  Methods of determining, from small-variable asymptotic expansions, the
characteristic exponents for variables tending to infinity are analyzed. The
following methods are considered: diff-log Pad\'e summation, self-similar
factor approximation, self-similar diff-log summation, self-similar Borel
summation, and self-similar Borel-Leroy summation. Several typical problems are
treated. The comparison of the results shows that all these methods provide
close estimates for the large-variable exponents. The reliable estimates are
obtained when different methods of summation are compatible with each other.
