Dynamical Tensor Approximation
نویسندگان
چکیده
منابع مشابه
Dynamical Tensor Approximation
For the approximation of time-dependent data tensors and of solutions to tensor differential equations by tensors of low Tucker rank, we study a computational approach that can be viewed as a continuous-time updating procedure. This approach works with the increments rather than the full tensor and avoids the computation of decompositions of large matrices. In this method, the derivative is pro...
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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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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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Approximating a tensor by another of lower rank is in general an ill posed problem. Yet, this kind of approximation is mandatory in the presence of measurement errors or noise. We show how tools recently developed in compressed sensing can be used to solve this problem. More precisely, a minimal angle between the columns of loading matrices allows to restore both existence and uniqueness of the...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2010
ISSN: 0895-4798,1095-7162
DOI: 10.1137/09076578x