  We consider extrapolation of the Arnoldi algorithm to accelerate computation
of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences
of Krylov vectors to form a small eigenproblem which is solved exactly. The two
dominant eigenvectors output from consecutive Arnoldi steps are then recombined
to form an extrapolated iterate, and this accelerated iterate is used to
restart the next Arnoldi process. We present numerical results testing the
algorithm on a variety of cases and find on most examples it substantially
improves the performance of restarted Arnoldi. The extrapolation is a simple
post-processing step which has minimal computational cost.
