  An algorithm is proposed for determining asymptotics of the sum of a
perturbative series in the strong coupling limit using given values of the
expansion coefficients. Operation of the algorithm is illustrated by test
examples, method for estimating errors is developed, and an optimization
procedure is described. Application of the algorithm to the $\phi^4$ theory
gives a behavior $\beta(g)\approx 7.4 g^{0.96}$ at large $g$ for its Gell-Mann
-- Low function. The fact that the exponent is close to unity can be
interpreted as a manifestation of the logarithmic branching of the type
$\beta(g)\sim g (\ln g)^{-\gamma}$ (with $\gamma\approx 0.14$), which is
confirmed by independent evidence. In any case, the $\phi^4$ theory is
internally consistent. The procedure of summing perturbartive series with
arbitrary values of expansion parameter is discussed.
