Solving bilinear tensor least squares problems and application to Hammerstein identification

Lars Eldén, Salman Ahmadi-Asl

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    1 Citation (Scopus)


    Bilinear tensor least squares problems occur in applications such as Hammerstein system identification and social network analysis. A linearly constrained problem of medium size is considered, and nonlinear least squares solvers of Gauss–Newton-type are applied to numerically solve it. The problem is separable, and the variable projection method can be used. Perturbation theory is presented and used to motivate the choice of constraint. Numerical experiments with Hammerstein models and random tensors are performed, comparing the different methods and showing that a variable projection method performs best.

    Original languageEnglish
    Article numbere2226
    JournalNumerical Linear Algebra with Applications
    Issue number2
    Publication statusPublished - Mar 2019


    • bilinear regression
    • bilinear tensor least squares problem
    • Gauss–Newton-type method
    • Hammerstein identification
    • separable
    • variable projection


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