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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A Regularized Newton method for the Efficient Approximation of Tensors Represented in the Canonical Tensor Format

Mike Espig and Wolfgang Hackbusch


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 $\ell_2$ minimization problem. The $\ell_2$ 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.

tensor representation, canonical tensor format, regularized Newton method

Related publications

2012 Repository Open Access
Mike Espig and Wolfgang Hackbusch

A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format

In: Numerische Mathematik, 122 (2012) 3, pp. 489-525