A Recursive Eigenspace Computation for the Canonical Polyadic Decomposition

The canonical polyadic decomposition (CPD) is a compact which expresses tensor as sum of its rank-1 components. A common step in the computation CPD computing generalized eigenvalue (GEVD) tensor. GEVD provides an algebraic approximation can then be used initialization optimization routines. While noiseless setting exactly recovers CPD, it has recently been shown that pencil-based computations such are not stable. In this article we present method for greatly improves accuracy GEVD. Our still fundamentally pencil based; however, rather than using single and all eigenvectors, use many different pencils each compute eigenspaces corresponding to sufficiently well-separated eigenvalues. resulting “generalized eigenspace decomposition" significantly more robust noise classical Accuracy examined both empirically theoretically. particular, provide deterministic perturbation theoretic bound predictive error computed factorization.