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Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...
Low-rank tensor completion addresses the task of filling in missing entries in multidimensional data. It has proven its versatility in numerous applications, including context aware recommender systems and multivariate function learning. To handle large-sc ...
The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d≥3, the singular values are generally different for different matricizations but not c ...
The MBI (maximum block improvement) method is a greedy approach to solving optimization problems where the decision variables can be grouped into a finite number of blocks. Assuming that optimizing over one block of variables while fixing all others is rel ...
We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...
In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT,k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group ac ...