  We introduce an iterative method for computing the first eigenpair
$(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet
data as the limit of $(\mu_{q,}u_{q}) $ as $q\rightarrow p^{-}$, where $u_{q}$
is the positive solution of the sublinear Lane-Emden equation
$-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
$u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of
$\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is
presented.
