On the perturbation of rank-one symmetric tensors


  • Michael J. O'Hara

    Corresponding author
    1. Lawrence Livermore National Laboratory, Livermore, CA, U.S.A.
    • Correspondence to: Michael J. O'Hara, Mailbox L-363, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore CA 94550, U.S.A.

      E-mail: mjohara@gmail.com

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The problem of symmetric rank-one approximation of symmetric tensors is important in independent components analysis, also known as blind source separation, as well as polynomial optimization. We derive several perturbative results that are relevant to the well-posedness of recovering rank-one structure from approximately-rank-one symmetric tensors. We also specialize the analysis of the shifted symmetric higher-order power method, an algorithm for computing symmetric tensor eigenvectors, to approximately-rank-one symmetric tensors. Copyright © 2012 John Wiley & Sons, Ltd.