  The canonical polyadic decomposition (CPD) is a fundamental tensor
decomposition which expresses a tensor as a sum of rank one tensors. In stark
contrast to the matrix case, with light assumptions, the CPD of a low rank
tensor is (essentially) unique. The essential uniqueness of CPD makes this
decomposition a powerful tool in many applications as it allows for extraction
of component information from a signal of interest.
  One popular algorithm for algebraic computation of a CPD is the generalized
eigenvalue decomposition (GEVD) which selects a matrix subpencil of a tensor,
then computes the generalized eigenvectors of the pencil. In this article, we
present a simplification of GEVD which improves the accuracy of the algorithm.
Surprisingly, the generalized eigenvector computation in GEVD is in fact
unnecessary and can be replaced by a QZ decomposition which factors a pair of
matrices as a product of unitary and upper triangular matrices. Computing a QZ
decomposition is a standard first step when computing generalized eigenvectors,
so our algorithm can been seen as a direct simplification of GEVD.
