Abstract
In the present survey, we consider a rank approximation algorithm for tensors represented in the canonical format in arbitrary pre-Hilbert tensor product spaces. It is shown that the original approximation problem is equivalent to a finite dimensional ℓ 2 minimization problem. The ℓ 2 minimization problem is solved by a regularized Newton method which requires the computation and evaluation of the first and second derivative of the objective function. A systematic choice of the initial guess for the iterative scheme is introduced. The effectiveness of the approach is demonstrated in numerical experiments.
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Espig, M., Hackbusch, W. A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format. Numer. Math. 122, 489–525 (2012). https://doi.org/10.1007/s00211-012-0465-9
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DOI: https://doi.org/10.1007/s00211-012-0465-9