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

Canonical Polyadic Decomposition via the generalized Schur decomposition