  We discuss the salient features of Zolotarev optimal rational approximation
for the inverse square root function, in particular, for its applications in
lattice QCD with overlap Dirac quark. The theoretical error bound for the
matrix-vector multiplication $ H_w (H_w^2)^{-1/2}Y $ is derived. We check that
the error bound is always satisfied amply, for any QCD gauge configurations we
have tested. An empirical formula for the error bound is determined, together
with its numerical values (by evaluating elliptic functions) listed in Table 2
as well as plotted in Figure 3. Our results suggest that with Zolotarev
approximation to $ (H_w^2)^{-1/2} $, one can practically preserve the exact
chiral symmetry of the overlap Dirac operator to very high precision, for any
gauge configurations on a finite lattice.
