  The problem of extrapolation and interpolation of asymptotic series is
considered. Several new variants of improving the accuracy of the self-similar
approximants are suggested. The methods are illustrated by examples typical of
chemical physics, when one is interested in finding the equation of state for a
strongly interacting system. A special attention is payed to the study of the
basic properties of fluctuating fluid membranes. It is shown that these
properties can be well described by means of the method of self-similar
approximants. For this purpose, the method has been generalized in order to
give accurate predictions at infinity for a function, whose behavior is known
only at the region of its variable close to zero. The obtained results for
fluctuating fluid membranes are in good agreement with the known numerical
data.
