  The Gaussian expansion has been developed since early 80s as a powerful
analytical method, which enables nonperturbative studies of various systems
using `perturbative' calculations. Recently the method has been used to suggest
that 4d space-time is generated dynamically in a matrix model formulation of
superstring theory. Here we clarify the nature of the method by applying it to
exactly solvable one-matrix models with various kinds of potential including
the ones unbounded from below and of the double-well type. We also formulate a
prescription to include a linear term in the Gaussian action in a way
consistent with the loop expansion, and test it in some concrete examples. We
discuss a case where we obtain two distinct plateaus in the parameter space of
the Gaussian action, corresponding to different large-N solutions. This
clarifies the situation encountered in the dynamical determination of the
space-time dimensionality in the previous works.
