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MiS Preprint
78/2010
A Regularized Newton method for the Efficient Approximation of Tensors Represented in the Canonical Tensor Format
Mike Espig and Wolfgang Hackbusch
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 $\ell_2$ 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.
