  The effective Fisher matrix method recently introduced by Cho et al. is a
semi-analytic approach to the Fisher matrix, in which a local overlap surface
is fitted by using a quadratic fitting function. Mathematically, the effective
Fisher matrix should be consistent with the analytic one at the infinitesimal
fitting scale. In this work, using the frequency-domain waveform (TaylorF2), we
give brief comparison results between the effective and analytic Fisher
matrices for several non-spinning binaries consisting of binary neutron stars
with masses of (1.4, 1.4)M_sun, black hole-neutron star of (1.4, 10)M_sun, and
binary black holes of (5, 5) and (10, 10)M_sun for a fixed signal to noise
ratio (SNR=20) and show a good consistency between two methods. We also give a
comparison result for an aligned-spin black hole-neutron star binary with a
black hole spin of \chi=1, where we define new mass parameters (Mc, \eta^-1,
\chi^7/2) to find good fitting functions to the overlap surface. The effective
Fisher matrix can also be computed by using the time-domain waveforms which are
generally more accurate than frequency-domain waveform. We show comparison
results between the frequency-domain and time-domain waveforms (TaylorT4) for
both the non-spinning aligned-spin binaries.
