  Efficient solvers for tensor eigenvalue problems are important tools for the
analysis of higher-order data sets. Here we introduce, analyze and demonstrate
an extrapolation method to accelerate the widely used shifted symmetric higher
order power method for tensor $Z$-eigenvalue problems. We analyze the
asymptotic convergence of the method, determining the range of extrapolation
parameters that induce acceleration, as well as the parameter that gives the
optimal convergence rate. We then introduce an automated method to dynamically
approximate the optimal parameter, and demonstrate it's efficiency when the
base iteration is run with either static or adaptively set shifts. Our
numerical results on both even and odd order tensors demonstrate the theory and
show we achieve our theoretically predicted acceleration.

Numerical Analysis;Numerical Analysis