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

Mike Espig and Wolfgang Hackbusch

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Submission date: 21. Dec. 2010
Pages: 32
published in: Numerische Mathematik, 122 (2012) 3, p. 489-525 
DOI number (of the published article): 10.1007/s00211-012-0465-9
Bibtex
Keywords and phrases: tensor representation, canonical tensor format, regularized Newton method
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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 minimization problem. The 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.