An optimization approach for dynamical Tucker tensor approximation
نویسندگان
چکیده
منابع مشابه
Dynamical approximation of hierarchical Tucker and tensor-train tensors
We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch & Lubich, 2007 and 2010) to the recently proposed Hierarchical Tucker tensor format (HT, Hackbusch & Kühn, 2009) and the Tensor Train format (TT, Oseledets, 2011), which are closely related to tensor decomposition methods used in quantum physics and chemistry. In this dynamic...
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We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch & Lubich, 2007 and 2010) to the recently proposed Hierarchical Tucker tensor format (HT, Hackbusch & Kühn, 2009) and the Tensor Train format (TT, Oseledets, 2011), which are closely related to tensor decomposition methods used in quantum physics and chemistry. In this dynamic...
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Abstract—In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. Using the differential geometric tools presented here, we construct standard optimization algorithms such as Steepest Descent and Conjugate Gradient for interpolating ...
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ژورنال
عنوان ژورنال: Results in Applied Mathematics
سال: 2019
ISSN: 2590-0374
DOI: 10.1016/j.rinam.2019.100002