  We extend the celebrated QR algorithm for matrices to symmetric tensors. The
algorithm, named QR algorithm for symmetric tensors (QRST), exhibits similar
properties to its matrix version, and allows the derivation of a shifted
implementation with faster convergence. We further show that multiple tensor
eigenpairs can be found from a local permutation heuristic which is effectively
a tensor similarity transform, resulting in the permuted version of QRST called
PQRST. Examples demonstrate the remarkable effectiveness of the proposed
schemes for finding stable and unstable eigenpairs not found by previous tensor
power methods.
