs [4] for the
$B \to D^*$ case, we present also the results of our procedure after its
application on these data. We find $ \vert V_{cb} \vert = (41.0 \pm 1.2) \cdot
10^{-3}$ and $\vert V_{cb} \vert = (41.3 \pm 1.7) \cdot 10^{-3}$ from $B \to D$
and $B \to D^*$ decays, respectively. These estimates are consistent within
$1\sigma$ with the most recent inclusive determination $\vert
V_{cb}\vert_{incl} = (42.16 \pm 0.50) \cdot 10^{-3}$ [5]. Furthermore, we
obtain $R(D) = 0.289(8)$ and $R(D^*) = 0.269(8)$, which are both compatible
with the latest experimental averages [6] at the $\sim$1.6$\sigma$ level.
