  We present a new scheme for extracting approximate values in ``the improved
perturbation method'', which is a sort of resummation technique capable of
evaluating a series outside the radius of convergence. We employ the
distribution profile of the series that is weighted by nth-order derivatives
with respect to the artificially introduced parameters. By those weightings the
distribution becomes more sensitive to the ``plateau'' structure in which the
consistency condition of the method is satisfied. The scheme works effectively
even in such cases that the system involves many parameters. We also propose
that this scheme has to be applied to each observables separately and be
analyzed comprehensively.
  We apply this scheme to the analysis of the IIB matrix model by the improved
perturbation method obtained up to eighth order of perturbation in the former
works. We consider here the possibility of spontaneous breakdown of Lorentz
symmetry, and evaluate the free energy and the anisotropy of space-time extent.
In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-
and SO(7)-symmetric vacua that have been observed. It is also found that there
are two distinct SO(4)-symmetric vacua that have almost the same value of free
energy but the extent of space-time is different. From the approximate values
of free energy, we conclude that the SO(4)-symmetric vacua are most preferred
among those three types of vacua.
